Mechanical Vibration and Shock Analysis, Random Vibration (eBook)

Christian Lalanne (Autor)

eBook Download: PDF | EPUB

2014 | 1. Auflage
649 Seiten
Wiley (Verlag)
978-1-118-93117-2 (ISBN)

Infos

The vast majority of vibrations encountered in the real environment are random in nature. Such vibrations are intrinsically complicated and this volume describes the process that enables us to simplify the required analysis, along with the analysis of the signal in the frequency domain.
The power spectrum density is also defined, together with the requisite precautions to be taken in its calculations as well as the processes (windowing, overlapping) necessary to obtain improved results.
An additional complementary method – the analysis of statistical properties of the time signal – is also described. This enables the distribution law of the maxima of a random Gaussian signal to be determined and simplifies the calculation of fatigue damage by avoiding direct peak counting.

Autor

Christian Lalanne is a Consultant Engineer who previously worked as an expert at the French Atomic Energy Authority and who has specialized in the study of vibration and shock for more than 40 years. He has been associated with the new methods of drafting testing specifications and associated informatic tools.

Inhalt

Chapter 1. Statistical Properties of a Random Process

Chapter 2. Random Vibration Properties in the Frequency Domain

Chapter 3. Rms Value of Random Vibration

Chapter 4. Practical Calculation of the Power Spectral Density

Chapter 5. Statistical Properties of Random Vibration in the Time Domain

Chapter 6. Probability Distribution of Maxima of Random Vibration

Chapter 7. Statistics of Extreme Values

Chapter 8. Response of a One-Degree-of-Freedom Linear System to Random Vibration

Chapter 9. Characteristics of the Response of a One-Degree-of-Freedom Linear System to Random Vibration

Chapter 10. First Passage at a Given Level of Response of a One-Degree-of-Freedom Linear System to a Random Vibration

Textauszug

List of Symbols

The list below gives the most frequent definition of the main symbols used in this book. Some of the symbols can have another meaning which will be defined in the text to avoid any confusion.

a	Threshold value of ℓ(t) or maximum of ℓ(t)

A	Maximum of A (t)

A(t)	Envelope of a signal

b

Exponent

c	Viscous damping constant

e(t)	Narrow band white noise

E()	Expectation of…

E1( )

First definition of error function

E2( )

Second definition of error function

Erf	Error function

E( )	Expected function of …

f	Frequency of excitation

fsamp.

Sampling frequency

fmax	Maximum frequency

f0	Natural frequency

g	Acceleration due to gravity

G	Particular value of power spectral density

G( )	Power spectral density for 0 ≤ f ≤ ∞

Measured value of G( )

Gℓu( )

Cross-power spectral density

h	Interval (f/f0) or f2/f1

h(t)	Impulse response

H( )	Transfer function

i

k

Stiffness

K	Number of subsamples

ℓ	Value of ℓ(t)

Mean value of ℓ(t)

Average maximum of Np peaks

ℓrms	Rms value of ℓ(t)

Rms value of

ℓ(t)	Generalized excitation (displacement)

First derivative of ℓ(t)

Second derivative of ℓ(t)

L	Given value of ℓ(t)

Lrms	Rms value of filtered signal

L(Ω)	Fourier transform of ℓ(t)

Fourier transform of

m

Mean

M	Number of points of PSD

Ma	Average number of maxima which exceeds threshold per unit time

Mn	Moment of order n

n	Order of moment or number of degrees of freedom

na	Average number of crossings of threshold a per unit time

Average number of crossings of threshold a with positive slope per unit time

n0	Average number of zero-crossings per unit time

Average number of zero-crossings with positive slope per second (average frequency)

Average number of maxima per unit time

N	Number of curves or Number of points of signal or Numbers of dB

Np	Number of peaks

Average number of crossings of threshold a with positive slope for given length of time

Average number of zero-crossings with positive slope for given length of time

Average number of positive maxima for given length of time

p( )	Probability density

pN ( )

Probability density of largest maximum over given duration

P	Probability

PSD	Power spectral density

q

qE

Probability that a maximum is positive

Probability that a maximum is negative

q( )	Probability density of maxima of ℓ(t)

q(θ)	Reduced response

First derivative of q(θ)

Second derivative of q(θ)

Q	Q factor (quality factor)

Q( )	Distribution function of maxima of ℓ(t)

Q(u)	Probability that a maximum is higher than a given threshold

r	Irregularity factor

rms	Root mean square (value)

r(t)	Temporal window

R	Slope in dB/octave or Ratio of the number of minima to the number of maxima

RE( )

Auto-correlation function of envelope

Rℓu	Cross-correlation function between ℓ(t) and u(t)

R(f)	Fourier transform of r(t)

R(t)	Envelope of maxima of u(t)

First derivative of R(t)

R(τ)	Auto-correlation function

s	Standard deviation

S0	Value of constant PSD

S( )	Power spectral density for –∞ ≤ f ≤ +∞

t

Time

T	Duration of sample of signal or duration of vibration

Ta	Average time between two successive maxima

u	Ratio of threshold a to rms value ℓrms of ℓ(t)

u0	Initial value of u(t)

Initial value of

Average of highest peaks

urms	Rms value of u(t)

Rms value of

Rms value of

u(t)	Generalized response

First derivative of u(t)

Second derivative of u(t)

v	Ratio a/urms

vrms	Rms value of

xrms	Rms value of x(t)

Absolute acceleration of base of one-degree-of-freedom system

Rms value of

Maximum value of

yrms	Rms value of y(t)

Rms value of

Rms value of

zrms	Rms value of z(t)

Rms value of

Rms value of

α	Time-constant of the probability density of the first passage of a threshold or Risk of up-crossing or

β	2 (1 – 2 ξ2)

Variable of chi-square with n degrees of freedom

δt

Time step

δ( )	Dirac delta function

Δτ	Effective time interval

Δf	Frequency interval between half-power points or frequency step of the PSD

ΔF	Bandwidth of analysis filter

Δℓ	Interval of amplitude of ℓ(t)

Δt	Time interval

ε	Statistical error or Euler’s constant (0.57721566490…)

γ ℓu	Coherence function between ℓ(t) and...

Produkt-Details

• Erscheint lt. Verlag: 16.4.2014
• Sprache: englisch
• Themenwelt: Naturwissenschaften ► Physik / Astronomie ► Mechanik
• Themenwelt: Technik ► Maschinenbau
• Schlagworte: Festkörpermechanik • Festkörpermechanik • Maschinenbau • mechanical engineering • solid mechanics
• ISBN-10: 1-118-93117-3 / 1118931173
• ISBN-13: 978-1-118-93117-2 / 9781118931172