三阶剪切变形板的振动特性研究  

STUDY ON VIBRATION CHARACTERISTIC OF THIRD ORDER SHEAR DEFORMATION THEORY OF PLATE

作　　者：陈丽华[1] 孙玥[1] 张伟[1] 

机构地区：[1]北京工业大学机电学院,北京100124

出　　处：《动力学与控制学报》2014年第1期50-55,共6页Journal of Dynamics and Control

基　　金：国家自然科学基金资助项目(11172011)~~

摘　　要：对于中厚板或层合板而言,横向剪切变形的影响是显著的,采用三阶剪切变形理论比采用经典薄板理论和一阶剪切变形理论能更好的满足精度的要求,而且能更好地描述板的剪切变形和剪应力沿厚度方向的分布情况.本文用解析的方法研究了简支、自由和固定三种边界条件的任意组合下三阶剪切变形板的自由振动问题.首先应用哈密顿原理建立自由振动方程,再通过引入中间变量使得原来耦合的自由振动方程得到解耦和简化,基于分离变量法,利用边界条件得到基函数的表达式,利用Rayleigh-Ritz法,求得三阶剪切变形板在任意边界条件下的固有频率和振型.本文得到的结果可以为厚板在工程中的应用提供理论依据,具有较高的工程实际应用价值.The effect of the transverse shear deformation for Reddy plates or laminated plates is significant. In this case, it can meet the requirements for calculate precision better to use the third order shear deformable theory than to use the classical thin plate theory and the first order shear deformation theory. And it is better to describe the distribution of the plate shear deformation and shear stress varying through the thickness when using the third order shear deformation theory. In this paper, an analytical method is presented for studying the free vibration characteristic of plate using the third order shear deformation theory on different boundary conditions, which are the any combinations of simply supported ,free and clamped. Hamilton principle is used to formulate the free vibration equations. Then, by introducing the intermediate variable the original coupling free vibration equations are decoupled and simplified. The fundamental function expressions are obtained basing on the method of separation of variables and the boundary conditions. And the natural frequencies and modal functions are obtained by using the Rayleigh - Ritz method. The method in this paper has a good generality for solving the vibration problems of thick plates under different boundary conditions. The result obtained in this paper can provide a theoretical basis for thick plates application in engineering, and it has relatively high application value.

关 键 词：板 三阶剪切变形理论 固有频率 振型 Rayleigh—Ritz法 

分 类 号：TU311.3[建筑科学—结构工程]