An Introduction to Random Vibrations, Spectral & Wavelet Analysis

by D. E. Newland

• ISBN13: 9780470221532
• ISBN10: 0470221534
• Format: Nonspecific Binding
• Copyright: 2012-04-03
• Publisher: Dover Publications

Summary

One of the first engineering books to cover wavelet analysis, this classic text describes and illustrates basic theory, with a detailed explanation of the workings of discrete wavelet transforms. Computer algorithms are explained and supported by examples and a set of problems, and an appendix lists ten computer programs for calculating and displaying wavelet transforms.

Table of Contents

Preface to the first edition	p. ix
Preface to the second edition	p. xi
Preface to the third edition	p. xii
Acknowledgements	p. xiv
List of symbols	p. xvii
Introduction to probability distributions and averages	p. 1
Probability density function	p. 2
Gaussian distribution	p. 7
Calculation of averages	p. 7
Probability distribution function	p. 10
Joint probability distributions, ensemble averages	p. 12
Second-order probability functions	p. 12
Second-order averages	p. 14
Conditional probability	p. 17
Second-order Gaussian distribution	p. 18
Ensemble averaging	p. 19
Correlation	p. 21
Autocorrelation	p. 25
Cross-correlation	p. 29
Fourier analysis	p. 33
Fourier integral	p. 35
Complex form of the Fourier transform	p. 38
Spectral density	p. 41
Narrow band and broad band processes	p. 44
Spectral density of a derived process	p. 46
Cross-spectral density	p. 48
Note on the units of spectral density	p. 51
Excitation - response relations for linear systems	p. 53
Classical approach	p. 54
Frequency response method	p. 55
Impulse response method	p. 58
Relationship between the frequency response and impulse response functions	p. 60
Calculation of response to an arbitrary input	p. 62
Transmission of random vibration	p. 67
Mean level	p. 68
Autocorrelation	p. 69
Spectral density	p. 71
Mean square response	p. 73
Cross-correlation	p. 77
Cross-spectral density	p. 78
Probability distributions	p. 79
Statistics of narrow band processes	p. 82
Crossing analysis	p. 85
Distribution of peaks	p. 90
Frequency of maxima	p. 92
Accuracy of measurements	p. 95
Analogue spectrum analysis	p. 96
Variance of the measurement	p. 97
Analysis of finite length records	p. 103
Confidence limits	p. 108
Digital spectral analysis I: Discrete Fourier transforms	p. 113
Discrete Fourier transforms	p. 114
Fourier transforms of periodic functions	p. 116
Aliasing	p. 118
Calculation of spectral estimates	p. 120
Digital spectral analysis II: Windows and smoothing	p. 125
Relationship between linear and circular correlation	p. 126
Fourier transform of a train of aperiodic functions	p. 129
Basic lag and spectral windows	p. 131
Smoothing spectral estimates	p. 137
Extending record length by adding zeros	p. 139
Summary	p. 142
Practical considerations	p. 146
The fast Fourier transform	p. 150
Basic theory	p. 150
Sample calculation	p. 152
Programming flow charts	p. 155
Practical value of FFT	p. 162
Alternative algorithms	p. 165
Pseudo random processes	p. 167
Random binary process	p. 168
Pseudo random binary signals	p. 172
Random multi-level process	p. 175
Spectrum of a multi-level process	p. 179
Generation of random numbers	p. 183
Synthesis of correlated noise sources	p. 185
Application notes	p. 189
Response of a resonant mode to broad band excitation	p. 189
Fatigue and failure due to random vibration	p. 191
Excitation by random surface irregularities	p. 196
Simulation of random environments	p. 201
Frequency response function and coherency measurements	p. 206
Local spectral density calculations	p. 218
Weibull distribution of peaks	p. 219
Multi-dimensional spectral analysis	p. 225
Two-dimensional Fourier series	p. 225
Properties of the two-dimensional DFT	p. 229
Spectral density of a multi-dimensional random process	p. 233
Discrete spectral density and circular correlation functions for a two-dimensional random process	p. 239
Two-dimensional windows	p. 245
Two-dimensional smoothing	p. 254
Artificial generation of a two-dimensional random process	p. 256
Generation of an isotropic surface	p. 258
Cross-spectral density between parallel tracks across a random surface	p. 263
Response of continuous linear systems to stationary random excitation	p. 268
Response to excitation applied at a point	p. 268
Response to distributed excitation	p. 277
Normal mode analysis	p. 280
Kinetic energy of a flat plate subjected to uncorrelated random excitation	p. 290
Single degree-of-freedom analogy	p. 292
Discrete wavelet analysis	p. 295
Basic ideas	p. 295
Dilation equations	p. 300
Dilation wavelets	p. 303
Properties of the wavelet coefficients	p. 307
Circular wavelet transforms	p. 322
Discrete wavelet transforms	p. 326
Properties of the DWT	p. 339
Mean-square maps	p. 348
Convolution by wavelets	p. 353
Two-dimensional wavelet transforms	p. 355
Harmonic wavelets	p. 359
Discrete harmonic wavelet transform	p. 364
Concluding comments	p. 370
Appendices
Table of integrals	p. 371
Computer programs	p. 373
The Gaussian probability integral	p. 379
Distribution of x[superscript 2 subscript k]	p. 381
Random numbers	p. 383
Distribution of reverse arrangements for a random series	p. 385
Wavelet programs	p. 387
Problems	p. 401
Answers to problems	p. 457
References	p. 465
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