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EXACT SOLUTIONS FOR STATIONARY RESPONSES OF SEVERAL CLASSES OF NONLINEAR SYSTEMS TO PARAMETRIC AND/OR EXTERNAL WHITE NOISE EXCITATIONS 被引量:2
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作者 朱位秋 《Applied Mathematics and Mechanics(English Edition)》 SCIE EI 1990年第2期165-175,共11页
The exact solutions for stationary responses of one class of the second order and three classes of higher order nonlinear systems to parametric and/or external while noise excitations are constructed by using Fokkcr-P... The exact solutions for stationary responses of one class of the second order and three classes of higher order nonlinear systems to parametric and/or external while noise excitations are constructed by using Fokkcr-Planck-Kolmogorov et/ualion approach. The conditions for the existence and uniqueness and the behavior of the solutions are discussed. All the systems under consideration are characterized by the dependence ofnonconservative fqrces on the first integrals of the corresponding conservative systems and arc catted generalized-energy-dependent f G.E.D.) systems. It is shown taht for each of the four classes of G.E.D. nonlinear stochastic systems there is a family of non-G.E.D. systems which are equivalent to the G.E.D. system in the sense of having identical stationary solution. The way to find the equivalent stochastic systems for a given G.E.D. system is indicated and. as an example, the equivalent stochastic systems for the second order G.E. D. nonlinear stochastic system are given. It is pointed out and illustrated with example that the exact stationary solutions for many non-G.E.D. nonlinear stochastic systems may he found by searching the equivalent G.E.D. systems. 展开更多
关键词 exact solutionS FOR stationary RESPONSES OF SEVERAL CLASSES OF NONLINEAR SYSTEMS TO PARAMETRIC AND/OR EXTERNAL WHITE NOISE EXCITATIONS
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