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| Nonlinear Vibration Analysis of Stochastic Thin Plates Based on Lindstedt-Poincar\'{e} Perturbation Method |
| Weiju Song, Yingmin Li, Zhoulian Zheng |
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Abstract Nonlinear vibration computational problem of stochastic thin plates
in large amplitude was investigated here. Based on the nonlinear
theory of large deflection of thin plates, we derived the governing
equations of nonlinear free vibration of isotropic thin plates. And
solved the governing equations by Lindstedt-Poincar\'{e}
Perturbation Method Presented herein are asymptotic analytical
solutions for the frequency function of the thin plates with fixed
parameters. Based on the theory of random field, after mathematical
treatments of the probability density function of random vector
expressions, such as determining the interval of integrating,
substituting variable and transforming integral order, then the
probability density function of nonlinear vibration frequency of
stochastic thin plates can be obtained directly. And combined with
Monte Carlo Simulation analysis and our previous work [1], the
result of the method in this paper is validated, which testifies
that the method in this paper is effective and of preferable
precision.
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| DOI:10.12733/jics20105735 |
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