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Structural Dynamics pp 146–213Cite as

Nonlinear Systems

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Abstract

The most powerful tool available for the analysis of the response of non-linear systems to random loading is the Markov vector approach. This, however, requires the excitation to be Gaussian white noise (although non-white processes can be modeled by passing white noise through a shaping filter, e.g. a Kanai-Tajimi filter). In this case the joint probability density of the state vector components is governed by the Fokker-Planck equation. Unfortunately, only very few closed-form solutions are known, most of them for SDOF systems. Even for in the SDOF case only some stationary solutions are available (e.g. Refs[3.3–1, 3.3–2, 3.3–3, 3.3–4]). This means that for more general cases approximate methods such as equivalent linearization have to be utilized. A detailed discussion is given in chapter 3.3.2.

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Authors and Affiliations

  1. Institute of Engineering Mechanics, University of Innsbruck, Austria

    C. G. Bucher & G. I. Schuëller

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  1. C. G. Bucher
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  1. Institut für Mechanik, Universität Innsbruck, A-6020, Innsbruck, Austria

    G. I. Schuëller

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© 1991 Springer-Verlag Berlin, Heidelberg

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Bucher, C.G., Schuëller, G.I. (1991). Nonlinear Systems. In: Schuëller, G.I. (eds) Structural Dynamics. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-88298-2_8

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  • DOI: https://doi.org/10.1007/978-3-642-88298-2_8

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