Nonlinear Dynamics

, Volume 6, Issue 2, pp 163–177 | Cite as

Nonlinearly damped systems under simultaneous broad-band and harmonic excitations

  • G. O. Cai
  • Y. K. Lin


The probability distribution of the response of a nonlinearly damped system subjected to both broad-band and harmonic excitations is investigated. The broad-band excitation is additive, and the harmonic excitations can be either additive or multiplicative. The frequency of a harmonic excitation can be either near or far from a resonance frequency of the system. The stochastic averaging method is applied to obtain the Itô type stochastic differential equations for an averaged system described by a set of slowly varying variables, which are approximated as components of a Markov vector. Then, a procedure based on the concept of stationary potential is used to obtain the exact stationary probability density for a class of such averaged systems. For those systems not belonging to this class, approximate solutions are obtained using the method of weighted residuals. Application of the exact and approximate solution procedures are illustrated in two specific cases, and the results are compared with those obtained from Monte Carlo simulations.

Key words

Random vibration nonlinear systems harmonic and random excitations resonance stochastic averaging method of weighted residuals 


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Copyright information

© Kluwer Academic Publishers 1994

Authors and Affiliations

  • G. O. Cai
    • 1
  • Y. K. Lin
    • 1
  1. 1.Center for Applied Stochastics ResearchFlorida Atlantic UniversityBoca RatonU. S. A.

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