Lecture 1 Introduction [vibration]
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Transcript of Lecture 1 Introduction [vibration]
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MBB4023 Vibration
Semester May 2011
Lecture 1
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What is vibration?
Vibration = Any motion that repeats itself afteran interval of time is called vibration oroscillation.
For example:1.The swinging of a pendulum.2.The motion of a plucked string.
The study of vibration deals with the study of oscillatory motions of bodies and the
forces associated with them.
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Basic component of vibration
Vibratory System consists of:1) spring or elasticity - a means for storing potential energy
2) mass or inertia - a means for storing kinetic energy
3) Damper - a means by which the energy is gradually lost
Involves transfer of potential energy to kinetic
energy and kinetic energy to potential energy alternately.
Note: If the systems is damped, some energy is dissipated in
each cycle of vibration which eventually all of it will disappear.
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Basic concept of vibration
At point 1: KE = 0PE = mgl(1 cos )
At point 2: PE = 0KE = Max
At point 3: KE = 0PE = PE @ 1
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1. Free Vibration:
A system is left to vibrate on its own after an initial disturbance and
no external force acts on the system. E.g. simple pendulum
2. Forced Vibration:
A system that is subjected to a repeating external force. E.g.
oscillation arises from diesel engines
- Resonanceoccurs when the frequency of the
external force coincides with one of the natural
frequencies of the system
Classification of Vibration
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1. Undamped Vibration:
When noenergy is lost or dissipated in friction or other resistance
during oscillations
2. Damped Vibration:
When anyenergy is lost or dissipated in friction or other resistance
during oscillations
3. Linear Vibration:
When allbasic components of a vibratory system, i.e. the spring, the
massand the damper behave linearly
Classification of Vibration
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Classification of Vibration
Nonlinear Vibration:
If anyof the components behave nonlinearly. Most vibration
systems behave nonlinearly with increasing amplitude.
Deterministic Vibration:
If the value or magnitude of the excitation (force or motion)
acting on a vibratory system is known at any given time
Nondeterministic or random Vibration:
When the value of the excitation at a given time cannot be
predicted. The response is also random and can be described
only in terms of statistical quantities.
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Step 1: Mathematical Modeling
Transform the physical system to model using gradual
refinement method.
Represent all important vibration components of the
system for the purpose of deriving the mathematical
equations governing the behavior of the system.
Vibration Analysis Procedure
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Step 2: Derivation of Governing Equations
Using the principles of dynamics and free body diagram, derive the
equations that describe the vibration of the system.
Equations are in the form of Ordinary Differential Equation (ODE) for the
discrete system and Partial Differential Equation (PDE) for a
continuous systems.
Methods:
1. Newtons 2nd Law of Motion
2. DAlemberts Principle
3. Energy method.
Vibration Analysis Procedure
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Step 3: Solution of the Governing Equations
Purpose - To determine the response of the vibrating system interms of vibration amplitude, frequency, phase angle, speed,
acceleration etc.
Methods used:Standard methods of solving differential equations.Laplace tranform.
Matrices.Numerical method.
Vibration Analysis Procedure
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Step 4: Interpretation of the Results
The solution provides the data required for vibration
interpretation. If analysis is done during the design stage, thevibration analysis result may cause some design change.
Vibration Analysis Procedure
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Definition and Terminology
Cycle - The movement of a vibrating body from its equilibriumposition to its extreme position in one direction back to its
equilibrium position and then to its extreme position in other
direction and back to its equilibrium position.
Amplitude - The maximum displacement of a vibrating body from
its equilibrium position. The unit is mm.
Period, - Time taken to complete one cycle of motion. Unit is
sec.
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Definition and Terminology
Frequency, f - The number of cycle per unit time, Hz. Itis also a reciprocal of period.
Phase Angle, - Angle between two oscillation, rad.
Natural frequency - Frequency with which the physical
system oscillate after initial disturbance without external
force applied, n and the unit is rad/sec.
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Definition and Terminology
Degree of Freedom
Minimum number of independent coordinates required to
determine the positions of all parts of a system at any instant oftime.
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Examples of single degree-of-freedom systems:
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