Random Vibration

The most comprehensive text and reference available on the study of random vibrations, this book was designed for graduate students and mechanical, structural, and aerospace engineers. In addition to coverage of background topics in probability, statistics, and random processes, it develops methods for analyzing and controlling random vibrations. 1995 edition.

The topic of Random Vibrations is the behavior of structural and mechanical systems when they are subjected to unpredictable, or random, vibrations. These vibrations may arise from natural phenomena such as earthquakes or wind, or from human-controlled causes such as the stresses placed on aircraft at takeoff and landing. Study and mastery of this topic enables engineers to design and maintain structures capable of withstanding random vibrations, thereby protecting human life. Random Vibrations will lead readers in a user-friendly fashion to a thorough understanding of vibrations of linear and nonlinear systems that undergo stochastic-random-excitation. Provides over 150 worked out example problems and, along with over 225 exercises, illustrates concepts with true-to-life engineering design problems Offers intuitive explanations of concepts within a context of mathematical rigor and relatively advanced analysis techniques. Essential for self-study by practicing engineers, and for instruction in the classroom.

I became interested in Random Vibration during the preparation of my PhD dissertation, which was concerned with the seismic response of nuclear reactor cores. I was initiated into this field through the cla.ssical books by Y.K.Lin, S.H.Crandall and a few others. After the completion of my PhD, in 1981, my supervisor M.Gera.din encouraged me to prepare a course in Random Vibration for fourth and fifth year students in Aeronautics, at the University of Liege. There was at the time very little material available in French on that subject. A first draft was produced during 1983 and 1984 and revised in 1986. These notes were published by the Presses Poly techniques et Universitaires Romandes (Lausanne, Suisse) in 1990. When Kluwer decided to publish an English translation ofthe book in 1992, I had to choose between letting Kluwer translate the French text in-extenso or doing it myself, which would allow me to carry out a sustantial revision of the book. I took the second option and decided to rewrite or delete some of the original text and include new material, based on my personal experience, or reflecting recent technical advances. Chapter 6, devoted to the response of multi degree offreedom structures, has been completely rewritten, and Chapter 11 on random fatigue is entirely new. The computer programs which have been developed in parallel with these chapters have been incorporated in the general purpose finite element software SAMCEF, developed at the University of Liege.

Random Vibration in Mechanical Systems focuses on the fundamental facts and theories of random vibration in a form particularly applicable to mechanical engineers. The book first offers information on the characterization and transmission of random vibration. Discussions focus on the normal or Gaussian random process; excitation-response relations for stationary random processes; response of a single-degree-of-freedom system to stationary random excitation; wide-band and narrow-band random processes; and frequency decomposition of stationary random processes. The text then examines failure due to random vibration, including failure due to first excursion up to a certain level; fatigue failure due to a stationary narrow-band random stress process; failure due to an accumulation of damage; failure due to response remaining above a certain level for too great a fraction of the time; and failure mechanisms. The manuscript is a vital reference for mechanical engineers and researchers interested in random vibration in mechanical systems.

This self-contained volume explains the general method of statistical linearization and its use in solving random vibration problems. Numerous examples show advanced undergraduate and graduate students many practical applications. 1990 edition.

This systematic treatment examines linear and nonlinear dynamical systems subject to parametric random vibrations. It formulates stochastic stability theorems and analytical techniques for determining random response of nonlinear systems. 1985 edition.

The vast majority of vibrations Encountered in the real Environment are random in nature. Such vibrations are intrinsically complicated, and 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 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.

This book discusses the theory, applicability and numerous examples of Miles’ equation in detail. Random vibration is one of the main design drivers in the context of the design, development and verification of spacecraft structures, instruments, equipment, etc, and Miles’ equation provides a valuable tool for solving random vibration problems. It allows mechanical engineers to make rapid preliminary random response predictions when the (complex) structure is exposed to mechanical and acoustical loads. The book includes appendices to support the theory and applications in the main chapters.

Focuses on the Basic Methodologies Needed to Handle Random ProcessesAfter determining that most textbooks on random vibrations are mathematically intensive and often too difficult for students to fully digest in a single course, the authors of Random Vibration: Mechanical, Structural, and Earthquake Engineering Applications decided to revise the cu