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Random Vibration and Mechanical Shock

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Handbook of Experimental Structural Dynamics

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Abstract

All physical systems are exposed to structural dynamic environments, including random vibration or mechanical shock, or both. These environments can cause structural or component failure. The capability to analyze dynamic response is critical not only for purposes of response prediction and design, but also for specification of random vibration and shock tests. This chapter develops the ideas and the mathematics underlying the structural dynamics of linear single-degree-of-freedom and multiple-degree-of-freedom structures, random processes, random vibration, mechanical shock, random vibration testing, and mechanical shock testing. Examples are provided and many recommendations are given for the performance of random vibration and shock tests.

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Abbreviations

a :

Acceleration

A :

Amplitude, Fourier transform of acceleration

Bw :

Bandwidth

c :

Viscous damping coefficient

d :

Displacement

Db :

Decibels

D f :

RMS duration of a function of frequency

D t :

RMS duration of a function of time

e :

Estimation error

E :

Energy of a shock

E [∙]:

Expectation

f :

Frequency (in Hertz), a function

\( \hat{g} \) :

One-sided spectral density estimator

G :

One-sided spectral density

h :

Impulse response function

H :

Frequency response function

k :

Stiffness coefficient

m :

Mass

m i :

A temporal moment

M :

Number of modes retained in modal analysis

N :

Number of averages used to form spectral density estimate

q :

Force

Q :

Fourier transform of q

RMS :

Root mean square

S :

Shock response spectrum

S r :

Sample rate

v :

Velocity

x :

Absolute displacement

X :

Fourier transform of x

y :

A function

Y :

Fourier transform of y

z :

A function

Z :

Fourier transform of z

{X(t)}:

Random process

x b :

Base excitation

z :

Relative displacement

γ :

Modal coordinates

γ 2 :

Coherence

Γ :

Fourier transform of γ

ζ :

Damping factor, A decay rate

θ :

Fourier transform of force

ξ :

Fourier transform of displacement

μ :

Mean

φ :

Matrix of mode shapes

ω :

Frequency (in radians/second)

ω n :

Natural frequency (in radians/second)

ω d :

Damped natural frequency (in radians/second)

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Author information

Authors and Affiliations

  1. Thomas Paez Consulting, Albuquerque, NM, USA

    Thomas L. Paez, Norman F. Hunter & David O. Smallwood

Authors
  1. Thomas L. Paez
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  2. Norman F. Hunter
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  3. David O. Smallwood
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Editor information

Editors and Affiliations

  1. University of Cincinnati, Cincinnati, OH, USA

    Randall Allemang

  2. Mechanical Engineering, University of Massachusetts Lowell, Lowell, MA, USA

    Peter Avitabile

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Paez, T.L., Hunter, N.F., Smallwood, D.O. (2020). Random Vibration and Mechanical Shock. In: Allemang, R., Avitabile, P. (eds) Handbook of Experimental Structural Dynamics. Springer, New York, NY. https://doi.org/10.1007/978-1-4939-6503-8_9-1

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  • DOI: https://doi.org/10.1007/978-1-4939-6503-8_9-1

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  • Publisher Name: Springer, New York, NY

  • Print ISBN: 978-1-4939-6503-8

  • Online ISBN: 978-1-4939-6503-8

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