具有中间支承的正交异性矩形板自由振动分析  

FREE VIBRATION ANALYSIS OF ORTHOTROPIC RECTANGULAR PLATES WITH INTERMEDIATE SUPPORTS

作　　者：杨端生[1] 黄炎[1] 李磊[1] 

机构地区：[1]长沙理工大学桥梁与结构工程学院,国防科技大学航天与材料工程学院,长沙410076,长沙410073

出　　处：《工程力学》2008年第4期111-114,120,共5页Engineering Mechanics

基　　金：国家自然科学基金资助项目(19872076)

摘　　要：应用一般解析解来求解具有中间支承的正交异性矩形板的自由振动问题。一般解析解能求解任意边界条件矩形板的振动问题。求解过程是将整块板看成是沿中间支承分开的两块板。沿支承边两块板的挠度均等于零;斜度和弯矩均相等。由全部边界条件和连续性条件可以求解各阶频率和振型。对几种具有简支边、平夹边或自由边的板进行了计算。Using a general analytical solution to solve the vibration problem of orthotropic rectangular plates with intermediate support, the general analytical solution can be used to solve the vibration problem of rectangular plates with arbitrary boundary conditions of all edges. The procedure is firstly dividing the plate into two plates along the intermediate line. The deflection is zero; the slope and moment are equal for the connected edges between two plates. The each natural frequency and corresponding vibration mode can be solved by making use of all boundary as well as continuous conditions. Some plates with boundary conditions of simply supported, clamped or free edges have been calculated.

关 键 词：正交异性 矩形板 一般解析解 振型 固有频率 

分 类 号：O326[理学—一般力学与力学基础]