Parametric Random Vibration

PARAMETRIC random vibration is an applied scientific discipline that covers problems from the broad field of applied dynamics, e.g. structural dynamics, aerodynamics, naval architecture etc. The system equations are characterized by random perturbed parameters while, in many practical situations, non-linearities and random forcing terms create additional complications. Various textbooks have appeared covering the field of random vibration of time-invariant systems. This monograph, a state of the art presentation of parametric random vibration, based on an enormous number of published papers and reports, is a great credit to the author. In the first chapter the reader is introduced to the basic definitions of parametric and autoparametric instabilities, chaotic motion, pseudo-random excitation and crypto-deter-ministic systems and a brief review of parametric random vibration is given. In random vibrations, the emphasis is on the response and stability of systems under wide band random parametric excitations. Unfortunately system equations with physical wide band noise excitation are very difficult to handle, therefore physical Gaussian wide band noise is often replaced by idealized white noise, or the wide band noise is generated by a shaping filter driven by white noise. This is usually the point where many engineers get lost. They are referred to books on stochastic processes and stochastic differential equations and are encouraged to go into theories which are embedded in mathematical abstraction. For these engineers the root of all evil (which is at the same time a source of pleasure for many mathematicians) is the unbounded variation of the Brownian motion, which has white noise as its derivative, in a formal sense. For these processes a new stochastic calculus is needed. In Chapters 2-4 the author provides the necessary tools for deriving response statistical functions and techniques for examining stochastic parameter stability, as required in later chapters. The author has chosen an engineering approach without mathematical abstraction, which implies that some important theorems are verified in a heuristic way, while many others are only mentioned. The result is a nice reference frame for readers with a reasonable background in stochastic processes and stochastic differential equations. Readers without this background will certainly get into trouble, for example, when reading the definitions of random variables and random processes. Obviously, the author could not resist the temptation to give some flavour of mathematical abstraction by introducing a random variable as a function of a sample space f~, which is confusing in the context it is used. …