粘弹性薄板的热振动  

THERMAL VIBRATION OF THIN VISCOELASTIC PLATES

作　　者：邢晶晶[1] 张能辉[1] 王明禄[1] 

机构地区：[1]上海市应用数学与力学研究所,上海200072

出　　处：《振动与冲击》2005年第5期23-25,共3页Journal of Vibration and Shock

基　　金：上海市教委青年基金(No.01QN70);国家自然科学基金(No.10172056);上海市重点学科建设资助项目

摘　　要：首先从热粘弹性材料的各向同性本构方程出发,利用Laplace变换方法,引入薄板的“结构函数”与“热函数”,建立了薄板热振动的数学模型。然后,采用近代卷积双线性形式和传统笛卡儿双线性形式找到了相应的简化Gurtin型变分原理。最后,利用Ritz法和Laplace变换技术,考察热载对粘弹性薄板响应的影响。Based on the isotropic constitutive equation of thermoviscoelastic materials, a mathematical model for thermal vibration of thin viscoelastic plates is set up by use of the structural function and the thermal function of the plate introduced by the Laplace transformation method. Meanwhile, the corresponding simplified Gurtin-type variational principle is presented by means of modern convolution bilinear forms and classical Cartesian bilinear forms. The influence of thermal loads on the response of the viscoelastic thin plate is studied by the Ritz's method and the Laplace transformation method.

关 键 词：粘弹性薄板 热振动 变分原理 RITZ法 

分 类 号：O32[理学—一般力学与力学基础]