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Mechanical Vibration and Shock Analysis, Random Vibration

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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 Read more...

Abstract: 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 - i

Author(s): Lalanne, Christian
Series: ISTE
Edition: 3rd ed
Publisher: Wiley
Year: 2014

Language: English
Pages: 649
City: Hoboken
Tags: Механика;Теория колебаний;

Content: Cover
Title Page
Copyright
Contents
Foreword to Series
Introduction
List of Symbols
Chapter 1. Statistical Properties of a Random Process
1.1. Definitions
1.1.1. Random variable
1.1.2. Random process
1.2. Random vibration in real environments
1.3. Random vibration in laboratory tests
1.4. Methods of random vibration analysis
1.5. Distribution of instantaneous values
1.5.1. Probability density
1.5.2. Distribution function
1.6. Gaussian random process
1.7. Rayleigh distribution
1.8. Ensemble averages: through the process
1.8.1. n order average
1.8.2. Centered moments. 1.8.3. Variance1.8.4. Standard deviation
1.8.5. Autocorrelation function
1.8.6. Cross-correlation function
1.8.7. Autocovariance
1.8.8. Covariance
1.8.9. Stationarity
1.9. Temporal averages: along the process
1.9.1. Mean
1.9.2. Quadratic mean --
rms value
1.9.3. Moments of order n
1.9.4. Variance --
standard deviation
1.9.5. Skewness
1.9.6. Kurtosis
1.9.7. Crest Factor
1.9.8. Temporal autocorrelation function
1.9.9. Properties of the autocorrelation function
1.9.10. Correlation duration
1.9.11. Cross-correlation
1.9.12. Cross-correlation coefficient
1.9.13. Ergodicity. 1.10. Significance of the statistical analysis (ensemble or temporal)1.11. Stationary and pseudo-stationary signals
1.13. Sliding mean
1.14. Test of stationarity
1.14.1. The reverse arrangements test (RAT)
1.14.2. The runs test
1.15 Identification of shocks and/or signal problems
1.16. Breakdown of vibratory signal into "events": choice of signal samples
1.17. Interpretation and taking into account of environment variation
Chapter 2. Random Vibration Properties in the Frequency Domain
2.1. Fourier transform
2.2. Power spectral density
2.2.1. Need
2.2.2. Definition. 2.3. Amplitude Spectral Density2.4. Cross-power spectral density
2.5. Power spectral density of a random process
2.6. Cross-power spectral density of two processes
2.7. Relationship between the PSD and correlation function of a process
2.8. Quadspectrum --
cospectrum
2.9. Definitions
2.9.1. Broadband process
2.9.2. White noise
2.9.3. Band-limited white noise
2.9.4. Narrow band process
2.9.5. Colors of noise
2.10. Autocorrelation function of white noise
2.11. Autocorrelation function of band-limited white noise
2.12. Peak factor. 2.13. Effects of truncation of peaks of acceleration signal on the PSD2.14. Standardized PSD/density of probability analogy
2.15. Spectral density as a function of time
2.16. Sum of two random processes
2.17. Relationship between the PSD of the excitation and the response of a linear system
2.18. Relationship between the PSD of the excitation and the cross-power spectral density of the response of a linear system
2.19. Coherence function
2.20. Transfer function calculation from random vibration measurements
2.20.1. Theoretical relations
2.20.2. Presence of noise on the input.