Coherent and systematic, this text explores the behavior of linear
and nonlinear dynamical systems subject to parametric random
vibrations, by means of the theory of stochastic processes,
stochastic differential equations, and applied dynamics. It
distills decades of research to formulate new stochastic stability
theorems and analytical techniques for determining the random
response of nonlinear systems. In addition, it resolves
controversies and paradoxes related to the interpretation of
certain stochastic processes and the use of analytical
methods.
After a brief overview of parametric vibration and its subclasses,
the text surveys the fundamental concepts of random processes and
their calculus rules, emphasizing the main elements necessary for
the analysis of parametric vibration problems. Subsequent chapters
address the stability and response analyses of linear and nonlinear
systems with random coefficients. The final chapter presents an
extensive compilation of experimental results from the literature
of the field.
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