154 - Understanding Dynamic Time Analyses

8/13/2019 154 - Understanding Dynamic Time Analyses

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Mechanica Analysis ModelLectureNotes

Dynamic Time Analyses

Dynamic Time Analyses are one of four analyses in Mechanica available for solvingvibration problems. When the time history of the source of vibration (external load orbase excitation) is known, you can use a Dynamic Time analysis. The results will bereported with respect to time as well. In a Dynamic Time analysis the user defines the

following:

Loading: The load definition for this analysis can be selected as Load Functionsor Base Excitation. Load Functions enable you to select existing load sets in themodel, and define a time history for them. Base Excitation requires you to enteran acceleration vector and its time history. Base Excitation is usually used forsituations in which the model is being shaken in the absence of a clear externalload.

Time Function: Whether Load Functions or Base Excitation is being used, youcan define your own time history for the load. By default Mechanica uses itsbuilt in impulse function which uses Diracs Delta function which is meant torepresent a sudden load that quickly diminishes. You can define the timefunction using a symbolic function of time or a time versus magnitude table.

Modes: All dynamic analyses require a Modal Analysis to be run. By default, theDynamic Time Analysis will make use of all modes, but you can limit thenumber of modes used with this option.

Damping Coefficient: This damping coefficient is a percentage value for relativedamping, which is the ratio between the damping in the system and a criticallydamped system.

Output Intervals: You can have automatic output intervals chosen by Mechanicaor define your own. When you make use of user-defined output intervals, you


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can view full results (including fringe plots) for the model at selected timevalues.

Best Practices

Dynamic Time analyses are favored when the time history of the input is known. It

produces a transient solution so the stress or displacement will be known at any

specific time. Unlike a static analysis, there are no predefined measures for a dynamictime analysis. As such, if the user wants to know what the maximum stress is versus

time, or what the value of the maximum stress over the entire model and over the

entire time domain is, a measure needs to be created. Measures that report a single

value (for example, maximum stress over model and over time domain) will be

reported in the Run Status or Summary file. Measures that report an array of values

(for example, maximum stress in model versus time) can only be viewed through a

graph in the results window.

UnderstandingDynamicTimeAnalysesDemonstrationUnderstandingDynamicTimeAnalyses_demo.mp4

UnderstandingDynamicTimeAnalysesProcedureProcedure: Understanding Dynamic Time Analyses

ScenarioCreate a dynamic time analysis using a symbolic function for time and create valid

measures for the analysis.

CreateDynTime conveyor2.prt

Task 1.Open the Mechanica application and create a dynamic time analysis.

1. Click Applications > Mechanica.

2. Click Mechanica Analyses/Studies from the main toolbar.

Every dynamic analysis requires a modal analysis to be defined. Note thatthe Modal_Analysis_6_modesmodal analysis has already been defined

for this model.

3. Click File > New Dynamic > Time...from the Analyses and Design Studies dialogbox.


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4. In the Loading area of the dialog box, select Base Excitationfrom the drop-down

menu.

5. Click Function to open the Functions dialog box.

6. Click New...to begin creating a new function.

7. In the Definition area of the dialog box, verify that Symbolicoption is selectedfrom the drop-down menu as shown in the figure.

8. Type 500*sin(pi*time)in the text box under the Definition drop-down menu as

shown in the figure.

This will create an acceleration that has an amplitude of 500 mm/s2and a

frequency of .5 Hz.

9. Click OKto complete the function definition and close the dialog box.

10. Click OKto close the Functions dialog box.

11. In the Direction area of the Dynamic Time Analysis Definition dialog box, type 1in

the X field. Verify that the Y and Z fields are set to 0.12. In the Damping Coefficient (%) area on the Modes tab, verify that the drop-down

menu is set to For all modesand type 4in the field below the drop-down menu.The dialog box should now appear as shown in the figure.

This value is applied as a 4% damping coefficient.


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13. Select the Previous Analysistab in the dialog box and note that theModal_Analysis_6_modesanalysis is selected.

14. Select the Outputtab in the dialog box, select the Stressescheck box and verify

that the Rotationscheck box is selected as shown in the figure.

15. Click OKto complete the Dynamic Time Analysis Definition.


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Task 2.Create measures valid for the dynamic time analysis.

No dynamic measures are predefined for a dynamic time analysis. If themaximum stress or displacement needs to be reported, you need to create

the measures manually.

1. Click Simulation Measure from the Mechanica toolbar and click Newin theMeasures dialog box.

2. Verify that the Quantity drop-down menu is set to Stress, the Component drop-

down menu is set to von Mises, and the first and second drop-down menus for

Spatial Evaluation are set to Maximumand Over Modelrespectively as shown in

the figure.


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3. Select the Time/Frequency Evalcheck box.

Note that the Valid for Analysis Types list now includes Dynamic Time

Analysis.

4. In the Dynamic Evaluation area of the dialog box, select At Each Stepfrom thefirst drop-down menu as shown in the figure.

This measure will calculate the maximum stress in the model at each time

interval. The results for this measure can only be viewed in a results window

graph display.

5. Click OKto complete the measure definition and close the dialog box.

6. Click Newin the Measures dialog box.

7. Verify that the Quantity drop-down menu is set to Stress, the Component drop-down menu is set to von Mises, and the first and second drop-down menus for

Spatial Evaluation are set to Maximumand Over Modelrespectively as shown in

the figure.



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Note that the Valid for Analysis Types list now includes Dynamic Time.

9. In the Dynamic Evaluation area of the dialog box, verify that Maximumis in the

first drop-down menu as shown in the figure.

10. Select the Time Stampcheck box.

This measure will calculate the highest stress in the model during the entire

time period of the analysis. This measure will report a single value that will

appear in the Run Status window or the summary file. The value of this

measure cannot be seen in the Results window. The time stamp option also

automatically creates a new measure that will report the time at which the

maximum stress occurred.

11. Click OKto complete the Measure Definition and close the dialog box.


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12. Click Closeto close the Measures dialog box.

13. Return to the Standard Pro/ENGINEER mode by clicking Applications >Standard.

14. Click Save from the main toolbar and click OKto save the model.

15. Click File > Erase > Current > Yesto erase the model from memory.

This completes the procedure.

UnderstandingDynamicTimeAnalysesExerciseExercise: Running a Dynamic Time Analysis

Objectives

After successfully completing this exercise, you will be able to:

Create a modal analysis and observe specific mode shapes. Create a dynamic time analysis. Determine the formula for the base excitation for this model. Define base excitation using a symbolic formula. Run the dynamic time analysis. Display results for the entire model at a specific time index. Examine how the maximum stress changes with the models mass.

ScenarioThe purpose of this exercise is to familiarize you with the options available in a dynamictime analysis and how to execute an analysis using base excitation input. Most of the

options available here will be applicable to other dynamic analysis types.

Any vibration problem is a function of three factors, the models mass, stiffness, andexternal load applied. Through the different analysis types discussed here, the three areas

will be covered.

In a dynamic time analysis, the user defines a load or excitation in the time domain and

Mechanica will calculate the time dependent response. In other words, if the load exists

for only a moment in time, this is the analysis that should be run. If the user is analyzinga persistent load that combines frequencies from several inputs, then a dynamicfrequency analysis would be more suitable. Both analysis definitions in Mechanica have

similar options, and between the exercises for dynamic time and dynamic frequency

exercises, users should become familiar with all the options that are available. Similarly,the dynamic time analysis will show how manipulating the models mass will affect the

results, while the dynamic frequency will investigate altering the models stiffness.

The Model:


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The model for this exercise is shown below. The model represents a water tower that is

meant for rural water storage. The model geometry is lacking in some details and is by nomeans complete. Some details such as the supporting pillars being solid instead of hollowshafts were selected intentionally to reduce run time. A mass element is added to

represent the water in the tank, and the mass is connected to the rest of the model using

a weighted link to distribute its weight effectively. All of the parts are assigned steel.

Figure 1

The Analysis:

A dynamic analysis is different from a static analysis in that the model is subject tovariable loads. As the loads vary, the model builds up its own inertia and stores strainenergy in each cycle. While a static analysis can be solved using Hookes law (F= kx), a

vibration problem solves the equation:

Where:

= acceleration

= velocity

x = displacement

m = mass

c = damping coefficient


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k = stiffness

Any dynamic analysis requires a Modal analysis to be run first. The purpose of a modalanalysis is to determine the natural frequencies of the model and the mode in which

they vibrate at those frequencies. Vibration loading can cause extreme stress anddisplacement when the frequency of the excitation matches one of the natural

frequencies. For the purpose of this exercise, the Modal analysis is run to determine the

first six modes of vibration. Why the number six? Knowing you have the right amount ofmodes is usually done one of two ways:

1. The user runs the modal analysis more than once until the highest frequencyreported is more or less beyond the range of frequencies that the model would be

operating in.

2. The user investigates the mass participation factor reported in the dynamic analysisand determines that the cumulative mass participation is sufficient and no moremodes are needed.

The first technique is more common, whereas the second technique is more suited for

expert analysts.

Figure 2

The dynamic time analysis definition is shown below. Each of the options displayed will be

explored. The items of particular interest will be enclosed in red boxes in the figuresbelow.


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Figure 3 Figure 4

The first item for Figure 3 is the load type. The items of interest to the user are:

1. Loading: The user has two options, Base Excitation or Load Functions. BaseExcitation is intended for users who want to enter their vibration input asacceleration. In essence, the model is being shaken.

2. Time Dependence: The function is the time variation of the acceleration. Thedefault option for this in Dynamic Time is the Impulse function. The Impulse

function provides acceleration for a short period of time and then ceases. The

details of the function itself can be queried in advanced mathematics/calculus booksunder the Dirac function. For the purpose of this exercise, the user will define a

specific function instead of using the default.


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3. Direction vector: This vector (X,Y,Z) defines the direction of the excitation. Thevalues placed here are multiplied by the function you place for time dependence.This will be elaborated on further.

4. Frame of Reference: The Relative To box defines how the measures will becalculated, relative to ground or relative to supports. The default option is ground,

but users will almost always want to choose supports. When results are calculatedrelative to ground, they combine the effects of the deformation of model

components and the rigid movement of the entire body. When results arecalculated relative to supports, only the deformation of the model is reported. In

the figure below Observer B is in an elevator and bouncing a basketball, whileobserver A is on the ground outside. From Observer As perspective, he can view

the bouncing of the ball, but as far as hes concerned, the overall movement of the

ball is upward. From Bs perspective, the ball is simply bouncing up and down, andis completely oblivious to the movement of the elevator. Observer As view of theballs displacement would be relative to ground, and Bs would be relative to

Supports. For most engineering applications, the option Supports should be

selected. If you are unsure whether Ground or Supports should be used, thenselect Supports.

Figure 5

In Figure 4, the highlighted items refer to output options available to the user:

1. Output Intervals: These are the intervals in time where the results will becalculated. Pro/MECHANICA can automatically set this option, but the user can


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mass is assigned to a point located where the CG of the water would have

been. The mass itself is connected to the tank by use of a weighted link. Any

inertial or gravitational forces generated by the mass would be transmitted

to the rest of the model through the weighted link.

2. Click Mechanica Analyses/Studies from the main toolbar.

3. Click File > New Modal....

4. In the Name field, type Modal_Analysis.

5. In the Number of Modes field, type 6. This limits the number of modes sought

during the solution.

6. Click OKto complete the modal analysis definition and return to the Mechanica

Analyses and Design Studies dialog box.

7. Verify that Modal_Analysisis selected in the Analyses and Design Studies dialog

box and click Start Run > Yesto start the design study.

8. Click Display Study Status once the analysis is started.

The analysis should take from three to five minutes to complete.

Task 2.Review the Modal_Analysisresults.

1. Review the results in the Run Status dialog box. In particular, scroll towards thebottom of the dialog box and examine the frequencies of the six modes. Your values

should match closely to those shown in the figure.

2. Click Closeto close the Run Status dialog box.

3. Click Closeto close the Diagnostics dialog box as well.


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4. Verify that Modal_Analysisis selected in the Analyses and Design Studies dialogbox and click Results to start Results mode.

5. Type MODE1in the Name field and Mode 1in the Title field.

6. Select the Mode1check box and clear all of the other check boxes in the Includecolumn in the Study Selection area of the dialog box.

7. Select the Display Optionstab and select the Animatecheck box.

8. Select the Overlay Undeformedcheck box.

9. Click OK and Showto show the results.


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10. Click Copy from the main toolbar in the Results window.


12. Select the check box for Mode2and clear all of the other check boxes in the Study

Selection area of the dialog box.

13. Click OK and Showto display the results.







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23. Type MODE_5in the Name field and Mode 5in the Title field.





27. Type MODE_6in the Name field and Mode 6in the Title field.





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You should be able to make the following observations: Modes 1 and 2 show

the model shaking from side to side in the Z and X directions. The third

shows the top of the tank up and down. The fourth mode shape is that of

the model twisting. The fifth and sixth mode show alternate bending modes

of the top of the tank. The importance of inspecting the modes will become

clear when the dynamic time analysis is analyzed. At this stage, it should be

noted that the displacements in a modal analysis are normalized, so themaximum displacement is always one. The stress is calculated based upon

that displacement, so it will not be an accurate indication of the stress the

model is under. In fact, the model does not have any loads at this point.

30. When you are finished reviewing the results, click File > Exit Results > Notoexit the Result window without saving any results.

Task 3.Create and run a dynamic time analysis

The next step in the process will be to create a dynamic time analysis. The

model will be subjected to 1g half-sine acceleration for duration of one

second. The acceleration will act entirely in the X direction. This load will

demonstrate how Mechanica calculates the input acceleration and familiarize

you with symbolic formulas.

1. If necessary, click Applications > Mechanica.


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2. If necessary, click Mechanica Analyses/Studies from the main toolbar.

3. From the Analyses and Design Studies dialog box, click File > New Dynamic >

Time....

4. Type Dynamic_Timein the Name field.

Base excitation is the default option because there are no external loadsdefined in the model. Base excitation is defined using the input fields for X,

Y, Z and the formula defined by the user (or default impulse function).

Mechanica will multiply what is in the input field with the formula. To explain

this in further detail, the actual mathematical equation of our base excitation

must first be determined. You may obtain the equation as part of the specs

you are designing the model for, but more than likely you will be told that

the input is a half sine function of a specific magnitude, frequency, and

duration. The first step here will be to determine the equation for a 1g half

sine function that lasts only one second. Any time dependent sinusoidal

function used in a vibration problem will more or less be in the format:

Where :

= base excitation acceleration A = Amplitude or peak value f = frequency t = time 2f = angular velocity

Based on the criteria set, A would be equal to 1g. The frequency f is not

given to you, but you know the function will be half a sine wave and lasts

one second. That means the full sine wave would last two seconds. A sine

wave that repeats itself every two seconds would have a frequency of Hz.

Note that unlike Pro/ENGINEER relations, trigonometric functions such as

sine or cosine in Mechanica are applied to radians, not degrees. So based on

the values of A and f, your equation can be rewritten as:

Since you know how the base excitation varies with time, you are ready to

input values into this equation. As mentioned earlier, Mechanica will multiply

whatever you input for the X, Y, and Z fields by the formula. Thus you

should use a value of 9.81 (this is the acceleration of gravity, g) for X and


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enter the formula.

5. Type 9.81in the X field as shown in the figure.

6. Click Function from the Base Acceleration Time Dependence area of the

dialog box.

7. Click New...from the Functions dialog box.

8. Type Dynamic_Time_Loadin the Name field and type in the Description areaas shown in figure.

9. Verify that Symbolicis selected in the drop-down menu in the Definition area ofthe dialog box.

10. Type if(time


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12. When you are finished, review the graph of the function and click File > Exit >

Done > OK > OKto return to the Dynamic Time Analysis Definition dialog box.

13. Select the Supportsradio button in the Relative to: area of the dialog box as

shown in the figure.

14. On the Modes tab, type 4in the field in the Damping Coefficient (%) area asshown in the figure.

Using a 100% Damping Coefficient value would result in a critically damped

model, which means it would only oscillate once under an initial disturbance.

The 4% value used here was obtained from data provided by the

Brookhaven National Laboratory [1]for welded/bolted steel structures.

Determining the correct value independent of any external references could

require empirical data. Hysteresis Damping, such as the kind generated by

rubber mounts, cannot be modeled or analyzed in Mechanica.


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15. Select the Outputtab and select the Stresses, Rotations, and Mass

Participation Factorscheck boxes.

16. Select User-defined Output Intervalsfrom the drop-down menu in theOutput Intervals area of the dialog box, type15in the Number of Master Intervals

field and click User-defined Steps.

17. Scroll to the bottom of the list of intervals, type 1.5in the last field (the field

for 15), and click Space Equally.

The operation results in 15 user-defined intervals spaced .1 seconds apart.

18. The dialog box should now appear as shown in the figure. Click OKto completethe dynamic time analysis definition and close the dialog box.

19. Click Closein the Analyses and Design Studies dialog box.


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Task 4.Create a simulation measure to track the maximum von Mises stress.

1. Click Simulation Measure from the Mechanica toolbar and click Newin the

Measures dialog box.

2. Type Maximum_Stressin the Name field.

3. Verify that the Quantity drop-down menu is set to Stress, the Component drop-

down menu is set to von Mises, and the first and second drop-down menus forSpatial Evaluation are set to Maximumand Over Modelrespectively as shown in

the figure.


5. Verify that the first and second drop-down menus for Dynamic Evaluation are set to

Maximumand Over Analysisrespectively as shown in the figure.

6. Select the Time Stampcheck box. The dialog box should now appear as shown inthe figure.


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The measure will evaluate the maximum Von Mises stress in the model over

the time period of the analysis and the time stamp at which it occurs.

7. Click OKto complete the measure definition and close the dialog box.

8. Click Closeto close the Measures dialog box.

Task 5.Run the Dynamic Time analysis and review the scalar results.

1. From the Main toolbar, click Mechanica Analyses/Studies .

2. Select Dynamic_Timefrom the Analyses and Design Studies list and click Start

Run > Yesto start the design study.

3. Click Display Study Status once the analysis is started.


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8. From the main menu, click Info > Model Maxand rotate the model as necessaryto view the area of maximum von Mises stress on the model.

The numerical values you see for your results may vary slightly from those

in the figure.


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In this situation the maximum stress is appearing at a very predictable

location. The water tank and base plate are heavy and the model is being

shaken back and forth. The support between the end of the pillar and the

base plate seems like it would be the area of high stress.

9. Click Edit Selected Definition and select the Display Options tab if necessary.

10. Select the Animatecheck box and click OK and Show.

Note how regardless of how many frames were specified in the dialog box,

the animation is shown with 15 frames. This is due to the fact that you

specifically specified 15 user-defined step for the analysis. A frame is

generated and displayed for each of these steps.

11. When you are finished reviewing the results, click File > Exit Results > Notoexit the Result window without saving any results.

Task 7.Modify the mass of the water in the tank (to represent situations where thetank is not full) and note the effects on the design's dynamic behavior.

The next step will be to examine how the mass of the model will affect the

stress. Practically speaking, the water tank may not be full all the time. The

mass of the water in the tank, represented by the mass idealization, iscalculated using three analysis features in the assembly model tree, in

addition to a relation. The analysis features measure the tanks internal

dimensions and compute what would be the fluid volume, and the relation

evaluates the mass. Feel free to examine the analysis features and relations,

but at this stage it need only be known that the portion the tank filled with

water is represented by the parameter named factor. The parameter can

vary from 0 to 1, and has been equal to 1 for the previous analyses.

1. If necessary, click Applications > Mechanica.

2. If necessary, click Mechanica Analyses/Studies .

3. Click File > New Sensitivity Design Study....

4. In the Name field, type tank_mass_factor.

5. Verify that the Type drop-down menu is set to Global Sensitivity.

6. Select Dynamic_Time (Dynamic Time)from the list of analyses.


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7. Click Select Parameter in the Variables section of the dialog box.

8. Select the FACTORparameter and click Selectas shown in the figure.

9. Type .1in the Start field and 1in the End field for FACTOR as shown in thefigure.

10. Type 9in the Steps field as shown in the figure.

11. Click OKto complete the sensitivity study definition and close the dialog box.


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Running the tank_mass_factor design study would take about 60 to 120

minutes. The remaining instructions for this exercise assume that you will

not have time to run this design study and direct you to the

tank_mass_factor_completeresults. Feel free to run the design study

and use its results instead if you have time.

Task 8.Review the results of the tank_mass_factor_completedesign study.

1. If necessary, click Closeto close the Analyses and Design Studies dialog box.

2. From the main toolbar, click Results to start Results mode.

3. From the Results mode main toolbar, click Result Window .

4. Select tank_mass_factor_completeand click Open.

5. Type VM_STRESSin the Name field and von Mises Stress vs. FACTORin the

Title field.

6. Verify that the Display type field is set to Graph.


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7. Click Define Measure to open the Measures dialog box.

8. Select Maximum_Stressfrom the user-defined list of measures and click OK.

9. The dialog should now appear as shown in the figure. Click OK and Showto show

the graph.

10. Examine the resulting graph. Note that your display might be slightly different,depending on which exercises you have completed from this course.

The graph demonstrates that the stress will get lower when the water mass

decreases; in other words, when the tank is not full.


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11. When you are finished reviewing the results, click File > Exit Results > Noto

exit the Result window without saving any results.

Task 9.Read the following pieces of information that pertain to dynamic time

analyses.

A dynamic time analysis comes with other options that have not beencovered in this exercise, such as the option to input the time function

as a table, use external loads, and so on. These options are covered

in a different exercise and are identical in their application to dynamictime analyses.

The options reviewed here have enabled the user to define baseexcitation, symbolic formulas using IF statements, defined measures

and demonstrated how a global sensitivity study can be used inconjunction with a dynamic analysis. Determining the equation forbase excitation using commonly known definitions was covered as

well.

When the option for Relative to is set to ground versus supports, thisonly affects displacement, velocity and acceleration measures.

Quantities such as stress are unaffected because they are computed

from the models deformation and not affected by rigid body motion.In a dynamic time analysis, Mechanica will always assume that theinitial displacement and velocity of the model is zero.

Dynamic Time analyses are effective for modeling problems withtransient loads or where the user wants to view the output in real

time or at a specific time index. Some problems however, such asthose with persistent multiple inputs across different frequencies, are

more suitable for analysis in the frequency domain, which will be

covered in a different exercise.


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1. If necessary, return to the Standard Pro/ENGINEER mode by clicking

Applications > Standard.

2. Click Save from the main toolbar and click OKto save the model.

3. Click File > Close Windowfrom the main menu.

4. Click File > Erase > Not Displayed > OKto erase the model from memory.

References:

A. Recommendations for Revision of Seismic Damping Values inRegulatory Guide 1.61, Brookhaven National Laboratory. NUREG/CR-

6919, page 5

This completes the exercise.

154 - Understanding Dynamic Time Analyses

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