基于完全概率的随机薄板结构非线性振动分析  

The Nonlinear Vibration Analysis of Stochastic Thin Plates Based on Full-probability

作　　者：陈占锋 向娟 宋维举 王肖巍[2] CHEN Zhan-feng;XIANG Juan;SONG Wei-ju;WANG Xiao-wei(College of Civil Engineering,City College of Science and Technology,Chong Qing University,Chonqing,402167,China;College of Civil Engineering,Chong Qing University,Chonqing 400045,China)

机构地区：[1]重庆大学城市科技学院土木工程学院,重庆402167 [2]重庆大学土木工程学院,重庆400045

出　　处：《科学技术与工程》2019年第22期259-264,共6页Science Technology and Engineering

基　　金：重庆市教育委员会科学技术研究项目(KJQN201802504)资助

摘　　要：根据大挠度薄板的弹性理论建立了矩形薄板的非线性振动控制方程,并用伽辽金变分法将其化简为常微分非线性动力学方程.利用Lindstedt-Poincareé摄动法求解得到固定参数薄板的振动频率解析解,应用随机向量函数的概率分布函数表达式,通过确定积分区间、变量替换、积分顺序变换等一系列数学上的处理,获得随机薄板结构非线性振动频率的概率密度函数.通过具体算例分析与蒙特-卡罗模拟结果等相比较,验证了理论分析的正确性表明该方法具有较高的精度和计算效率.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,the normal differential and non-linear kinetic equation of isotropic thin plates was derived.And asymptotic analytical solutions for the frequency function of the thin plates with fixed parameters were solved by Lindstedt-Poincaréperturbation method.According to 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 etc.,the result of the method in this paper was validated.Numerical examples show that the method in this paper has the advantages of accuracy and effectiveness.

关 键 词：随机薄板 非线性 Lindstedt-Poincareé摄动法 概率密度 

分 类 号：TU313[建筑科学—结构工程]