考虑地基耦合效应时中厚矩形板的非线性自由振动分析  

Nonlinear Free Vibration Analysis Including Coupled Effect of Elastic Foundation for Moderate Thickness Rectangular Plates

作　　者：肖勇刚[1] 傅衣铭[1] 查旭东[2] 

机构地区：[1]湖南大学,长沙410082 [2]长沙理工大学,长沙410076

出　　处：《力学季刊》2004年第3期322-329,共8页Chinese Quarterly of Mechanics

基　　金：国家自然科学基金资助项目(50208004)交通部资助项目(200231582512)

摘　　要：基于各向同性中厚板理论,考虑板的非线性效应和地基耦合效应,应用Hamilton变分原理,建立了双参数地基上周边自由中厚矩形板的非线性运动控制方程,提出了一组满足问题全部边界条件的试函数。应用伽辽金法和谐波平衡法对方程进行求解。讨论了板的结构参数和地基的物理参数对弹性地基上周边自由中厚矩形板的非线性自由振动特性的影响。Based on the theory of isotropic moderate thickness plates and using Hamilton variation principle, the nonlinear equations of motion including the nonlinear effect of plates and the coupled effect of foundation were derived for the moderate thickness rectangular plates on two parameter foundation. The suitable expressions of trial functions satisfied all boundary conditions of the problem were proposed. By using Galerkin method and harmonic balance method, the nonlinear equations were solved. The effects of the structural parameters of plates and the physical parameters of foundation on the nonlinear free vibration behaves for the moderate thickness rectangular plates on elastic foundation with freely supported boundary were discussed.

关 键 词：中厚矩形板 弹性地基 非线性振动 伽辽金法 谐波平衡法 

分 类 号：O343.2[理学—固体力学]