应用基于解析试函数的广义协调四边形厚板元分析中厚板的自由振动  

VIBRATION ANALYSIS OF MODERATE THICK PLATE BY GENERALIZED CONFORMING QUADRILATERAL THICK PLATE ELEMENT BASED ON ANALYTICAL TRIAL FUNCTIONS

作　　者：黄修长[1] 钱振华[1] 李俊[1] 华宏星[1] 

机构地区：[1]上海交通大学机械系统与振动国家重点实验室,上海200240

出　　处：《工程力学》2011年第9期39-43,共5页Engineering Mechanics

摘　　要：自从广义协调元提出以来,多种性能优异的板单元被构造且得到广泛应用,但是将广义协调元用于板的动力分析目前仅局限于薄板,该文将基于解析试函数的广义协调四边形厚板元ATF-PQ4b用于板的动力分析。该单元是将静力条件下中厚板的齐次微分方程的多项式解析解作为试函数,从而推导得到单元刚度矩阵和质量矩阵。笔者编写了相关的MATLAB程序用于计算固有频率和绘制模态振型。通过多个数值算例的验证,表明该单元具有简单、高效等优点。Since the generalized conforming element has been put forward, a number of plate elements with good performance are announced and widely used. Meanwhile the dynamic analysis of plates is limited to the thin plate. Long Yu-Qiu and Fu Xiang-Rong proposed a generalized conforming quadrilateral thick plate element ATF-PQ4b which uses the polynomial analytical solution of governing equations of Mindlin-Reissner plates as trial functions. In this paper, the element is employed to calculate the natural frequencies and modal shape of plates by the program coded by MATLAB. Numerical examples show that the generalized conforming quadrilateral thick plate element based on analytical trial functions is simple and efficient.

关 键 词：广义协调元 解析试函数法 中厚板 自由振动 ATF—PQ46 

分 类 号：O326[理学—一般力学与力学基础] O343.2[理学—力学]