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Introduction to Random Vibrations, Spectral and Wavelet Analysis Third Edition

ISBN-10: 0486442748
ISBN-13: 9780486442747
Edition: 3rd 2005 (Revised)
Authors: D. E. Newland
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Book details

List price: $29.95
Edition: 3rd
Copyright year: 2005
Publisher: Dover Publications, Incorporated
Publication date: 7/26/2005
Binding: Paperback
Pages: 477
Size: 6.25" wide x 9.25" long x 1.00" tall
Weight: 1.430

Martin Gardner is the author of more than seventy books on a vast range of topics including "Did Adam & Eve Have Navels?", "Calculus Made Easy", & "The Annotated Alice". He lives in Hendersonville, North Carolina.

Preface to the first edition
Preface to the second edition
Preface to the third edition
Acknowledgements
List of symbols
Introduction to probability distributions and averages
Probability density function
Gaussian distribution
Calculation of averages
Probability distribution function
Joint probability distributions, ensemble averages
Second-order probability functions
Second-order averages
Conditional probability
Second-order Gaussian distribution
Ensemble averaging
Correlation
Autocorrelation
Cross-correlation
Fourier analysis
Fourier integral
Complex form of the Fourier transform
Spectral density
Narrow band and broad band processes
Spectral density of a derived process
Cross-spectral density
Note on the units of spectral density
Excitation - response relations for linear systems
Classical approach
Frequency response method
Impulse response method
Relationship between the frequency response and impulse response functions
Calculation of response to an arbitrary input
Transmission of random vibration
Mean level
Autocorrelation
Spectral density
Mean square response
Cross-correlation
Cross-spectral density
Probability distributions
Statistics of narrow band processes
Crossing analysis
Distribution of peaks
Frequency of maxima
Accuracy of measurements
Analogue spectrum analysis
Variance of the measurement
Analysis of finite length records
Confidence limits
Digital spectral analysis I: Discrete Fourier transforms
Discrete Fourier transforms
Fourier transforms of periodic functions
Aliasing
Calculation of spectral estimates
Digital spectral analysis II: Windows and smoothing
Relationship between linear and circular correlation
Fourier transform of a train of aperiodic functions
Basic lag and spectral windows
Smoothing spectral estimates
Extending record length by adding zeros
Summary
Practical considerations
The fast Fourier transform
Basic theory
Sample calculation
Programming flow charts
Practical value of FFT
Alternative algorithms
Pseudo random processes
Random binary process
Pseudo random binary signals
Random multi-level process
Spectrum of a multi-level process
Generation of random numbers
Synthesis of correlated noise sources
Application notes
Response of a resonant mode to broad band excitation
Fatigue and failure due to random vibration
Excitation by random surface irregularities
Simulation of random environments
Frequency response function and coherency measurements
Local spectral density calculations
Weibull distribution of peaks
Multi-dimensional spectral analysis
Two-dimensional Fourier series
Properties of the two-dimensional DFT
Spectral density of a multi-dimensional random process
Discrete spectral density and circular correlation functions for a two-dimensional random process
Two-dimensional windows
Two-dimensional smoothing
Artificial generation of a two-dimensional random process
Generation of an isotropic surface
Cross-spectral density between parallel tracks across a random surface
Response of continuous linear systems to stationary random excitation
Response to excitation applied at a point
Response to distributed excitation
Normal mode analysis
Kinetic energy of a flat plate subjected to uncorrelated random excitation
Single degree-of-freedom analogy
Discrete wavelet analysis
Basic ideas
Dilation equations
Dilation wavelets
Properties of the wavelet coefficients
Circular wavelet transforms
Discrete wavelet transforms
Properties of the DWT
Mean-square maps
Convolution by wavelets
Two-dimensional wavelet transforms
Harmonic wavelets
Discrete harmonic wavelet transform
Concluding comments
Appendices
Table of integrals
Computer programs
The Gaussian probability integral
Distribution of x[superscript 2 subscript k]
Random numbers
Distribution of reverse arrangements for a random series
Wavelet programs
Problems
Answers to problems
References

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