非線形不規則振動応答の呈する非正規性に関する考察

概要

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Probability distribution function of the dynamic response of the nonlinear system is non-Gaussian. But, in the existing theoretical analyses, to simplify the procedure, probability distribution is commonly assumed to be Gaussian. Therefore, such statistical responses as standard deviation and maximum value may have inadmissible errors in some cases. The purpose of the paper is to have a close examination on these errors and to get a consistent approximate method, by which the effect of the non-Gaussian distribution of the response can be taken into considerations. To get a non-Gaussian approximated solution, forth order Edgeworth's series is used to represent a non-Gaussian probability distribution function. From the Fokker-Planck equation, that is the partial differential equation of the probability distribution, by applying integrals by parts, simultaneous equations of the moment of the response will be obtained. From the investigations for some typical nonlinear systems, following conclusions are obtained : 1) Gaussian assumption may bring about inadmissible errors, especially in the case of estimating a maximum response. 2) Forth order Edgeworth's series can effectively be used to represent a non-Gaussian probability distribution function of most of the nonlinear systems.
社団法人日本建築学会の論文
1982-02-28