An Introduction to Random Vibrations, Spectral & Wavelet Analysis Third Edition

by Newland, D. E.

• ISBN13: 9780486442747
• ISBN10: 0486442748
• Edition: 3rd
• Format: Paperback
• Copyright: 2005-07-26
• 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	ix
Preface to the second edition	xi
Preface to the third edition	xii
Acknowledgements	xiv
List of symbols	xvii
Introduction to probability distributions and averages	1	(11)
Probability density function	2	(5)
Gaussian distribution	7	(1)
Calculation of averages	7	(3)
Probability distribution function	10	(2)
Joint probability distributions, ensemble averages	12	(9)
Second-order probability functions	12	(2)
Second-order averages	14	(3)
Conditional probability	17	(1)
Second-order Gaussian distribution	18	(1)
Ensemble averaging	19	(2)
Correlation	21	(12)
Autocorrelation	25	(4)
Cross-correlation	29	(4)
Fourier analysis	33	(8)
Fourier integral	35	(3)
Complex form of the Fourier transform	38	(3)
Spectral density	41	(12)
Narrow band and broad band processes	44	(2)
Spectral density of a derived process	46	(2)
Cross-spectral density	48	(3)
Note on the units of spectral density	51	(2)
Excitation - response relations for linear systems	53	(14)
Classical approach	54	(1)
Frequency response method	55	(3)
Impulse response method	58	(2)
Relationship between the frequency response and impulse response functions	60	(2)
Calculation of response to an arbitrary input	62	(5)
Transmission of random vibration	67	(15)
Mean level	68	(1)
Autocorrelation	69	(2)
Spectral density	71	(2)
Mean square response	73	(4)
Cross-correlation	77	(1)
Cross-spectral density	78	(1)
Probability distributions	79	(3)
Statistics of narrow band processes	82	(13)
Crossing analysis	85	(5)
Distribution of peaks	90	(2)
Frequency of maxima	92	(3)
Accuracy of measurements	95	(18)
Analogue spectrum analysis	96	(1)
Variance of the measurement	97	(6)
Analysis of finite length records	103	(5)
Confidence limits	108	(5)
Digital spectral analysis I: Discrete Fourier transforms	113	(12)
Discrete Fourier transforms	114	(2)
Fourier transforms of periodic functions	116	(2)
Aliasing	118	(2)
Calculation of spectral estimates	120	(5)
Digital spectral analysis II: Windows and smoothing	125	(25)
Relationship between linear and circular correlation	126	(3)
Fourier transform of a train of aperiodic functions	129	(2)
Basic lag and spectral windows	131	(6)
Smoothing spectral estimates	137	(2)
Extending record length by adding zeros	139	(3)
Summary	142	(4)
Practical considerations	146	(4)
The fast Fourier transform	150	(17)
Basic theory	150	(2)
Sample calculation	152	(3)
Programming flow charts	155	(7)
Practical value of FFT	162	(3)
Alternative algorithms	165	(2)
Pseudo random processes	167	(22)
Random binary process	168	(4)
Pseudo random binary signals	172	(3)
Random multi-level process	175	(4)
Spectrum of a multi-level process	179	(4)
Generation of random numbers	183	(2)
Synthesis of correlated noise sources	185	(4)
Application notes	189	(36)
Response of a resonant mode to broad band excitation	189	(2)
Fatigue and failure due to random vibration	191	(5)
Excitation by random surface irregularities	196	(5)
Simulation of random environments	201	(5)
Frequency response function and coherency measurements	206	(12)
Local spectral density calculations	218	(1)
Weibull distribution of peaks	219	(6)
Multi-dimensional spectral analysis	225	(43)
Two-dimensional Fourier series	225	(4)
Properties of the two-dimensional DFT	229	(4)
Spectral density of a multi-dimensional random process	233	(6)
Discrete spectral density and circular correlation functions for a two-dimensional random process	239	(6)
Two-dimensional windows	245	(9)
Two-dimensional smoothing	254	(2)
Artificial generation of a two-dimensional random process	256	(2)
Generation of an isotropic surface	258	(5)
Cross-spectral density between parallel tracks across a random surface	263	(5)
Response of continuous linear systems to stationary random excitation	268	(27)
Response to excitation applied at a point	268	(9)
Response to distributed excitation	277	(3)
Normal mode analysis	280	(10)
Kinetic energy of a flat plate subjected to uncorrelated random excitation	290	(2)
Single degree-of-freedom analogy	292	(3)
Discrete wavelet analysis	295	(106)
Basic ideas	295	(5)
Dilation equations	300	(3)
Dilation wavelets	303	(4)
Properties of the wavelet coefficients	307	(15)
Circular wavelet transforms	322	(4)
Discrete wavelet transforms	326	(13)
Properties of the DWT	339	(9)
Mean-square maps	348	(5)
Convolution by wavelets	353	(2)
Two-dimensional wavelet transforms	355	(4)
Harmonic wavelets	359	(5)
Discrete harmonic wavelet transform	364	(6)
Concluding comments	370	(1)
Appendices
Appendix 1 Table of integrals	371	(2)
Appendix 2 Computer programs	373	(6)
Appendix 3 The Gaussian probability integral	379	(2)
Appendix 4 Distribution of Χ2k	381	(2)
Appendix 5 Random numbers	383	(2)
Appendix 6 Distribution of reverse arrangements for a random series	385	(2)
Appendix 7 Wavelet programs	387	(14)
Problems	401	(56)
Answers to problems	457	(8)
References	465	(7)
Index	472