Random vibration
著者
書誌事項
Random vibration
（Mechanical vibration & shock / Christian Lalanne, v.3）
Penton, 2002
大学図書館所蔵 全4件
注記
Includes bibliography and index.
内容説明・目次
内容説明
The vast majority of vibrations encountered in the real environment are random. By their very nature, such vibrations are complicated. This volume describes the enabling process for simplification of the analysis required and the analysis of the signal in the frequency domain. Power spectrum density is defined, with precautions needed to be taken in its calculation described together with the processes (windowing, overlapping) needed to improve results. A further, complementary method, the analysis of statistical properties of the time signal, is described. This enables determination of the distribution law of the maxima of a random gaussian signal to be determined and simplification of calculation of fatigue damage to be made by the avoidance of the direct counting of peaks.
目次
- Chapter 1. Statistical properties of a random process Definitions
- Random vibrations in the real environment
- Random vibrations in the test laboratory
- Methods of analysis of random vibrations
- Distribution of instantaneous values
- Gaussian random process
- Rayleigh distribution
- Overall averages - 'through the process' process
- Temporal averages - 'along the process' study
- Statistical analysis (overall or temporal)
- Stationary and pseudo-stationary signals
- Summary chart of principal definitions Chapter 2. Properties of random vibrations in the field of frequencies Fourier transform
- Spectral concentration of power
- Spectral concentration of cross power. Spectral concentration of power of a process
- Spectral concentration of cross power of two processes
- Relation between the DSP and the function of correlation of a process
- Cospectrum. Quadspectre
- Definitions Autocorrelation function of white noise: Autocorrelation function of noise with limited band
- Peak factor
- Standardized analogy DSP / density of probability
- Spectral concentration as function of time
- Relation between DSP of excitation and response of linear system
- Relation between DSP of excitation and interspectral density of power of response of linear system
- Function of coherence
- Effects of truncation of peaks of acceleration signal
- Creation of a random signal of given DSP Chapter 3. Effective value of a random vibration Effective value of signal according to DSP
- Relations between DSP of acceleration, velocity and displacement
- Pictorial display of DSP
- Practical calculation of effective values of acceleration, velocity and displacement
- Cases: Periodicity of signals
- Case: periodic signal superimposed on random noise Chapter 4. Practical calculation of spectral concentration of power Calculation of DSP starting from effective value of the filtered signal
- Calculation of DSP from Fourier transform
- FFT
- Particular case of a periodic excitation
- Statistical error
- Statistical error analysis
- Recovery
- Calculation of DSP for given statistical error
- Choice of the bandwidth of the filter
- Probability so that the measured DSP lies between (a standard deviation
- statistical error of other quantities Chapter 5. Properties of the random vibrations in the field of times Averages
- Statistical properties of the instantaneous values of a random signal
- Moments
- Average frequency of DSP defined by segments of straight line
- Fourth moment of DSP defined by segments of straight line
- Generalization. Moment of order N Chapter 6. Law of distribution of maxima of random vibration Density of probability of maxima
- Average number of maxima per unit of time
- Average interval of time between two successive maxima
- Average correlation between two successive maxima
- Properties of the factor of irregularity
- Error related to the use of Rayleigh law instead of density of complete probability
- Distribution function of peaks
- Mean number of superior maxima with a given threshold (by unit of time)
- Mean number of maxima, one above a given threshold between two moments
- Average interval of time between two successive maxima
- Average number of maxima located above a level given by excursion of the signal above this threshold
- Time during which the signal is above a given value
- Probability that a maximum is positive or negative
- Density of probability of positive maximum
- Probability that a positive maximum is lower than given threshold Average number of positive maxima per unit of time
- Jump of average amplitude between two successive extremes. Chapter 7. Statistics of extreme values Density of probability of maxima greater than a given value
- Return period
- Peak expected among peaks
- Logarithmic increase
- Average maximum of peaks
- Variance of maxima
- Mode (the most probable maximum value)
- Maximum value exceeded for risk
- (Application: case of a centered normal process with narrow band
- Centered normal process with wide strip
- Asymptotic laws
- Choice of a type of analysis
- Study of the envelope of a process with narrow band Appendices **A.1. Summary: laws of probability **A.2. Analyis: 1/ath octave **A.3. Conversion of an acoustic spectrum into a spectral concentration of power **A.4. Mathematical functions **A.5. Transfer functions supplement Principal notations - Bibliography - Index
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