Random Vibrations: Theory and Practice Paul H. Wirsching 1995

Description: Random Vibrations: Theory and PracticeWirsching, Paul H. Published by Wiley-Interscience, 1995 ISBN 10: 0471585793 / ISBN 13: 9780471585794 The most comprehensive text and reference available on the study of random vibrations, this book was designed for graduate students and for mechanical, structural, and aerospace engineers. Random Vibrations: Theory and Practice encompasses all the key topics, including fundamental background material, random vibration development with applications to design, and random signal analysis. The broad scope of this text makes it useful both as a clear and thorough introduction to the field and as an authoritative reference for practitioners who wish to investigate special topics.In addition to coverage of background topics in probability, statistics, and random processes, this text develops methods for analyzing and controlling random vibrations. It explains how to avoid fatigue and fracture brought on by random vibration stresses and describes how to analyze random signals obtained for field and test measurements. Detailed examples employ random signals taken from actual random sources, and an abundance of figures, tables and charts support and clarify the text. Common terms and phrasesacceleration amplitude analysis approximation assumed autocorrelation function Chapter coefficient component confidence intervals Consider correlation cross-correlation cross-correlation function cross-spectral density crossing cycles damping defined delta function denoted density estimate derivative developed discrete displacement ensemble equal to zero ergodic example expected value factor fatigue first-passage formula Fourier transform frequency response function fx(x gain function given independent input integral linear mean and variance mean-square measured method mode moment-generating function narrow-band nonstationary random process normal distribution Note parameters peak plotted probability density function probability distribution problem random process random process X(t random vibrations Rayleigh Rayleigh distribution result S-N curve sample realization shown in Figure signal spectral density estimate spectral density function square standard deviation standard normal stationary random process stress structural Sx(w t₁ temporal weighting theorem weakly stationary white noise X₁ μχ σχ In mechanical engineering, random vibration is motion which is non-deterministic, meaning that future behavior cannot be precisely predicted. The randomness is a characteristic of the excitation or input, not the mode shapes or natural frequencies. Some common examples include an automobile riding on a rough road, wave height on the water, or the load induced on an airplane wing during flight. Structural response to random vibration is usually treated using statistical or probabilistic approaches. Mathematically, random vibration is characterized as an ergodic and stationary process. A measurement of the acceleration spectral density (ASD) is the usual way to specify random vibration. The root mean square acceleration (Grms) is the square root of the area under the ASD curve in the frequency domain. The Grms value is typically used to express the overall energy of a particular random vibration event and is a statistical value used in mechanical engineering for structural design and analysis purposes. Typical random vibration in the time domainWhile the term power spectral density (PSD) is commonly used to specify a random vibration event, ASD is more appropriate when acceleration is being measured and used in structural analysis and testing. Crandall is uniformly considered as the father of random vibrations (see also books by Bolotin,[5] Elishakoff et al.[6][7][8]). Random vibration testingTest specifications can be established from real environment measurements using an ASD envelope or a fatigue damage equivalence criterion (Extreme response spectrum and Fatigue damage spectrum). Random vibration testing is one of the more common types of vibration testing services performed by vibration test labs. Some of the more common random vibration test standards are MIL-STD-810, RTCA DO-160, and IEC 60068-2-64.

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