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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


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