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Mechanical Vibration and Shock Analysis, Second Edition
Volume 3: Random Vibration
The vast majority of vibrations encountered in a real-world environment are random in nature. Such vibrations are intrinsically complicated, but this volume describes a process enabling the simplification of the analysis required, and the analysis of the signal in the frequency domain. Power spectrum density is also defined, with the requisite precautions to be taken in its calculation described together with the processes (windowing, overlapping) necessary for improved results. A further complementary method, the analysis of statistical properties of the time signal, is described. This enables the distribution law of the maxima of a random Gaussian signal to be determined and simplifies calculation of fatigue damage to be made by the avoidance of the direct counting of peaks.
The Mechanical Vibration and Shock Analysis five-volume series has been written with both the professional engineer and the academic in mind. Christian Lalanne explores every aspect of vibration and shock, two fundamental and extremely significant areas of mechanical engineering, from both a theoretical and practical point of view. The five volumes cover all the necessary issues in this area of mechanical engineering. The theoretical analyses are placed in the context of both the real world and the laboratory, which is essential for the development of specifications.
Mechanical Vibration & Shock, Volume 3, Random Vibration, 2nd Edition.
1. Statistical properties of a random process.
2. Properties of random vibration in the frequency domain.
3. RMS value of random vibration.
4. Practical calculation of power spectral density.
5. Statistical properties of random vibration in the time domain.
6. Probability distribution of maxima of random vibration.
7. Statistics of extreme values.
8. Response of a one-degree-of-freedom linear system to random vibration.
9. Characteristics of the response of a one-degree-of-freedom linear system to random vibration.
10. First passage at a given level of response of a one-degree-of-freedom linear system to a random vibration.