弹性中厚板模态特性的近似计算方法  

AN APPROACH TO CALCULATION OF MODAL CHARACTERISTICS OF ELASTIC MODERATE -THICK PLATES

作　　者：楼梦麟[1] 王文剑[1] 

机构地区：[1]同济大学土木工程防灾国家重点实验室,上海200092

出　　处：《工程力学》1999年第5期138-144,共7页Engineering Mechanics

摘　　要：文中介绍了求解中厚板振动模态特性的一个近似方法一模态摄动法。这一方法是在薄板模态子空间内实施，最后将复杂的偏微分方程的求解转化为一个代数方程组的求解。对于四过简支板，得到一个十分简单的计算公式。文中还对剪切变形和转动惯量以及剪切折合系数对四过简支厚板固有频率的影响进行了分析。算例表明，这一方法简单且具有较好的精度。An approach, defined as the mode perturbation metho4 has been developed for modal analysis of the elastic moderate-thick plates. The solution of moan characteristics of the moderate thick p1ate is obtained approximately in subspace based on the lowe modal functions of the thin plate which has same numerical parameters and boundary condition with the moderate-thick plate except the thickness. By this method the complicated problem of differential equation of mohon is turned into the simple problem of algebraic eopations which is easy to solve. As to rectangular simplysupported moderate-thick plates, very simplified resuls are give in this paper Several numerical examples show that this method is praticable and has good preciaion. Finally, the shape effects of shear deformation and rotary inertia as well as the shape factor of the cross section on the natural frequencies of the plates are discussed.

关 键 词：中厚板 模态特性 模态摄动法 弹性 近似解 

分 类 号：O326[理学—一般力学与力学基础]