Parametric Random Vibration

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.

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 is a systematic presentation of several classes of analytical techniques in non-linear random vibration. The book also includes a concise treatment of Markovian and non-Markovian solutions of non-linear differential equations.

Many problems of engineering interest involve linear dynamic systems with random loading and random properties which may or may not vary in time; these systems are said to undergo random parametric vibration. Reliability methods, and other approaches using a full probabilistic description of the problem, are not capable of handling time dependent random properties unless the variation can be expressed in terms of a few random variables. On the other hand, response statistics of systems in random parametric vibration are often useful to designers and analysts. However, current approaches which could be used to compute these response statistics are slow, inaccurate, or unfeasible. This work offers a new statistical approach to obtain response statistics of linear dynamic systems in random parametric vibration. This approach, called the random matrix method, is a distant cousin to an existing Taylor-expansion perturbation approach, but is faster, more efficient, more accurate, and more stochastically stable; it is also superior to Monte Carlo approaches. The random matrix method first discretizes the problem, so that the equations of motion can be expressed as a random matrix equation. Statistics of an inverse matrix are obtained using a Neumann expansion, and response statistics can be obtained from the statistics of the load and the inverse matrix. This method is capable of analysis in either the frequency or time domain and can handle both stationary and nonstationary load and properties. Three different problems with time-dependent properties will be analyzed by the random matrix method and by Monte Carlo techniques for comparison. First, response statistics will be obtained for a generic single degree of freedom oscillator with stationary stiffness and load. Then, the ride comfort of a car, a multiple degree of freedom system with stationary tire stiffness, will be investigated. Finally, a fatigue damage analysis of a light aircraft's landing gear will be conducted; note that this problem involves a single degree of freedom system with nonstationary random damping and load. In all cases, the magnitude of random property effects on response will be examined, to see if random properties need to be taken into account for these systems.

The subject of random vibrations of elastic systems has gained, over the past decades, great importance, specifically due to its relevance to technical problems in hydro- and aero-mechanics. Such problems involve aircraft, rockets and oil-drilling platforms; elastic vibrations of structures caused by acoustic radiation of a jet stream and by seismic disturbances must also be included. Appli cations of the theory of random vibrations are indeed numerous and the development of this theory poses a challenge to mathematicians, mechanicists and engineers. Therefore, a book on random vibrations by a leading authority such as Dr. V.V. Bolotin must be very welcome to anybody working in this field. It is not surprising that efforts were soon made to have the book translated into English. With pleasure I acknowledge the co-operation of the very competent translater, I Shenkman; of Mrs. C. Jones, who typeJ the first draft; and of Th. Brunsting, P. Keskikiikonen and R. Piche, who read it and suggested where required, corrections and changes. I express my gratitude to Martinus Nijhoff Publishers BV for entrust ing me with the task of editing the English translation, and to F.J. van Drunen, publishers of N. Nijhoff Publishers BV, who so kindly supported my endeavours. Special acknowledgement is due to Mrs. L. Strouth, Solid Mechanics Division, University of Waterloo, for her competent and efficient preparation of the final manuscript.

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.

Introduction to Random Vibrations presents a brief review of probability theory, a concise treatment of random variables and random processes, and a comprehensive exposition of the theory of random vibrations.

Annotation This text synthesizes a wealth of useful information for analyzing random vibrations and structures into one coherent body of knowledge. It takes a practical yet progressive look at two major fields related to random analysis: linear and geometrically nonlinear structures, and the behavior of random structures under random loads. System harmonics and oscillations, random functions, and the theory of random vibration are covered extensively throughout the text, which includes innovative methods for calculating the probability of failure for dynamic systems. Simplified examples demonstrate applications for daily use and present new approaches to failure analysis. The author evaluates the use of random process methods for the stochastic analysis of crack growth in detail, providing a better description of failures resulting from crack propagation. For young engineers, the book touches on finite element programs such as ANSYS and the probabilistic analysis program PROBAN, facilitating solutions to more complex problems. It also illustrates how to write a FORTRAN program to build a numerical procedure suitable for the design needs.