In the first part of this Chapter. a variety of techniques for predicting nonlinear dynamic system response to random excitation are discussed. These include methods based on modelling the response as a continuous Markov process. leading to diffusion equations, statistical linearization, the method of equivalent nonlinear equations and closure methods. Special attention is paid to the stochastic averaging method, which is a combination of an averaging technique and Markov process modelling. It is shown that the stochastic averaging method is particularly useful for estimating the “first-passage” probability that the system response stays within a safe domain, within a specified period of Lime. Results obtained by this method are presented for oscillators with both linear and nonlinear damping and restoring terms. An alternative technique for solving the first-passage problem, based on the computation of level crossing statistics. is also described: this is especially useful in more general situations, where the stochastic averaging is inapplicable.


Nonlinear Oscillator Random Vibration Linear Oscillator Random Excitation Stochastic Average 
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Copyright information

© Springer-Verlag Wien 1991

Authors and Affiliations

  • J. R. Roberts
    • 1
  1. 1.University of SussexSussexUK

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