introduction to mechanical shock & vibration_2011
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Shock & VibrationME518
Lesson # 1 : Introduction
Dr. Herand Bedrossian
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Overview of Shock & Vibration Shock & Vibrat ionis the study of the behavior of structures and
their responses to dynamic loading
Examples of dynamic loading: Road & traffic induced
Wind/Gust
Earthquakes
Ocean waves
Shocks and Blasts
Impact loads
Rotating machinery
Acoustics
Aerodynamics
Engine starts and stops, etc.
Almost any type of structural system may be subjected to one formor another or combinations of dynamic loading during its lifetime
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Overview of Structural Dynamics
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Review of Shock & Vibrations
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0m x c x kx
0
i tm x c x kx F e
( )m x c x kx F t
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Dynamic Modeling of Structural Components
All systems can be classified into one oftwo distinct types of mathematical
models
Continuous
A model that possesses aninf in i tenumber of degrees of
freedom (Represented by PDEs)
Discrete/Lumped-Mass Models
A model that possesses a f in i tenumber of degrees of freedom
(Represented by ODEs)
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Building Structure Represented as an
Equivalent SDOF System
( )m x c x kx F t
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Introduction to Shock & Vibration
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Examples of SDOF Systems
System 1: Simple Spring Mass Translational System
System 2: Simple Rotational System
System 3: Simple Flexural System
System 4: Simple Pendulum System
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Free Response of SDOF System
0m x kx
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0m x c x kx
Initial
Conditions
Free Response of a Damped SDOF
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Harmonic/Periodic Excitation
0
i tm x c x kx F e
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0
i t
m x c x kx F e
Forced Response of SDOF System
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Examples of Transient Loads
0F
( )F t
Step Load
Ramp Load
Impulse Load
General Load
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Transient Excitation
TransientExcitation
Transient
Response
Duhamel IntegralOr
Numerical Methods
( )m x c x kx F t
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Impulsive/Shock Loads
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Shock Excitation
ShockExcitation Response
Shock Response
Spectrum
( )m x c x kx F t
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Example of MDOF System
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Analytical Dynamic Models
1960s
Analytical models of
varying complexity used in
studying Apollo Saturn V
space vehicle dynamics(30 300 DOF)
Today : > 1,000,000
DOF
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Simple 2 DOF Forced Vibration Model
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Forced Vibration Models
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Forced Response of 2DOF System
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Forced Response of MDOF System