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MSC.Nastran Version 68 Basic Dynamic Analysis Users Guide Main Index Corporate MSC.Software Corporation 2 MacArthur Place Santa Ana, CA 92707 USA Telephone: (800) 345-2078

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MSC.Nastran Version 68Basic Dynamic AnalysisUsers GuideMain IndexCorporateMSC.Software Corporation2 MacArthur PlaceSanta Ana, CA 92707 USATelephone: (800) 345-2078Fax: (714) 784-4056EuropeMSC.Software GmbHAm Moosfeld 1381829 Munich, GermanyTelephone: (49) (89) 43 19 87 0Fax: (49) (89) 43 61 71 6Asia PacificMSC.Software Japan Ltd.Shinjuku First West 8F23-7 Nishi Shinjuku1-Chome, Shinjyku-Ku, Tokyo 160-0023, JapanTelephone: (81) (03) 6911 1200Fax: (81) (03) 6911 1201Worldwide Webwww.mscsoftware.comDisclaimerThis documentation, as well as the software described in it, is furnished under license and may be used only in accordance with the terms of such license.MSC.Software Corporation reserves the right to make changes in specifications and other information contained in this document without prior notice.The concepts, methods, and examples presented in this text are for illustrative and educational purposes only, and are not intended to be exhaustive or to apply to any particular engineering problem or design. MSC.Software Corporation assumes no liability or responsibility to any person or company for direct or indirect damages resulting from the use of any information contained herein.User Documentation: Copyright 2004 MSC.Software Corporation. Printed in U.S.A. All Rights Reserved.This notice shall be marked on any reproduction of this documentation, in whole or in part. Any reproduction or distribution of this document, in whole or in part, without the prior written consent of MSC.Software Corporation is prohibited.The software described herein may contain certain third-party software that is protected by copyright and licensed from MSC.Software suppliers. MSC, MSC/ , MSC., MSC.Dytran, MSC.Fatigue, MSC.Marc, MSC.Patran, MSC.Patran Analysis Manager, MSC.Patran CATXPRES, MSC.Patran FEA, MSC.Patran Laminate Modeler, MSC.Patran Materials, MSC.Patran Thermal, MSC.Patran Queue Manager and PATRAN are trademarks or registered trademarks of MSC.Software Corporation in the United States and/ or other countries. NASTRAN is a registered trademark of NASA. PAM-CRASH is a trademark or registered trademark of ESI Group. SAMCEF is a trademark or registered trademark of Samtech SA. LS-DYNA is a trademark or registered trademark of Livermore Software Technology Corporation. ANSYS is a registered trademark of SAS IP, Inc., a wholly owned subsidiary of ANSYS Inc. ABAQUS is a registered trademark of ABAQUS Inc. ACIS is a registered trademark of Spatial Technology, Inc. CATIA is a registered trademark of Dassault Systemes, SA. EUCLID is a registered trademark of Matra Datavision Corporation. FLEXlm is a registered trademark of GLOBEtrotter Software, Inc. HPGL is a trademark of Hewlett Packard. PostScript is a registered trademark of Adobe Systems, Inc. PTC, CADDS and Pro/ ENGINEER are trademarks or registered trademarks of Parametric Technology Corporation or its subsidiaries in the United States and/ or other countries.Unigraphics, Parasolid and I-DEAS are registered trademarks of Electronic Data Systems Corporation or its subsidiaries in the United States and/ or other countries. All other brand names, product names or trademarks belong to their respective owners.Main IndexC O N T E N T SMSC.Nastran Basic Dynamics Users Guide Preface s About this Book, xvis Acknowledgements, xviis List of MSC.Nastran Books, xviiis Technical Support, xixs Internet Resources, xxiis Permission to Copy and Distribute MSC Documentation, xxiii1sFundamentals of Dynamic Analysiss Overview, 2s Equations of Motion, 3s Dynamic Analysis Process, 12s Dynamic Analysis Types, 142Finite Element Input Datas Overview, 16s Mass Input, 17s Damping Input, 23s Units in Dynamic Analysis, 27s Direct Matrix Input, 29 Direct Matrix Input, 29 DMIG Bulk Data User Interface, 30 DMIG Case Control User Interface, 313Real Eigenvalue Analysiss Overview, 34s Reasons to Compute Normal Modes, 36s Overview of Normal Modes Analysis, 37s Methods of Computation, 43 Lanczos Method, 43 Givens and Householder Methods, 44 Modified Givens and Modified Householder Methods, 44MSC.Nastran Basic Dynamics Users GuideMain Index Automatic Givens and Automatic Householder Methods, 44 Inverse Power Method, 45 Sturm Modified Inverse Power Method, 45s Comparison of Methods, 46s User Interface for Real Eigenvalue Analysis, 48 User Interface for the Lanczos Method, 48 User Interface for the Other Methods, 50s Solution Control for Normal Modes Analysis, 54 Executive Control Section, 54 Case Control Section, 54 Bulk Data Section, 55s Examples, 56 Two-DOF Model, 57 Cantilever Beam Model, 60 Bracket Model, 66 Car Frame Model, 71 Test Fixture Model, 76 Quarter Plate Model, 78 DMIG Example, 814Rigid-body Modes s Overview, 88s SUPORT Entry, 90 Treatment of SUPORT by Eigenvalue Analysis Methods, 90 Theoretical Considerations, 91 Modeling Considerations, 94s Examples, 96 Unconstrained Beam Model, 96 Unconstrained Bracket Example, 1015Frequency Response Analysiss Overview, 104s Direct Frequency Response Analysis, 106 Damping in Direct Frequency Response, 106s Modal Frequency Response Analysis, 108 Damping in Modal Frequency Response, 109 Mode Truncation in Modal Frequency Response Analysis, 112 Dynamic Data Recovery in Modal Frequency Response Analysis, 112s Modal Versus Direct Frequency Response, 114s Frequency-Dependent Excitation Definition, 115 Frequency-Dependent Loads RLOAD1 Entry, 115 Frequency-Dependent Loads RLOAD2 Entry, 116 Spatial Distribution of Loading -- DAREA Entry, 117 Time Delay DELAY Entry, 117 Phase Lead DPHASE Entry, 118Main Index Dynamic Load Tabular Function -- TABLEDi Entries, 118 DAREA Example, 121 Static Load Sets LSEQ Entry, 122 LSEQ Example, 123 Dynamic Load Set Combination DLOAD, 124s Solution Frequencies, 125 FREQ, 125 FREQ1, 126 FREQ2, 126 FREQ3, 126 FREQ4, 127 FREQ5, 128s Frequency Response Considerations, 129s Solution Control for Frequency Response Analysis, 130s Examples, 133 Two-DOF Model, 133 Cantilever Beam Model, 139 Bracket Model, 1456Transient Response Analysiss Overview, 150s Direct Transient Response Analysis, 151 Damping in Direct Transient Response, 152 Initial Conditions in Direct Transient Response, 154s Modal Transient Response Analysis, 156 Damping in Modal Transient Response Analysis, 157 Mode Truncation in Modal Transient Response Analysis, 160 Dynamic Data Recovery in Modal Transient Response Analysis, 161s Modal Versus Direct Transient Response, 162s Transient Excitation Definition, 163 Time-Dependent Loads -- TLOAD1 Entry, 163 Time-Dependent Loads TLOAD2 Entry, 165 Spatial Distribution of Loading DAREA Entry, 166 Time Delay -- DELAY Entry, 166 Dynamic Load Tabular Function TABLEDi Entries, 166 DAREA Example, 169 Static Load Sets -- LSEQ Entry, 170 LSEQ Example, 171 Dynamic Load Set Combination -- DLOAD, 172s Integration Time Step, 174s Transient Excitation Considerations, 175s Solution Control for Transient Response Analysis, 176s Examples, 179 Two-DOF Model, 179 Cantilever Beam Model, 182 Bracket Model, 190Main Index7Enforced Motion s Overview, 196s The Large Mass Method in Direct Transient and Direct Frequency Response, 197s The Large Mass Method in Modal Transient and Modal Frequency Response, 199s User Interface for the Large Mass Method, 201 Frequency Response, 202 Transient Response, 203s Examples, 204 Two-DOF Model, 204 Cantilever Beam Model, 2118Restarts In Dynamic Analysiss Overview, 218s Automatic Restarts, 219s Structure of the Input File, 220s User Interface, 221 Cold Start Run, 221 Restart Run, 221s Determining the Version for a Restart, 226s Examples, 2289Plotted Output s Overview, 242s Structure Plotting, 243s X-Y Plotting, 24910Guidelines for Effective Dynamic Analysiss Overview, 288s Overall Analysis Strategy, 289s Units, 292s Mass, 293s Damping, 294s Boundary Conditions, 297s Loads, 298s Meshing, 299s Eigenvalue Analysis, 301s Frequency Response Analysis, 302Main Index Number of Retained Modes, 302 Size of the Frequency Increment, 302 Relationship of Damping to the Frequency Increment, 302 Verification of the Applied Load, 303s Transient Response Analysis, 304 Number of Retained Modes, 304 Size of the Integration Time Step, 304 Duration of the Computed Response, 305 Value of Damping, 305 Verification of the Applied Load, 305s Results Interpretation and Verification, 306s Computer Resource Requirements, 30811Advanced Dynamic Analysis Capabilitiess Overview, 312s Dynamic Reduction, 313s Complex Eigenvalue Analysis, 314s Response Spectrum Analysis, 315s Random Vibration Analysis, 317s Mode Acceleration Method, 318s Fluid Structure Interaction, 319 Hydroelastic Analysis, 319 Virtual Fluid Mass, 319 Coupled Acoustics, 319 Uncoupled Acoustics, 320s Nonlinear Transient Response Analysis, 321 Geometric Nonlinearity, 321 Material Nonlinearity, 321 Contact, 322 Nonlinear-Elastic Transient Response Analysis, 322 Nonlinear Normal Modes Analysis, 324s Superelement Analysis, 325 Component Mode Synthesis, 325s Design Optimization and Sensitivity, 326s Control System Analysis, 328s Aeroelastic Analysis, 329 Aerodynamic Flutter, 329s DMAP, 331AGlossary of Terms s Glossary of Terms, 334Main IndexBNomenclature for Dynamic Analysiss Nomenclature for Dynamic Analysis, 338 General, 338 Structural Properties, 339 Multiple Degree-of-Freedom System, 340CThe Set Notation System Used in Dynamic Analysiss Overview, 342 Displacement Vector Sets, 342DSolution Sequences for Dynamic Analysiss Overview, 348 Structured Solution Sequences for Basic Dynamic Analysis, 348 Rigid Formats for Basic Dynamic Analysis, 348ECase Control Commands for Dynamic Analysiss Overview, 350 Input Specification, 350 Analysis Specification, 350 Output Specification, 350ECase Control Commands for Dynamic AnalysisACCELERATION 352B2GG 354BC 354DISPLACEMENT 355DLOAD 357FREQUENCY 358IC 358K2GG 360M2GG 361METHOD 361MODES 362OFREQUENCY 363OLOAD 365OTIME 367SACCELERATION 368SDAMPING 369SDISPLACEMENT 370SUPORT1 371SVECTOR 371SVELOCITY 372TSTEP 373VELOCITY 374Main IndexFBulk Data Entries for Dynamic Analysiss Overview, 378FBulk Data Entries for Dynamic AnalysisCDAMP1 381CDAMP2 381CDAMP3 382CDAMP4 383CMASS1 384CMASS2 385CMASS3 386CMASS4 386CONM1 387CONM2 388CVISC 389DAREA 390DELAY 391DLOAD 392DMIG 393DPHASE 396EIGR 396EIGRL 400FREQ 404FREQ1 404FREQ2 405FREQ3 406FREQ4 408FREQ5 410LSEQ 411PDAMP 412PMASS 413PVISC 413RLOAD1 414RLOAD2 416SUPORT 418SUPORT1 419TABDMP1 420TABLED1 422TABLED2 423TABLED3 424TABLED4 426TIC 426TLOAD1 427TLOAD2 429TSTEP 432Main IndexGParameters for Dynamic Analysiss Overview, 436HFile Management Sections Overview, 444s Definitions, 445s MSC.Nastran Database, 446s File Management Commands, 447 INIT, 447 ASSIGN, 448 EXPAND, 450 INCLUDE, 452 Summary, 452IGrid Point Weight Generators Overview, 454s Commonly Used Features, 455s Example with Direction Dependent Masses, 458JNumerical Accuracy Considerationss Overview, 470 Linear Equation Solution, 470 Eigenvalue Analysis, 470 Matrix Conditioning, 471 Definiteness of Matrices, 472 Numerical Accuracy Issues, 472 Sources of Mechanisms, 473 Sources of Nonpositive Definite Matrices, 474 Detection and Avoidance of Numerical Problems, 474KDiagnostic Messages for Dynamic Analysiss Overview, 480LReferences and Bibliographys Overview, 500s General References, 501s Bibliography, 502 DYNAMICS GENERAL, 502Main Index DYNAMICS ANALYSIS / TEST CORRELATION, 513 DYNAMICS COMPONENT MODE SYNTHESIS, 518 DYNAMICS DAMPING, 522 DYNAMICS FREQUENCY RESPONSE, 523 DYNAMICS MODES, FREQUENCIES, AND VIBRATIONS, 524 DYNAMICS RANDOM RESPONSE, 536 DYNAMICS REDUCTION METHODS, 537 DYNAMICS RESPONSE SPECTRUM, 538 DYNAMICS SEISMIC, 538 DYNAMICS TRANSIENT ANALYSIS, 540INDEX MSC.Nastran Basic Dynamics Users Guide, 543 543Main IndexPage xivMain IndexMSC.Nastran Basic Dynamics Users GuidePrefaces About this Books List of MSC.Nastran Bookss Technical Supports Internet Resourcess Permission to Copy and Distribute MSC DocumentationMain Index xviAbout this BookThe MSC.Nast ran Basic Dynamics Users Guide is a guide to the proper use of MSC.Nastran for solving various dynamic analysis problems. This guide serves as both an introduction to dynamic analysis for the new user and a reference for the experienced user. The major emphasis focuses on understanding the physical processes in dynamics and properly applying MSC.Nastran to model dynamic processes while restricting mathematical derivations to a minimum.The basic types of dynamic analysis capabilities available in MSC.Nastran are described in this guide. These common dynamic analysis capabilities include normal modes analysis, transient response analysis, frequency response analysis, and enforced motion. These capabilities are described and illustrative examples are presented. Theoretical derivations of the mathematics used in dynamic analysis are presented only as they pertain to the proper understanding of the use of each capability.To effectively use this guide, it is important for you to be familiar with MSC.Nastrans static analysis capability and the principles of dynamic analysis. Basic finite element modeling and analysis techniques are covered only as they pertain to MSC.Nastran dynamic analysis. For more information on static analysis and modeling, refer to the MSC.Nastran Linear Static Analysis Users Guide and to the Get t ing St art ed wit h MSC.Nast ran Users Guide.This guide is an update to the MSC.Nast ran Basic Dynamics Users Guide for Version 68, which borrowed much material from the MSC.Nastran Handbook for Dynamic Analysis. However, not all topics covered in that handbook are covered here. Dynamic reduction, response spectrum analysis, random response analysis, complex eigenvalue analysis, nonlinear analysis, control systems, fluid-structure coupling and the Lagrange Multiplyer Method will be covered in the MSC.Nast ran Advanced Dynamic Analysis Users Guide.Main Indexxvii CHAPTERPrefaceAcknowledgementsMuch of the basis of this guide was established by Michael Gockel with the MSC.Nastran Handbook for Dynamic Analysis. This guide has used that information as a starting point. John Muskivitch began the guide and was the primary contributor. Other major contributors included David Bella, Franz Brandhuber, Michael Gockel, and John Lee. Other technical contributors included Dean Bellinger, John Caffrey, Louis Komzsik, Ted Rose, and Candace Hoecker. Ken Ranger and Sue Rice provided the bracket and test fixture models, respectively, and John Furno helped to run those models.This guide benefitted from intense technical scrutiny by Brandon Eby, Douglas Ferg, John Halcomb, David Herting, Wai Ho, Erwin Johnson, Kevin Kilroy, Mark Miller, and William Rodden. Gert Lundgren of LAPCAD Engineering provided the car model. Customer feedback was received from Mohan Barbela of Martin-Marietta Astro-Space, Dr. Robert Norton of Jet Propulsion Laboratory, Alwar Parthasarathy of SPAR Aerospace Limited, Canada, and Manfred Wamsler of Mercedes-Benz AG. The efforts of all have made this guide possible, and their contributions are gratefully acknowledged.Grant SittonJune 1997Main Index xviiiList of MSC.Nastran BooksBelow is a list of some of the MSC.Nastran documents. You may order any of these documents from the MSC.Software BooksMart site at www.engineering-e.com.Installation and Release Guides Installation and Operations Guide Release GuideReference Books Quick Reference Guide DMAP Programmers Guide Reference ManualUsers Guides Getting Started Linear Static Analysis Basic Dynamic Analysis Advanced Dynamic Analysis Design Sensitivity and Optimization Thermal Analysis Numerical Methods Aeroelastic Analysis Superelement User Modifiable ToolkitMain Indexxix CHAPTERPrefaceTechnical SupportFor help with installing or using an MSC.Software product, contact your local technical support services. Our technical support provides the following services: Resolution of installation problems Advice on specific analysis capabilities Advice on modeling techniques Resolution of specific analysis problems (e.g., fatal messages) Verification of code error.If you have concerns about an analysis, we suggest that you contact us at an early stage.You can reach technical support services on the web, by telephone, or e-mail:Web Go to the MSC.Software website at www.mscsoftware.com, and click on Support. Here, you can find a wide variety of support resources including application examples, technical application notes, available training courses, and documentation updates at the MSC.Software Training, Technical Support, and Documentation web page.Phone and FaxUnited StatesTelephone: (800) 732-7284Fax: (714) 784-4343Frimley, CamberleySurrey, United KingdomTelephone: (44) (1276) 67 10 00Fax: (44) (1276) 69 11 11Munich, GermanyTelephone: (49) (89) 43 19 87 0Fax: (49) (89) 43 61 71 6Tokyo, JapanTelephone: (81) (3) 3505 02 66Fax: (81) (3) 3505 09 14Rome, ItalyTelephone: (390) (6) 5 91 64 50Fax: (390) (6) 5 91 25 05Paris, FranceTelephone: (33) (1) 69 36 69 36Fax: (33) (1) 69 36 45 17Moscow, RussiaTelephone: (7) (095) 236 6177Fax: (7) (095) 236 9762Gouda, The NetherlandsTelephone: (31) (18) 2543700Fax: (31) (18) 2543707Madrid, SpainTelephone: (34) (91) 5560919Fax: (34) (91) 5567280Main Index xxEmail Send a detailed description of the problem to the email address below that corresponds to the product you are using. You should receive an acknowledgement that your message was received, followed by an email from one of our Technical Support Engineers. TrainingThe MSC Institute of Technology is the world's largest global supplier of CAD/ CAM/ CAE/ PDM training products and services for the product design, analysis and manufacturing market. We offer over 100 courses through a global network of education centers. The Institute is uniquely positioned to optimize your investment in design and simulation software tools.Our industry experienced expert staff is available to customize our course offerings to meet your unique training requirements. For the most effective training, The Institute also offers many of our courses at our customer's facilities.The MSC Institute of Technology is located at:2 MacArthur PlaceSanta Ana, CA 92707Phone: (800) 732-7211 Fax: (714) 784-4028The Institute maintains state-of-the-art classroom facilities and individual computer graphics laboratories at training centers throughout the world. All of our courses emphasize hands-on computer laboratory work to facility skills development. We specialize in customized training based on our evaluation of your design and simulation processes, which yields courses that are geared to your business.In addition to traditional instructor-led classes, we also offer video and DVD courses, interactive multimedia training, web-based training, and a specialized instructor's program.Table 0-1 MSC.Patran SupportMSC.Nastran SupportMSC.Nastran for Windows SupportMSC.visualNastran Desktop 2D SupportMSC.visualNastran Desktop 4D SupportMSC.Abaqus SupportMSC.Dytran SupportMSC.Fatigue SupportMSC.Interactive Physics SupportMSC.Marc SupportMSC.Mvision SupportMSC.SuperForge SupportMSC Institute Course Informationmscpatran.support@mscsoftware.commscnastran.support@mscsoftware.comvn4w.support@mscsoftware.comvn2d.support@mscsoftware.comvndesktop.support@mscsoftware.commscabaqus.support@mscsoftware.commscdytran.support@mscsoftware.commscfatigue.support@mscsoftware.comip.support@mscsoftware.commscmarc.support@mscsoftware.commscmvision.support@mscsoftware.commscsuperforge.support@mscsoftware.commsctraining.support@mscsoftware.comMain Indexxxi CHAPTERPrefaceCourse Information and Registration. For detailed course descriptions, schedule information, and registration call the Training Specialist at (800) 732-7211 or visit www.mscsoftware.com. Main Index xxiiInternet ResourcesMSC.Software (www.mscsoftware.com)MSC.Software corporate site with information on the latest events, products and services for the CAD/ CAE/ CAM marketplace.Simulation Center (simulate.engineering-e.com)Simulate Online. The Simulation Center provides all your simulation, FEA, and other engineering tools over the Internet.Engineering-e.com (www.engineering-e.com)Engineering-e.com is the first virtual marketplace where clients can find engineering expertise, and engineers can find the goods and services they need to do their jobCATIASOURCE (plm.mscsoftware.com)Your SOURCE for Total Product Lifecycle Management Solutions.Main Indexxxiii CHAPTERPrefacePermission to Copy and Distribute MSC DocumentationIf you wish to make copies of this documentation for distribution to co-workers, complete this form and send it to MSC.Software. MSC will grant written permission if the following conditions are met: All copyright notices must be included on all copies. Copies may be made only for fellow employees. No copies of this manual, or excerpts thereof, will be given to anyone who is not an employee of the requesting company.Please complete and mail to MSC for approval:MSC.SoftwareAttention: Legal Department2 MacArthur PlaceSanta Ana, CA 92707Name:_____________________________________________________________Title: ______________________________________________________________Company: _________________________________________________________Address:_____________________________________________________________________________________________________________________________Telephone:_________________Email: __________________________________Signature:______________________________ Date: ______________________Please do not write below this line.APPROVED: MSC.Software CorporationName:_____________________________________________________________Title: ______________________________________________________________Signature:______________________________ Date: ______________________Main Index xxiv_____________________________________________________________________Place StampHereMSC.Software CorporationAttention: Legal Department2 MacArthur PlaceSanta Ana, CA 92707Fold hereFold hereMain IndexMSC.Nastran Basic Dynamics Users GuideCHAPTER1Fundamentals of Dynamic Analysiss Overviews Equations of Motions Dynamic Analysis Processs Dynamic Analysis TypesMain Index 21.1 OverviewIn static structural analysis, it is possible to describe the operation of MSC.Nastran without a detailed discussion of the fundamental equations. Due to the several types of dynamic analyses and the different mathematical form of each, some knowledge of both the physics of dynamics and the manner in which the physics is represented is important to using MSC.Nastran effectively and efficiently for dynamic analysis.You should become familiar with the notation and terminology covered in this chapter. This knowledge will be valuable to understand the meaning of the symbols and the reasons for the procedures employed in later chapters. References and Bibliography on page 499 provides a list of references for structural dynamic analysis.Dynamic Analysis Versus Static Analysis. Two basic aspects of dynamic analysis differ from static analysis. First, dynamic loads are applied as a function of time. Second, this time-varying load application induces time-varying response (displacements, velocities, accelerations, forces, and stresses). These time-varying characteristics make dynamic analysis more complicated and more realistic than static analysis.This chapter introduces the equations of motion for a single degree-of-freedom dynamic system (see Equations of Motion on page 3), illustrates the dynamic analysis process (see Dynamic Analysis Process on page 12), and characterizes the types of dynamic analyses described in this guide (see Dynamic Analysis Types on page 14). Those who are familiar with these topics may want to skip to subsequent chapters.Main Index3 CHAPTER 11.2 Equations of MotionThe basic types of motion in a dynamic system are displacement u and the first and second derivatives of displacement with respect to time. These derivatives are velocity and acceleration, respectively, given below:Eq. 1-1Velocity and Acceleration. Velocity is the rate of change in the displacement with respect to time. Velocity can also be described as the slope of the displacement curve. Similarly, acceleration is the rate of change of the velocity with respect to time, or the slope of the velocity curve.Single Degree-of-Freedom System. The most simple representation of a dynamic system is a single degree-of-freedom (SDOF) system (see Figure 1-1). In an SDOF system, the time-varying displacement of the structure is defined by one component of motion . Velocity and acceleration are derived from the displacement.Figure 1-1 Single Degree-of-Freedom (SDOF) SystemDynamic and Static Degrees-of-Freedom. Mass and damping are associated with the motion of a dynamic system. Degrees-of-freedom with mass or damping are often called dynamic degrees-of-freedom; degrees-of-freedom with stiffness are called static degrees-of-freedom. It is possible (and often desirable) in models of complex systems to have fewer dynamic degrees-of-freedom than static degrees-of-freedom.The four basic components of a dynamic system are mass, energy dissipation (damper), resistance (spring), and applied load. As the structure moves in response to an applied load, forces are induced that are a function of both the applied load and the motion in the individual components. The equilibrium equation representing the dynamic motion of the system is known as the equation of motion.u dudt------ v velocity = = =u d2udt2--------- dvdt------ a acceleration = = = =u t ( ) ut ( )ut ( )m = mass (inertia)b = damping (energy dissipationk = stiffness (restoring force)p = applied forceu = displacement of mass= velocity of mass= acceleration of massuup t ( )u t ( )bkmMain Index 4Equation of Motion. This equation, which defines the equilibrium condition of the system at each point in time, is represented asEq. 1-2The equation of motion accounts for the forces acting on the structure at each instant in time. Typically, these forces are separated into internal forces and external forces. Internal forces are found on the left-hand side of the equation, and external forces are specified on the right-hand side. The resulting equation is a second-order linear differential equation representing the motion of the system as a function of displacement and higher-order derivatives of the displacement.Inertia Force. An accelerated mass induces a force that is proportional to the mass and the acceleration. This force is called the inertia force .Viscous Damping. The energy dissipation mechanism induces a force that is a function of a dissipation constant and the velocity. This force is known as the viscous damping force . The damping force transforms the kinetic energy into another form of energy, typically heat, which tends to reduce the vibration.Elastic Force. The final induced force in the dynamic system is due to the elastic resistance in the system and is a function of the displacement and stiffness of the system. This force is called the elastic force or occasionally the spring force .Applied Load. The applied load on the right-hand side of Eq. 1-2 is defined as a function of time. This load is independent of the structure to which it is applied (e.g., an earthquake is the same earthquake whether it is applied to a house, office building, or bridge), yet its effect on different structures can be very different.Solution of the Equation of Motion. The solution of the equation of motion for quantities such as displacements, velocities, accelerations, and/ or stressesall as a function of timeis the objective of a dynamic analysis. The primary task for the dynamic analyst is to determine the type of analysis to be performed. The nature of the dynamic analysis in many cases governs the choice of the appropriate mathematical approach. The extent of the information required from a dynamic analysis also dictates the necessary solution approach and steps.Dynamic analysis can be divided into two basic classifications: free vibrations and forced vibrations. Free vibration analysis is used to determine the basic dynamic characteristics of the system with the right-hand side of Eq. 1-2 set to zero (i.e., no applied load). If damping is neglected, the solution is known as undamped free vibration analysis.Free Vibration Analysis. In undamped free vibration analysis, the SDOF equation of motion reduces toEq. 1-3Eq. 1-3 has a solution of the formEq. 1-4mut ( ) but ( ) ku t ( ) + + p t ( ) =mut ( )but ( )ku t ( )p t ( )mut ( ) ku t ( ) + 0 =u t ( ) A nt sin B nt cos + =Main Index5 CHAPTER 1The quantity is the solution for the displacement as a function of time . As shown in Eq. 1-4, the response is cyclic in nature.Circular Natural Frequency. One property of the system is termed the circular natural frequency of the structure . The subscript indicates the natural for the SDOF system. In systems having more than one mass degree of freedom and more than one natural frequency, the subscript may indicate a frequency number. For an SDOF system, the circular natural frequency is given byEq. 1-5The circular natural frequency is specified in units of radians per unit time.Natural Frequency. The natural frequency is defined byEq. 1-6The natural frequency is often specified in terms of cycles per unit time, commonly cycles per second (cps), which is more commonly known as Hertz (Hz). This characteristic indicates the number of sine or cosine response waves that occur in a given time period (typically one second).The reciprocal of the natural frequency is termed the period of response given byEq. 1-7The period of the response defines the length of time needed to complete one full cycle of response.In the solution of Eq. 1-4, and are the integration constants. These constants are determined by considering the initial conditions in the system. Since the initial displacement of the system and the initial velocity of the system are known, and are evaluated by substituting their values into the solution of the equation for displacement and its first derivative (velocity), resulting inEq. 1-8These initial value constants are substituted into the solution, resulting inEq. 1-9Eq. 1-9 is the solution for the free vibration of an undamped SDOF system as a function of its initial displacement and velocity. Graphically, the response of an undamped SDOF system is a sinusoidal wave whose position in time is determined by its initial displacement and velocity as shown in Figure 1-2.u t ( ) tn nnkm---- =fnfnn2------ =TnTn1fn----2n------ = =A Bu t 0 = ( ) ut 0 = ( ) A BB u t 0 = ( ) = and A ut 0 = ( )n---------------------- =u t ( ) u0 ( )n----------- nt sin u 0 ( ) nt cos + =Main Index 6Figure 1-2 SDOF System -- Undamped Free VibrationsIf damping is included, the damped free vibration problem is solved. If viscous damping is assumed, the equation of motion becomesEq. 1-10Damping Types. The solution form in this case is more involved because the amount of damping determines the form of the solution. The three possible cases for positive values of are Critically damped Overdamped UnderdampedCritical damping occurs when the value of damping is equal to a term called critical damping . The critical damping is defined asEq. 1-11For the critically damped case, the solution becomesEq. 1-12Under this condition, the system returns to rest following an exponential decay curve with no oscillation.A system is overdamped when and no oscillatory motion occurs as the structure returns to its undisplaced position.Underdamped System. The most common damping case is the underdamped case where . In this case, the solution has the formEq. 1-13Time tAmplitude ut()mut ( ) but ( ) ku t ( ) + + 0 =bbcrbcr2 km 2mn= =u t ( ) A Bt + ( )e bt 2m =b bcr>b bcr 0 indicates amplitude, phase format.)NCOL Number of columns in a rectangular matrix. Used only for IFO = 9. See Remarks 5. and 6. (Integer > 0)GJ Grid, scalar or extra point identification number for column index. (Integer > 0)CJ Component number for grid point GJ. (0 < Integer < 6; blank or zero if GJ is a scalar or extra point.)Gi Grid, scalar, or extra point identification number for row index. (Integer > 0)Ci Component number for Gi for a grid point. ( ; blank or zero if Gi is a scalar or extra point.)Ai, Bi Real and imaginary (or amplitude and phase) parts of a matrix element. If the matrix is real (TIN = 1 or 2), then Bi must be blank. (Real)Field Contents0 CJ < 6 Main Index395 APPENDIX2. The header entry containing IFO, TIN and TOUT is required. Each nonnull column is started with a GJ, CJ pair. The entries for each row of that column follows. Only nonzero terms need be entered. The terms may be input in arbitrary order. A GJ, CJ pair may be entered more than once, but input of an element of the matrix more than once will produce a fatal message.3. Field 3 of the header entry must contain an integer 0.4. For symmetric matrices (IFO = 6), a given off-diagonal element may be input either below or above the diagonal. While upper and lower triangle terms may be mixed, a fatal message will be issued if an element is input both below and above the diagonal.5. The recommended format for rectangular matrices requires the use of NCOL and IFO = 9. The number of columns in the matrix is NCOL. (The number of rows in all DMIG matrices is always either p-set or g-set size, depending on the context.) The GJ term is used for the column index. The CJ term is ignored.6. If NCOL is not used for rectangular matrices, two different conventions are available: If IFO = 9, GJ and CJ will determine the sorted sequence, but will otherwise be ignored; a rectangular matrix will be generated with the columns submitted being in the 1 to N positions, where N is the number of logical entries submitted (not counting the header entry). If IFO = 2, the number of columns of the rectangular matrix will be equal to the index of the highest numbered non-null column (in internal sort). Trailing null columns of the g- or p-size matrix will be truncated.7. The matrix names must be unique among all DMIGs.8. TIN should be set consistent with the number of decimal digits required to read the input data adequately. For a single-precision specification on a short-word machine, the input will be truncated after about eight decimal digits, even when more digits are present in a double-field format. If more digits are needed, a double precision specification should be used instead. However, note that a double precision specification requires a D type exponent even for terms that do not need an exponent. For example, unity may be input as 1.0 in single precision, but the longer form 1.0D0 is required for double precision.9. On long-word machines, almost all matrix calculations are performed in single precision and on short-word machines, in double precision. It is recommended that DMIG matrices also follow these conventions for a balance of efficiency and reliability. The recommended value for TOUT is 0, which instructs the program to inspect the system cell that measures the machine precision at run time and sets the precision of the matrix to the same value. TOUT = 0 allows the same DMIG input to be used on any machine. If TOUT is contrary to the machine type specified (for example, a TOUT of 1 on a short-word machine), unreliable results may occur.10. If any DMIG entry is changed or added on restart then a complete re-analysis is performed. Therefore, DMIG entry changes or additions are not recommended on restart.Main Index 396Defines the phase lead term in the equation of the dynamic loading function.Format:Example:Remarks:1. One or two dynamic load phase lead terms may be defined on a single entry.2. SID must be referenced on a RLOADi entry. Refer to the RLOAD1 or RLOAD2 entry for the formulas that define how the phase lead is used.3. A DAREA and/ or LSEQ entry should be used to define a load at Pi and Ci.4. In superelement analysis, DPHASE entries may only be applied to loads on points in the residual structure.Defines data needed to perform real eigenvalue analysis.Format:Example:DPHASEDynamic Load Phase Lead1 2 3 4 5 6 7 8 9 10DPHASE SID P1 C1 TH1 P2 C2 TH2DPHASE 4 21 6 2.1 8 6 7.2Field ContentsSID Identification number of DPHASE entry. (Integer > 0)Pi Grid, extra, or scalar point identification number. (Integer > 0)Ci Component number. (Integers 1 through 6 for grid points; zero or blank for extra or scalar points)THi Phase lead in degrees. (Real)EIGRReal Eigenvalue Extraction Data1 2 3 4 5 6 7 8 9 10EIGR SID METHOD F1 F2 NE NDNORM G CEIGR 13 LAN 12Main Index397 APPENDIXField ContentsSID Set identification number. (Unique Integer > 0)METHOD Method of eigenvalue extraction. (Character)Modern Methods:LAN Lanczos MethodAHOU Automatic selection of HOU or MHOU method. See Remark 13.Obsolete Methods:INV Inverse Power method.SINV Inverse Power method with enhancements.GIV Givens method of tridiagonalization.MGIV Modified Givens method.HOU Householder method of tridiagonalization.MHOU Modified Householder method.AGIV Automatic selection of METHOD = GIV or MGIV. See Remark 13.NORM Method for normalizing eigenvectors. (Character: MASS, MAX, or POINT; Default = MASS)MASS Normalize to unit value of the generalized mass. (Default)MAX Normalize to unit value of the largest component in the analysis set.POINT Normalize to a positive or negative unit value of the component defined in fields 3 and 4. The POINT option is not supported for METH=LAN. (Defaults to MASS if defined component is zero.)G Grid or scalar point identification number. Required only if NORM = POINT. (Integer > 0)C Component number. Required only if NORM = POINT and G is a geometric grid point. (1 < Integer < 6)Main Index 398Remarks:1. The EIGR entry must be selected with the Case Control command METHOD = SID.2. See Real Eigenvalue Analysis on page 33 of the MSC.Nastran Basic Dynamics Users Guide for a discussion of method selection.3. The units of F1 and F2 are cycles per unit time.4. The continuation entry is optional. If the continuation entry is not specified, then mass normalization is performed.5. The contemporary methods are LAN and AHOU. The other methods are in a maintenance-only status, with no enhancements planned for them. They may be eliminated in a future release of MSC.Nastran.6. The LAN method is the most general-purpose method, and may be used on both small- and large-size problems. It takes advantage of sparsity of input matrices, leading to greater efficiency on large-size problems. Because Lanczos performance is tuned for medium to large problems, this has caused difficulties with very small problems. Thus, by default, on problems with fewer than 20 degrees-of-freedom when the LAN method is selected, the method is switched to AHOU. The criteria for automatic switching is controlled by SYSTEM(359) on the NASTRAN entry. The NE, G, and C fields are Table 6-1 Relationship Between METHOD Field and Other Fields forObsolete MethodsFieldMETHOD FieldINV or SINV GIV, MGIV, HOU, or MHOUF1, F2 Frequency range of interest. F1 must be input. If METHOD = SINV and ND, is blank, then F2 must be input. (Real > 0.0)Frequency range of interest. If ND is not blank, F1 and F2 are ignored. If ND is blank, eigenvectors are found with natural frequencies that lie in the range between F1 and F2. (Real > 0.0; F1 < F2)NE Estimate of number of roots in range (Required for METHOD = INV). Not used by SINV method. (Integer > 0)Not used.ND Desired number of roots. If this field is blank and METHOD = SINV, then all roots between F1 and F2 are searched and the limit is 600 roots. (Integer > 0, Default is for METHOD = INV only.)Desired number of eigenvectors. If ND is zero, the number of eigenvectors is determined from F1 and F2. If all three are blank, then ND is automatically set to one more than the number of degrees-of-freedom listed on SUPORTi entries. (Integer > 0; Default = 0)3 NE Main Index399 APPENDIXignored for the LAN method. The NORM field may be set to MASS (the default value) or NORM. The conventions used when both the Fi and ND fields are specified are described in Table 1 of the EIGRL entry description. The EIGRL entry is an alternate method to select the LAN method. It has several other input options for special cases. When both and EIGRL and EIGR have the same SID and that SID is selected by a METHOD command the EIGRL entry takes precedence. 7. The AHOU method is competitive with the LAN method when there are small, dense matrices and many eigenvectors are required. This most commonly occurs when static or dynamic reduction is performed. The AHOU method does not take advantage of matrix sparsity, so that computation cost rises with the cube of the number of DOFs. The AHOU method responds to all permitted values for all the other fields except NE, which is ignored.8. All methods require a positive semi-definite (psd) mass matrix for stable solutions. The mass matrix may be tested for this condition for all methods of solution by setting SYSTEM(303). A value of -4 should be sufficient to identify problem matrices. A fatal error exit is taken when it is not met. All MSC.Nastran metric elements are designed to produce psd mass matrices. CMASSi elements, DMIG matrices selected by the M2GG command, and matrices input via INPUTT4 are special methods that allow addition of non-psd terms by use of non-metric element input. If none of this type of special input is present and the fatal error exit is taken you may have encountered an error in a metric element. Contact your local MSC technical representative for corrective action in this case.9. The LAN and AHOU methods allow singular but positive semi-definite mass matrices.10. The tridiagonal methods include the xGIV and xHOU methods, where x is described in the following comments. All tridiagonal methods compute all eigenvalues, and the number of eigenvectors specified by the Fi and Nd fields, as described in Table 13.11. If x is blank (for example, the HOU method is selected) the mass matrix must be non-singular.12. If x is M (for example, the MHOU method is selected) the mass matrix may be singular. A modified, shifted problem is solved in an inverse basis with this method. Some precision in the solution and longer computation time is exchanged for a more stable solution.13. If x is A (for example, the AHOU method is selected) an attempt is made to solve the problem without shifting, in the interest of cost reduction and maximum precision. If the mass matrix is determined to be poorly conditioned for inversion the basis is automatically shifted with the modified method.14. If NORM = MAX, components that are not in the analysis set may have values larger than unity.15. If NORM = POINT, the selected component should be in the analysis set (a-set). (The program uses NORM = MAX when it is not in the analysis set.) The displacement value at the selected component will be positive or negative unity.Main Index 40016. The SINV method is an enhanced version of the INV method. It uses Sturm sequence number techniques to make it more likely that all roots in the range have been found. It is generally more reliable and more efficient than the INV method.17. For the INV and SINV methods, convergence is achieved at . Convergence is tested by other criteria for the other methods.18. For the SINV method only, if F2 is blank, the first shift will be made at F1, and only one eigensolution above F1 will be calculated. If there are no modes below F1, it is likely that the first mode will be calculated. If there are modes below F1 (including rigid body modes defined by SUPORT entries), a mode higher than the first mode above F1 may be calculated.19. When F1, F2, and ND are all zero or blank, ND is reset to 1. A User Warning Message is produced for this condition, which is interpreted as likely to be due to an inadvertent omission by the user.Defines data needed to perform real eigenvalue (vibration or buckling) analysis with the Lanczos method.Format:Example:EIGRLReal Eigenvalue Extraction Data, Lanczos Method1 2 3 4 5 6 7 8 9 10EIGRL SID V1 V2 ND MSGLVL MAXSET SHFSCL NORMoption_1 = value_1 option_2 = value_2, etc.EIGRL 1 0.1 3.2 10NORM=MAX NUMS=2Field ContentsSID Set identification number. (Unique Integer > 0)V1, V2 For vibration analysis: frequency range of interest. For buckling analysis: eigenvalue range of interest. See Remark 4. (Real or blank, )ND Number of roots desired. See Remark 4. (Integer > 0 or blank)MSGLVL Diagnostic level. (0 < Integer < 4; Default = 0)MAXSET Number of vectors in block or set. Default is machine dependent. See Remark 14. SHFSCL Estimate of the first flexible mode natural frequency. See Remark 10. (Real or blank)NORM Method for normalizing eigenvectors (Character: MASS or MAX)106 5 1016 V1 V2 < 5. 1016Main Index401 APPENDIXRemarks:1. Real eigenvalue extraction data sets must be selected with the Case Control command METHOD = SID.2. The units of V1 and V2 are cycles per unit time in vibration analysis, and are eigenvalues in buckling analysis. Each eigenvalue is the factor by which the prebuckling state of stress is multiplied to produce buckling in the shape defined by the corresponding eigenvector.3. NORM = MASS is ignored in buckling analysis and NORM = MAX will be applied.4. The roots are found in order of increasing magnitude; that is, those closest to zero are found first. The number and type of roots to be found can be determined from Table 6-2.MASS Normalize to unit value of the generalized mass. Not available for buckling analysis. (Default for normal modes analysis.)MAX Normalize to unit value of the largest displacement in the analysis set. Displacements not in the analysis set may be larger than unity. (Default for buckling analysis.)ALPH Specifies a constant for the calculation of frequencies (Fi) at the upper boundary segments for the parallel method based on the following formula. See Remark 13. (Integer > 0.0; Default = 1.0):NUMS Number of frequency segments for the parallel method. (Integer > 0; Default = 1)Fi Frequency at the upper boundary of the i-th segment. See Remark 13. (Real or blank; )option_i=value_iAssigns a value to the fields above except for SID. ALPH, NUMS, and Fi must be specified in this format. V1, V2, ND, MSGLVL, MAXSET, SHFSCL, and NORM may be specified in this format as long as their corresponding field is blank in the parent entry.Table 6-2 Number and Type of Roots Found with EIGRL EntryV1 V2 ND Number and Type of Roots FoundV1 V2 ND Lowest ND or all in range, whichever is smaller.V1 V2 blank All in rangeField ContentsFi V2 V1 ( )1 ALPHi1. ALPHNUMS-------------------------------------------- =V1 F1 F2 F15 V2 < < < 0)Fi Frequency value in units of cycles per unit time. (Real > 0.0)FREQ1Frequency List, Alternate Form 1fN fN 1 fN fN 1 DFREQ < fMAX fMIN 105 fMAX fMINMain Index405 APPENDIXFormat:Example:Remarks:1. FREQ1 entries must be selected with the Case Control command FREQUENCY= SID.2. The units for F1 and DF are cycles per unit time.3. The frequencies defined by this entry are given bywhere i = 1 to (NDF + 1).4. All FREQi entries with the same frequency set identification numbers will be used. Duplicate frequencies will be ignored. and are considered duplicated if,where DFREQ is a user parameter, with a default of . and are the maximum and minimum excitation frequencies of the combined FREQi entries.5. In modal analysis, solutions for modal DOFs from rigid body modes at zero excitation frequencies may be discarded. Solutions for nonzero modes are retained.Defines a set of frequencies to be used in the solution of frequency response problems by specification of a starting frequency, final frequency, and the number of logarithmic increments desired.Format:1 2 3 4 5 6 7 8 9 10FREQ1 SID F1 DF NDFFREQ1 6 2.9 0.5 13Field ContentsSID Set identification number. (Integer > 0)F1 First frequency in set. (Real > 0.0)DF Frequency increment. (Real > 0.0)NDF Number of frequency increments. (Integer > 0; Default = 1)FREQ2Frequency List, Alternate Form 21 2 3 4 5 6 7 8 9 10FREQ2 SID F1 F2 NFfi F1 = DF + i 1 ( ) fN fN 1 fN fN 1 DFREQ < fMAX fMIN 105 fMAX fMINMain Index 406Example:Remarks:1. FREQ2 entries must be selected with the Case Control command FREQUENCY= SID.2. The units for F1 and F2 are cycles per unit time.3. The frequencies defined by this entry are given bywhere and In the example above, the list of frequencies will be 1.0, 1.4142, 2.0, 2.8284, 4.0, 5.6569 and 8.0 cycles per unit time.4. All FREQi entries with the same frequency set identification numbers will be used. Duplicate frequencies will be ignored. and are considered duplicated if,where DFREQ is a user parameter, with a default of . and are the maximum and minimum excitation frequencies of the combined FREQi entries.5. In modal analysis, solutions for modal DOFs from rigid body modes at zero excitation frequencies may be discarded. Solutions for nonzero modes are retained.Defines a set of excitation frequencies for modal frequency-response solutions by specifying number of excitation frequencies between two modal frequencies.Format:Example:FREQ2 6 1.0 8.0 6Field ContentsSID Set identification number. (Integer > 0)F1 First frequency. (Real > 0.0)F2 Last frequency. (Real > 0.0, F2 > F1)NF Number of logarithmic intervals. (Integer > 0; Default = 1)FREQ3Frequency List, Alternate 31 2 3 4 5 6 7 8 9 10FREQ3 SID F1 F2 TYPE NEF CLUSTERFREQ3 6 20.0 200.0 LINEAR 10 2.0fi F1 = e i 1 ( )dd1NF-------- F2F1------- ln = i 1 2 NF 1 + ( ) , , , =fN fN 1 fN fN 1 DFREQ < fMAX fMIN 105 fMAX fMINMain Index407 APPENDIXRemarks:1. FREQ3 applies only to modal frequency-response solutions (SOLs 11, 111, 146, and 200) and is ignored in direct frequency response solutions.2. FREQ3 entries must be selected with the Case Control command FREQUENCY= SID.3. In the example above, there will be 10 frequencies in the interval between each set of modes within the bounds 20 and 2000, plus 10 frequencies between 20 and the lowest mode in the range, plus 10 frequencies between the highest mode in the range and 2000.4. Since the forcing frequencies are near structural resonances, it is important that some amount of damping be specified.5. All FREQi entries with the same set identification numbers will be used. Duplicate frequencies will be ignored. and are considered duplicated ifwhere DFREQ is a user parameter, with a default of . an are the maximum and minimum excitation frequencies of the combined FREQi entries.6. CLUSTER is used to obtain better resolution near the modal frequencies where the response varies the most. CLUSTER > 1.0 provides closer spacing of excitation frequency towards the ends of the frequency range, while values of less than 1.0 provide closer spacing towards the center of the frequency range. For example, if the frequency range is between 10 and 20, NEF = 11, TYPE = "LINEAR"; then, the excitation frequencies for various values of CLUSTER would be as shown in Table 6-4.Field ContentsSID Set identification number. (Integer > 0)F1 Lower bound of modal frequency range in cycles per unit time. (Real > 0.0 for TYPE = LINEAR and Real = 0.0 for TYPE = LOG)F2 Upper bound of modal frequency range in cycles per unit time. (Real > 0.0, F2 > F1, Default = F1)TYPE LINEAR or LOG. Specifies linear or logarithmic interpolation between frequencies. (Character; Default = "LINEAR")NEF Number of excitation frequencies within each subrange including the end points. The first subrange is between F1 and the first modal frequency within the bounds. The second subrange is between first and second modal frequencies between the bounds. The last subrange is between the last modal frequency within the bounds and F2. (Integer > 1, Default = 10)CLUSTER Specifies clustering of the excitation frequency near the end points of the range. See Remark 6. (Real > 0.0; Default = 1.0)fN fN 1 fN fN 1 DFREQ < fMAX fMIN 105 fMAX fMINfk12--- = f1 f2+ ( )12--- f2 f1 ( ) 1 CLUSTER + SIGN ( ) Main Index 408where7. In design optimization (SOL 200), the excitation frequencies are derived from the natural frequencies computed at each design cycle.8. In modal analysis, solutions for modal DOFs from rigid body modes at zero excitation frequencies may be discarded. Solutions for nonzero modes are retained.Defines a set of frequencies used in the solution of modal frequency-response problems by specifying the amount of spread around each natural frequency and the number of equally spaced excitation frequencies within the spread.= is a parametric coordinate between -1 and 1k = varies from 1 to NEF (k = 1, 2, ..., NEF)= is the lower limit of the frequency subrange= is the upper limit o the subrange= is the k-th excitation frequency= is the frequency, or the logarithm of the frequency, depending on the value specified for TYPETable 6-4 CLUSTER Usage ExampleExcitation Frequency NumberCLUSTERc=0.25 c-0.50 c-1.0 c-2.0 c-4.0Excitation Frequencies in Hertz1 -1.0 10.00 10.0 10.0 10.00 10.002 -0.8 12.95 11.8 11.0 10.53 10.273 -0.6 14.35 13.2 12.0 11.13 10.604 -0.4 14.87 14.2 13.0 11.84 11.025 -0.2 14.99 14.8 14.0 12.76 11.666 0.0 15.00 15.0 15.0 15.00 15.007 0.2 15.01 15.2 16.0 17.24 18.348 0.4 15.13 15.8 17.0 18.16 18.989 0.6 15.65 16.8 18.0 18.87 19.4010 0.8 17.05 18.2 19.0 19.47 19.7311 1.0 20.00 20.0 20.0 20.00 20.00FREQ4Frequency List, Alternate Form 4 1 2 k 1 ( ) + NEF 1 ( ) f1f2fkfMain Index409 APPENDIXFormat:Example:Remarks:1. FREQ4 applies only to modal frequency-response solutions (SOLs 11, 111, 146, and 200 and is ignored in direct frequency-response solutions.2. FREQ4 entries must be selected with the Case Control command FREQUENCY= SID.3. There will be NFM excitation frequencies between and , for each natural frequency in the range F1 to F2.4. In the example above there will be 21 equally spaced frequencies across a frequency band of to for each natural frequency that occurs between 20 and 2000. See Figure 6-1 for the definition of frequency spread.Figure 6-1 Frequency Spread DefinitionExcitation frequencies may be based on natural frequencies that are not within the range (F1 and F2) as long as the calculated excitation frequencies are within the range. Similarly, an excitation frequency calculated based on natural frequencies within the range (F1 through F2) may be excluded if it falls outside the range.5. The frequency spread can be used also to define the half-power bandwidth. The half-power bandwidth is given by , where is the damping ratio. Therefore, if FSPD is specified equal to the damping ratio for the mode, NFM specifies the number of excitation frequency within the half-power bandwidth. See Figure 6-2 for the definition of half-power bandwidth.1 2 3 4 5 6 7 8 9 10FREQ4 SID F1 F2 FSPD NFMFREQ4 6 20.0 200.0 0.30 21Field ContentsSID Set identification number. (Integer > 0)F1 Lower bound of frequency range in cycles per unit time. (Real > 0.0, Default = 0.0)F2 Upper bound of frequency range in cycles per unit time. (Real > 0.0, F2 > F1, Default = 1.0E20)FSPD Frequency spread, +/ - the fractional amount specified for each mode which occurs in the frequency range F1 to F2. (1.0 > Real > 0.0, Default = 0.10)NFM Number of evenly spaced frequencies per spread mode. (Integer > 0; Default = 3; If NFM is even, NFM + 1 will be used.)1 FSPD ( ) fN 1 FSPD + ( ) fN0.7 fN 1.3 fN1 FSPD ( ) fN fN1 FSPD + ( ) fN2 fN Main Index 410Figure 6-2 Half-Power Bandwidth Definition6. Since the forcing frequencies are near structural resonances, it is important that some amount of damping be specified.7. All FREQi entries with the same set identification numbers will be used. Duplicate frequencies will be ignored. and are considered duplicated ifwhere DFREQ is a user parameter with a default of . The values and are the maximum and minimum excitation frequencies of the combined FREQi entries.8. In design optimization (SOL 200), the excitation frequencies are derived from the natural frequencies computed at each design cycle.9. In modal analysis, solutions for modal DOFs from rigid body modes at zero excitation frequencies may be discarded. Solutions for nonzero modes are retained.Defines a set of frequencies used in the solution of modal frequency-response problems by specification of a frequency range and fractions of the natural frequencies within that range.Format:Example:Remarks:1. FREQ5 applies only to modal frequency-response solutions (SOLs 11, 111, 146, and 200) and is ignored in direct frequency response solutions.FREQ5Frequency List, Alternate Form 51 2 3 4 5 6 7 8 9 10FREQ5 SID F1 F2 FR1 FR2 FR3 FR4 FR5FR6 FR7 -etc.-FREQ5 6 20.0 200.0 1.0 0.6 0.8 0.9 0.951.05 1.1 1.2Field ContentsSID Set identification number. (Integer > 0)F1 Lower bound of frequency range in cycles per unit time. (Real > 0.0; Default = 0.0)F2 Upper bound of frequency range in cycles per unit time. (Real > 0.0, F2 > F1, Default = 1.0E20)FRi Fractions of the natural frequencies in the range F1 to F2. (Real > 0.0)Peak ResponseHalf-Power Point (.707 Peak)FrequencyHalf-PowerBandwidthAmplitudefN2 fN fN fN 1 fN fN 1 DFREQ < fMAX fMIN 105 fMAX fMINMain Index411 APPENDIX2. FREQ5 entries must be selected with the Case Control command FREQUENCY= SID.3. The frequencies defined by this entry are given bywhere are the natural frequencies in the range F1 through F2.4. In the example above, the list of frequencies will be 0.6, 0.8, 0.9, 0.95, 1.0, 1.05, 1.1, and 1.2 times each natural frequency between 20 and 2000. If this computation results in excitation frequencies less then F1 and greater than F2, those computed excitation frequencies are ignored.Excitation frequencies may be based on natural frequencies that are not within the range (F1 and F2) as long as the calculated excitation frequencies are within the range. Similarly, an excitation frequency calculated based on natural frequencies within the range (F1 through F2) may be excluded if it falls outside the range.5. Since the forcing frequencies are near structural resonances, it is important that some amount of damping be specified.6. All FREQi entries with the same set identification numbers will be used. Duplicate frequencies will be ignored. and are considered duplicated ifwhere DFREQ is a user parameter with a default of . The values and are the maximum and minimum excitation frequencies of the combined FREQi entries.7. In design optimization (SOL 200), the excitation frequencies are derived from the natural frequencies computed at each design cycle.8. In modal analysis, solutions for modal DOFs from rigid body modes at zero excitation frequencies may be discarded. Solutions for nonzero modes are retainedDefines a sequence of static load sets.Format:Example:LSEQStatic Load Set Definition1 2 3 4 5 6 7 8 9 10LSEQ SID EXCITEID LID TIDLSEQ 100 200 1000 1001fi FRi = fNifNifN fN 1 fN fN 1 DFREQ < fMAX fMIN 105 fMAX fMINMain Index 412Remarks:1. LSEQ will not be used unless selected in the Case Control Section with the LOADSET command.2. The number of static load vectors created for each superelement depends upon the type of analysis. In static analysis, the number of vectors created is equal to the number of unique EXCITEID IDs on all LSEQ entries in the Bulk Data; in dynamic analysis, the number of vectors created is equal to the number of unique EXCITEID IDs on all RLOAD1, RLOAD2, TLOAD1, TLOAD2 and ACSRCE entries in the Bulk Data.3. EXCITEID may be referenced by CLOAD, RLOAD1, RLOAD2, TLOAD1, and TLOAD2 entries in order to apply the static load in nonlinear, static and dynamic analysis.4. Element data recovery for thermal loads is not currently implemented in dynamics.5. The SID-EXCITEID number pair must be unique with respect to similiar pairs on all other LSEQ entries in the Bulk Data.6. In a nonsuperelement analysis, LID and TID cannot both be blank. In superelement analysis, they may both be blank as long as static loads are prescribed in the upstream superelements.7. It is no longer necessary to employ LOADSET/ LSEQ data to specify static loading data for use in dynamic analysis. In the absence of LSEQ Bulk Data entries, all static loads whose load set IDs match the EXCITEID IDs on all RLOAD1, RLOAD2, TLOAD1, TLOAD2 and ACSRCE entries in the Bulk Data are automatically processed.Specifies the damping value of a scalar damper element using defined CDAMP1 or CDAMP3 entries.Format:Field ContentsSID Set identification of the set of LSEQ entries. See Remark 5. (Integer > 0)EXCITEID The EXCITEID set identification assigned to this static load vector. See Remark 5. (Integer > 0)LID Load set identification number of a set of static load entries such as those referenced by the LOAD Case Control command. (Integer > 0 or blank)TID Temperature set identification of a set of thermal load entries such as those referenced by the TEMP(LOAD) Case Control command. (Integer > 0 or blank)PDAMPScalar Damper Property1 2 3 4 5 6 7 8 9 10PDAMP PID1 B1 PID2 B2 PID3 B3 PID4 B4Main Index413 APPENDIXExample:Remarks:1. Damping values are defined directly on the CDAMP2 and CDAMP4 entries, and therefore do not require a PDAMP entry. 2. A structural viscous damper, CVISC, may also be used for geometric grid points.3. Up to four damping properties may be defined on a single entry.4. For a discussion of scalar elements, see Scalar Elements (CELASi, CMASSi, CDAMPi) on page 193 of the MSC.Nastran Reference Guide.Specifies the mass value of a scalar mass element (CMASS1 or CMASS3 entries).Format:Example:Remarks:1. Mass values are defined directly on the CMASS2 and CMASS4 entries, and therefore do not require a PMASS entry.2. Up to four mass values may be defined by this entry.3. For a discussion of scalar elements, see Scalar Elements (CELASi, CMASSi, CDAMPi) on page 193 of the MSC.Nastran Reference Guide.Defines properties of a one-dimensional viscous damping element (CVISC entry).PDAMP 14 2.3 2 6.1Field ContentsPIDi Property identification number. (Integer > 0)Bi Force per unit velocity. (Real)PMASSScalar Mass Property1 2 3 4 5 6 7 8 9 10PMASS PID1 M1 PID2 M2 PID3 M3 PID4 M4PMASS 7 4.29 6 13.2Field ContentsPIDi Property identification number. (Integer > 0)Mi Value of scalar mass. (Real)PVISCViscous Damping Element PropertyMain Index 414Format:Example:Remarks:1. Viscous properties are material independent; in particular, they are temperature independent.2. One or two viscous element properties may be defined on a single entry.Defines a frequency-dependent dynamic load of the formfor use in frequency response problems.Format:Example:1 2 3 4 5 6 7 8 9 10PVISC PID1 CE1 CR1 PID2 CE2 CR2PVISC 3 6.2 3.94Field ContentsPIDi Property identification number. (Integer > 0)CE1, CE2 Viscous damping values for extension in units of force per unit velocity. (Real)CR1, CR2 Viscous damping values for rotation in units of moment per unit velocity. (Real)RLOAD1Frequency Response Dynamic Excitation, Form 11 2 3 4 5 6 7 8 9 10RLOAD1 SID EXCITEID DELAY DPHASE TC TD TYPERLOAD1 5 3 1Field ContentsSID Set identification number. (Integer > 0)EXCITEID Identification number of the DAREA or SPCD entry set that defines A. See Remarks 5. and 6. (Integer > 0)P f ( ) { } A C f ( ) i D f ( ) + [ ]ei 2f { }{ } =Main Index415 APPENDIXRemarks:1. Dynamic excitation sets must be selected with the Case Control command DLOAD = SID.2. If any of DELAY, DPHASE, TC, or TD fields are blank or zero, the corresponding , , or will both be zero. Either TC or TD may be blank or zero, but not both.3. RLOAD1 excitations may be combined with RLOAD2 excitations only by specification on a DLOAD entry. That is, the SID on a RLOAD1 entry must not be the same as that on a RLOAD2 entry.4. SID must be unique for all RLOAD1, RLOAD2, TLOAD1, TLOAD2, and ACSRCE entries.5. The type of the dynamic excitation is specified by TYPE (field 8) according to the following table:6. TYPE (field 8) also determines the manner in which EXCITEID (field 3) is used by the program as described below:DELAY Defines time delay . (Integer > 0, real or blank.) If it is a non-zero integer, it represents the identification number of DELAY Bulk Data entry that defines . If it is real, then it directly defines the value of that will be used for all degrees of freedom that are excited by this dynamic load entry. See also Remark 2.DPHASE Defines phase angle . (Integer > 0, real or blank.) If it is a non-zero integer, it represents the identification number of DPHASE Bulk Data entry that defines (in degrees). If it is real, then it directly defines the vlaue of (in degrees) that will be used for all degrees of freedom that are excited by this dynamic load entry. See also Remark 2.TC Set identification number of the TABLEDi entry that gives . See Remark 2. (Integer > 0)TD Set identification number of the TABLEDi entry that gives . See Remark 2. (Integer > 0)TYPE Defines the type of the dynamic excitation. See Remarks 5. and 6. (Integer, character or blank; Default = 0)TYPE TYPE of Dynamic Excitation0, L, LO, LOA or LOAD Applied load (force or moment) (Default)1, D, DI, DIS or DISP Enforced displacement using SPC/ SPCD data2, V, VE, VEL or VELO Enforced velocity using SPC/ SPCD data3, A, AC, ACC or ACCE Enforced acceleration SPC/ SPCD dataField Contents C f ( )D f ( )C f ( ) D f ( )Main Index 416Excitation specified by TYPE is applied load There is no LOADSET request in Case ControlEXCITEID may also reference DAREA, static and thermal load set entries. There is a LOADSET request in Case ControlThe program may also reference static and thermal load set entries specified by the LID or TID field in the selected LSEQ entries corresponding to the EXCITEID.Excitation specified by TYPE is enforced motion There is no LOADSET request in Case ControlEXCITEID will reference SPCD entries. There is a LOADSET request in Case ControlThe program will reference SPCD entries specified by the LID field in the selected LSEQ entries corresponding to the EXCITEID.Defines a frequency-dependent dynamic excitation of the form.for use in frequency response problems.Format:Example:RLOAD2Frequency Response Dynamic Excitation, Form 21 2 3 4 5 6 7 8 9 10RLOAD2 SID EXCITEID DELAY DPHASE TB TP TYPERLOAD2 5 3 7Field ContentsSID Set identification number. (Integer > 0)EXCITEID Identification number of the DAREA or SPCD entry set that defines A. See Remarks 5. and 6. (Integer > 0)DELAY .Defines time delay . (Integer > 0, real or blank.) If it is a non-zero integer, it represents the identification number of DELAY Bulk Data entry that defines . If it is real, then it directly defines the value of that will be used for all degrees of freedom that are excited by this dynamic load entry. See also Remark 2.P f ( ) { } A B f ( ) ei f ( ) 2f + { } { } = Main Index417 APPENDIXRemarks:1. Dynamic excitation sets must be selected with the Case Control command DLOAD = SID.2. If any of DELAY, DPHASE, or TP fields are blank or zero, the corresponding , , or will be zero.3. RLOAD2 excitations may be combined with RLOAD1 excitations only by specification on a DLOAD entry. That is, the SID on a RLOAD2 entry must not be the same as that on a RLOAD1 entry.4. SID must be unique for all RLOAD1, RLOAD2, TLOAD1, TLOAD2, and ACSRCE entries.5. The type of the dynamic excitation is specified by TYPE (field 8) according to the following table:6. TYPE (field 8) also determines the manner in which EXCITEID (field 3) is used by the program as described below:Excitation specified by TYPE is applied load There is no LOADSET request in Case ControlEXCITEID may also reference DAREA, static and thermal load set entries. There is a LOADSET request in Case ControlDPHASE Defines phase angle . (Integer > 0, real or blank.) If it is a non-zero integer, it represents the identification number of DPHASE Bulk Data entry that defines (in degrees). If it is real, then it directly defines the vlaue of (in degrees) that will be used for all degrees of freedom that are excited by this dynamic load entry. See also Remark 2.TB Set identification number of the TABLEDi entry that gives . (Integer > 0)TP Set identification number of the TABLEDi entry that gives in degrees. (Integer > 0)TYPE Defines the type of the dynamic excitation. See Remarks 5. and 6. (Integer, character or blank; Defaults = 0)TYPE TYPE of Dynamic Excitation0, L, LO, LOA or LOAD Applied load (force or moment) (Default)1, D, DI, DIS or DISP Enforced displacement using SPC/ SPCD data2, V, VE, VEL or VELO Enforced velocity using SPC/ SPCD data3, A, AC, ACC or ACCE Enforced acceleration SPC/ SPCD dataField ContentsB f ( ) f ( ) f ( )Main Index 418The program may also reference static and thermal load set entries specified by the LID or TID field in the selected LSEQ entries corresponding to the EXCITEID.Excitation specified by TYPE is enforced motion There is no LOADSET request in Case ControlEXCITEID will reference SPCD entries. There is a LOADSET request in Case ControlThe program will reference SPCD entries specified by the LID field in the selected LSEQ entries corresponding to the EXCITEID.Defines determinate reaction degrees-of-freedom in a free body.Format:Example:Remarks:1. The SUPORT entry specifies reference degrees-of-freedom for rigid body motion. It is not intended to be used in place of a constraint (i.e., SPCi entry or PS on the GRID entry).2. SUPORT and/ or SUPORT1 entries are required to perform inertia relief in static analysis (SOLs 1 and 101).In SOL 1, the presence of a SUPORT or selection of a SUPORT1 entry automatically invokes inertia relief analysis.In SOL 101, PARAM,INREL,-1 must also be specified or the SUPORTi entries will be treated as constraints.3. Be careful not to spell SUPORT with two Ps.SUPORTFictitious Support1 2 3 4 5 6 7 8 9 10SUPORT ID1 C1 ID2 C2 ID3 C3 ID4 C4SUPORT 16 215Field ContentsIDi Grid or scalar point identification number. (Integer > 0)Ci Component numbers. (Integer 0 or blank for scalar points. Any unique combination of the Integers 1 through 6 for grid points with no embedded blanks.)Main Index419 APPENDIX4. Degrees-of-freedom specified on this entry form members of the mutually exclusive r-set. They may not be specified on other entries that define mutually exclusive sets. See Degree-of-Freedom Sets on page 843 for a list of these entries.5. From 1 to 24 support degrees-of-freedom may be defined on a single entry.6. See Rigid Body Supports on page 331 of the MSC.Nastran Reference Guide for a discussion of supported degrees-of-freedom (members of the r-set).7. An alternative to SUPORT is the SUPORT1 entry, which is requested by the SUPORT1 Case Control command.Defines determinate reaction degrees-of-freedom (r-set) in a free body-analysis. SUPORT1 must be requested by the SUPORT1 Case Control command.Format:Example:Remarks:1. The SUPORT entry specifies reference degrees-of-freedom for rigid body motion. It is not intended to be used in place of a constraint; (i.e., SPCi entry or PS on the GRID entry).2. SUPORT and/ or SUPORT1 entries are required to perform inertia relief in static analysis; i.e., SOLs 1 and 101.In SOL 1, the presence of a SUPORT or selection of a SUPORT1 entry automatically invokes inertia relief analysis.In SOL 101, PARAM,INREL,-1 must also be specified or the SUPORTi entries will be treated as constraints.3. SUPORT1 must be requested by the SUPORT1 Case Control command. The degrees-of-freedom specified on SUPORT1 will be combined with those on the SUPORT entry.4. Be careful not to spell SUPORT with two Ps.SUPORT1Fictitious Support, Alternate Form1 2 3 4 5 6 7 8 9 10SUPORT1 SID ID1 C1 ID2 C2 ID3 C3SUPORT1 5 16 215Field ContentsSID Identification number of the support set. See Remark 1. (Integer > 0)IDi Grid or scalar point identification number. (Integer > 0)Ci Component numbers. (Integer 0 or blank for scalar points. Any unique combination of the Integers 1 through 6 for grid points with no embedded blanks.)Main Index 4205. Degrees-of-freedom specified on this entry form members of the mutually exclusive r-set. They may not be specified on other entries that define mutually exclusive sets. See Degree-of-Freedom Sets on page 843 for a list of these entries.6. From 1 to 18 support degrees-of-freedom may be defined on a single entry.7. See Rigid Body Supports on page 331 of the MSC.Nastran Reference Guide for a discussion of supported degrees-of-freedom (members of the r-set).8. In superelement analysis, SUPORT1 may be specified for points belonging to the residual structure only.Defines modal damping as a tabular function of natural frequency.Format:Example:Remarks:1. Modal damping tables must be selected with the Case Control command SDAMPING = TID.2. The frequency values, fi, must be specified in either ascending or descending order, but not both.3. Discontinuities may be specified between any two points except the two starting points or two end points. For example, in Figure 6-3 discontinuities are allowed only between points f2 through f7. Also, if g is evaluated at a discontinuity, then the average value of g is used. In Figure 6-3, the value of g at f = f3 is .4. At least one continuation entry must be specified.TABDMP1Modal Damping Table1 2 3 4 5 6 7 8 9 10TABDMP1 TID TYPEf1 g1 f2 g2 f3 g3 -etc.-TABDMP1 22.5 .01057 2.6 .01362 ENDTField ContentsTID Table identification number. (Integer > 0)TYPE Type of damping units. (Character: G, CRIT, or Q; Default is G)fi Natural frequency value in cycles per unit time. (Real > 0.0)gi Damping value. (Real)g g3 g4 + ( ) 2 =Main Index421 APPENDIX5. Any fi or gi entry may be ignored by placing SKIP in either of the two fields used for that entry.6. The end of the table is indicated by the existence of ENDT in either of the two fields following the last entry. An error is detected if any continuations follow the entry containing the end-of-table flag ENDT.7. The TABDMP1 uses the algorithmwhere f is input to the table and g is returned. The table look-up is performed using linear interpolation within the table and linear extrapolation outside the table using the last two end points. See Figure 6-3. No warning messages are issued if table data is input incorrectly.Figure 6-3 Example of Table Extrapolation and Discontinuity8. This form of damping is used only in modal formulations of complex eigenvalue analysis, frequency response analysis, or transient response analysis. The type of damping used depends on the solution sequence (structural damping is displacement-dependent, and viscous damping is velocity-dependent). See Formulation of Dynamic Equations in SubDMAP GMA on page 403 of the MSC.Nastran Reference Guide for the equations used.9. PARAM,KDAMP may be used in solution sequences that perform modal frequency and modal complex analysis, to select the type of damping.See Formulation of Dynamic Equations in SubDMAP GMA on page 403 of the MSC.Nastran Reference Guide for a full explanation.10. If TYPE is G or blank, the damping values gi, etc., are in units of equivalent viscous dampers, as follows:(See Formulation of Dynamic Equations in SubDMAP GMA on page 403 of the MSC.Nastran Reference Guide) If TYPE is CRIT, the damping values gi, etc., are in the units of fraction of critical damping . If TYPE is Q, the damping values gi are in the units of the amplification or quality factor, Q. These constants are related by the following equations:KDAMP Result1 (Default) B Matrix-1g gT f ( ) =gT f ( )fExtrapolatedgfDiscontinuityAllowedDiscontinuityNot AllowedLinearExtrapolationof Segmentf1-f2f1f valueRange of Tablef2 f3 f5 f6 f7f4f81 ig + ( )Kbigii----- Ki=C C0Main Index 422Defines a tabular function for use in generating frequency-dependent and time-dependent dynamic loads.Format:Example:Remarks:1. xi must be in either ascending or descending order, but not both.2. Discontinuities may be specified between any two points except the two starting points or two end points. For example, in Figure 6-4 discontinuities are allowed only between points x2 through x7. Also, if y is evaluated at a discontinuity, then the average value of y is used. In Figure 6-4, the value of y at x=x3 is . If the y-axis is a LOG axis then the jump at the discontinuity is evaluated as .3. At least one continuation must be specified.4. Any xi-yi pair may be ignored by placing the character string SKIP in either of the two fields.5. The end of the table is indicated by the existence of the character string ENDT in either of the two fields following the last entry. An error is detected if any continuations follow the entry containing the end-of-table flag ENDT.TABLED1Dynamic Load Tabular Function, Form 11 2 3 4 5 6 7 8 9 10TABLED1 TID XAXIS YAXISx1 y1 x2 y2 x3 y3 -etc.- ENDTTABLED1 32-3.0 6.9 2.0 5.6 3.0 5.6 ENDTField ContentsTID Table identification number. (Integer > 0)XAXIS Specifies a linear or logarithmic interpolation for the x-axis. See Remark 6. (Character: LINEAR or LOG; Default = LINEAR)YAXIS Specifies a linear or logarithmic interpolation for the y-axis. See Remark 6. (Character: LINEAR or LOG; Default = LINEAR)xi, yi Tabular values. (Real)ENDT Flag indicating the end of the table.C C0 g 2 =Q1 2C C0 ( ) 1 g =y y3 y4 + ( ) 2 =y y3y4 =Main Index423 APPENDIX6. TABLED1 uses the algorithmwhere x is input to the table and y is returned. The table look-up is performed using interpolation within the table and extrapolation outside the table using the two starting or end points. See Figure 6-4. The algorithms used for interpolation or extrapolation are:where xj and yj follow xi and yi.No warning messages are issued if table data is input incorrectly.Figure 6-4 Example of Table Extrapolation and Discontinuity7. Linear extrapolation is not used for Fourier transform methods. The function is zero outside the range of the table.8. For frequency-dependent loads, xi is measured in cycles per unit time.9. Tabular values on an axis if XAXIS or YAXIS = LOG must be positive. A fatal message will be issued if an axis has a tabular value < 0.Defines a tabular function for use in generating frequency-dependent and time-dependent dynamic loads. Also contains parametric data for use with the table.Format:XAXIS YAXIS yT(x)LINEAR LINEARLOG LINEARLINEAR LOGLOG LOGTABLED2Dynamic Load Tabular Function, Form 21 2 3 4 5 6 7 8 9 10TABLED2 TID X1x1 y1 x2 y2 x3 y3 -etc.-y yT x ( ) =xj x xj xi ---------------- yi x xi xj xi ---------------- yj +l n xj x ( )l n xj xi ( )-------------------------- yi l n x xi ( )l n xj xi ( )-------------------------- yj +xj x xj xi ---------------- l n yi x xi xj xi ---------------- l n yj + expl n xj x ( )ln xj xi ( )-------------------------- ln yi l n x xi ( )l n xj xi ( )-------------------------- ln yi + expxExtrapolatedyxDiscontinuityAllowedDiscontinuityNot AllowedLinearExtrapolationof Segmentx1-x2x1x valueRange of Tablex2 x3, x5 x6 x7,x4x8Main Index 424Example:Remarks:1. xi must be in either ascending or descending order, but not both.2. Discontinuities may be specified between any two points except the two starting points or two end points. For example, in Figure 6-5 discontinuities are allowed only between points x2 and x7. Also if y is evaluated at a discontinuity, then the average value of y is used. In Figure 6-5, the value of y at x=x3 is .3. At least one continuation entry must be specified.4. Any xi-yi pair may be ignored by placing SKIP in either of the two fields.5. The end of the table is indicated by the existence of ENDT in either of the two fields following the last entry. An error is detected if any continuations follow the entry containing the end-of-table flag ENDT.6. TABLED2 uses the algorithmwhere x is input to the table and y is returned. The table look-up is performed using linear interpolation within the table and linear extrapolation outside the table using the two starting or end points. See Figure 6-5. No warning messages are issued if table data is input incorrectly.Figure 6-5 Example of Table Extrapolation and Discontinuity7. Linear extrapolation is not used for Fourier transform methods. The function is zero outside the range of the table.8. For frequency-dependent loads, X1 and xi are measured in cycles per unit time.Defines a tabular function for use in generating frequency-dependent and time-dependent dynamic loads. Also contains parametric data for use with the table.TABLED2 15 -10.51.0 -4.5 2.0 -4.2 2.0 2.8 7.0 6.5SKIP SKIP 9.0 6.5 ENDTField ContentsTID Table identification number. (Integer > 0)X1 Table parameter. See Remark 6. (Real)xi, yi Tabular values. (Real)TABLED3Dynamic Load Tabular Function, Form 3y y3 y4 + ( ) 2 =y yT x X1 ( ) =xExtrapolatedyxDiscontinuityAllowedDiscontinuityNot AllowedLinearExtrapolationof Segmentx1-x2x1x valueRange of Tablex2 x3 x5 x6 x7x4x8Main Index425 APPENDIXFormat:Example:Remarks:1. xi must be in either ascending or descending order, but not both.2. Discontinuities may be specified between any two points except the two starting points or two end points. For example, in Figure 6-6 discontinuities are allowed only between points x2 and x7. Also if y is evaluated at a discontinuity, then the average value of y is used. In Figure 6-6, the value of y at x=x3 is .3. At least one continuation entry must be present.4. Any xi-yi pair may be ignored by placing SKIP in either of the two fields.5. The end of the table is indicated by the existence of ENDT in either of the two fields following the last entry. An error is detected if any continuations follow the entry containing the end-of-table flag ENDT.6. TABLED3 uses the algorithmwhere x is input to the table and y is returned. The table look-up is performed using interpolation within the table and linear extrapolation outside the table using the two starting or end points. See Figure 6-6. No warning messages are issued if table data is input incorrectly.Figure 6-6 Example of Table Extrapolation and Discontinuity7. Linear extrapolation is not used for Fourier transform methods. The function is zero outside the range of the table.8. For frequency-dependent loads, X1, X2, and xi are measured in cycles per unit time.1 2 3 4 5 6 7 8 9 10TABLED3 TID X1 X2x1 y1 x2 y2 x3 y3 -etc.-TABLED3 62 126.9 30.02.9 2.9 3.6 4.7 5.2 5.7 ENDTField ContentsTID Table identification number. (Integer > 0)X1, X2 Table parameters. (Real; X2 0.0)xi, yi Tabular values. (Real)y y3 y4 + ( ) 2 =y yTx X1 X2-----------------\ .| |=xExtrapolatedyxDiscontinuityAllowedDiscontinuityNot AllowedLinearExtrapolationof Segmentx1-x2x1x valueRange of Tablex2 x3 x5 x6 x7x4x8Main Index 426Defines the coefficients of a power series for use in generating frequency-dependent and time-dependent dynamic loads. Also contains parametric data for use with the table.Format:Example:Remarks:1. At least one continuation entry must be specified.2. The end of the table is indicated by the existence of ENDT in the field following the last entry. An error is detected if any continuations follow the entry containing the end-of-table flag ENDT.3. TABLED4 uses the algorithmwhere x is input to the table, y is returned, and N is the number of pairs. Whenever x < X3, use X3 for x; whenever x > X4, use X4 for x. There are N + 1 entries in the table. There are no error returns from this table look-up procedure.4. For frequency-dependent loads, xi is measured in cycles per unit time.Defines values for the initial conditions of variables used in structural transient analysis. Both displacement and velocity values may be specified at independent degrees-of-freedom. This entry may not be used for heat transfer analysis.TABLED4Dynamic Load Tabular Function, Form 41 2 3 4 5 6 7 8 9 10TABLED4 TID X1 X2 X3 X4A0 A1 A2 A3 A4 A5 -etc.-TABLED4 28 0.0 1.0 0.0 100.2.91 -0.0329 6.51-5 0.0 -3.4-7 ENDTField ContentsTID Table identification number. (Integer > 0)Xi Table parameters. (Real; X2 0.0; X3 0)G Grid, scalar, or extra point or modal coordinate identification number. (Integer > 0). See Remark 4.C Component numbers. (Any one of the integers 1 through 6 for grid points, integer zero or blank for scalar or extra points and 1 for modal coordinates.)U0 Initial displacement. (Real)V0 Initial velocity. (Real)TLOAD1Transient Response Dynamic Excitation, Form 1P t ( ) { } A F t ( ) { } =Main Index 428Format:Example:Remarks:1. Dynamic excitation sets must be selected with the Case Control command DLOAD = SID.2. The type of the dynamic excitation is specified by TYPE (field 5) according to the following table:3. TYPE (field 5) also determines the manner in which EXCITEID (field 3) is used by the program as described belowExcitation specified by TYPE is applied load1 2 3 4 5 6 7 8 9 10TLOAD1 SID EXCITEID DELAY TYPE TIDTLOAD1 5 7 LOAD 13Field ContentsSID Set identification number. (Integer > 0)EXCITEID Identification number of DAREA or SPCD entry set or a thermal load set (in heat transfer analysis) that defines A. See Remarks 2. and 3. (Integer > 0)DELAY Defines time delay . (Integer > 0, real or blank) If it is a non-zero integer, it represents the identification number of DELAY Bulk Data entry that defines . If it is real, then it directly defines the value of that will be used for all degrees of freedom that are excited by this dynamic load entry. See also Remark 9.TYPE Defines the type of the dynamic excitation. See Remarks 2. and 3. (Integer, character or blank; Default = 0)TID Identification number of TABLEDi entry that gives . (Integer > 0)TYPE TYPE of Dynamic Excitation0, L, LO, LOA or LOAD Applied load (force or moment) (Default)1, D, DI, DIS, or DISP Enforced displacement using large mass or SPC/ SPCD data2, V, VE, VEL or VELO Enforced velocity using large mass or SPC/ SPCD data3, A, AC, ACC or ACCE Enforced acceleration using large mass or SPC/ SPCD data F t ( )Main Index429 APPENDIX There is no LOADSET request in Case ControlEXCITEID may also reference DAREA, static, and thermal load set entries There is a LOADSET request in Case ControlThe program may also reference static and thermal load set entries specified by the LID or TID field in the selected LSEQ entries corresponding to the EXCITEID.Excitation specified by TYPE is enforced motion There is no LOADSET request in Case ControlEXCITEID will reference SPCD entries. If such entries indicate null enforced motion, the program will then assume that the excitation is enforced motion using large mass and will reference DAREA and static and thermal load set entries just as in the case of applied load excitation. There is a LOADSET request in Case ControlThe program will reference SPCD entries specified by the LID field in the selected LSEQ entries corresponding to the EXCITEID. If such entries indicate null enforced motion, the program will then assume that the excitation is enforced motion using large mass and will reference static and thermal load set entries corresponding to the DAREA entry in the selected LSEQ entries, just as in the case of applied load excitation.4. EXCITEID may reference sets containing QHBDY, QBDYi, QVECT, QVOL and TEMPBC entries when using the heat transfer option.5. TLOAD1 loads may be combined with TLOAD2 loads only by specification on a DLOAD entry. Th