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Title of Journal: Nonlinear Dyn

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Abbravation: Nonlinear Dynamics

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Springer Netherlands

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DOI

10.1002/chin.199408320

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1573-269X

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To obtain approximate probability density function

Authors: M Abedi A Asnafi K Karami
Publish Date: 2014/07/04
Volume: 78, Issue: 3, Pages: 1717-1727
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Abstract

The probability density function plays an essential role to investigate the behaviors of stochastic linear or nonlinear systems This function can be evaluated by several approaches but due to its analytical theme the Fokker–Planck–Kolmlgorov FPK approach is preferable FPK equation is a nonlinear PDE gives the probability density function for a stochastic linear or nonlinear system Many researches have been done in literature tried to specify the conditions in which the FPK equation gives an exact solution Although the exact probability density function can be achieved by solving the FPK equation even for some nonlinear systems many types of systems cannot satisfy the conditions for exact solution In this article the axially moving viscoelastic plates under both external and parametric white noise excitation as one of the newest and applicable research areas are studied Due to strong nonlinearities recognized in the governing equation of the system the exact probability density function cannot be obtained however via an approximate method some precise approximate solutions for different but comprehensive case studies are evaluated validated and discussed

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