含附加结构的圆形和环形板振动的积分方程方法  

A Study on Free Vibration of Circular and Annular Plates with Attached Substructures at Arbitrary Positions by Integral Equation Method

作　　者：王卫东[1] 程钢[2] 程泉[1] 

机构地区：[1]山东大学土建与水利学院工程力学系,济南250061 [2]山东建筑大学机电工程学院,济南250101

出　　处：《振动．测试与诊断》2010年第4期389-393,共5页Journal of Vibration,Measurement & Diagnosis

基　　金：国家自然科学基金资助项目(编号:50775132);山东省中青年科学家科研奖励基金资助项目(编号:BS2009CL047);山东省博士后创新项目专项资金资助项目(编号:200803042)

摘　　要：为了分析任意位置含附加结构的圆形和环形板结构的振动特性,运用特殊函数论、傅里叶级数和积分方程理论,采用由第1类和第2类贝塞尔函数组成的平方可积空间L2[a,b]上的完备正交函数系构造圆形和环形板结构的静力学格林函数,将任意位置带有附加结构的圆形和环形板结构的自由振动问题转化为积分方程特征值问题,进而将积分方程特征值问题转化为无穷阶矩阵的标准特征值问题,给出分析这类结构振动特性的积分方程方法。典型算例计算结果表明,该方法不仅算法简捷、收敛速度快,而且能从整体上对带有附加结构的圆形和环形板的非轴对称振动进行研究,为这类结构的优化设计和安全性评估提供了有效的途径。In practice,circular and annular plates usually have intermediate supports,and are eccentrically attached with subsystems due to their limited space.In order to analyze the vibration characteristics of the plates,the integral equation method is adopted.By using the theory of special functions,Fourier-Bessel function and Green function constructed from a complete set of orthornormal funcitons of the space of square-integrable funtims L2(a,b) consisting of Bessel functions of the first and the second kind,the free vibraction problem of the plates is transformed into the eigenvalue problem of the integral equation,and then into a standard eigenvalue problem of a matrix with infinite order.Calculated results show the effectiveness and feasibility of the method.Not only the method is simple and quick,but it can be used to analyze the nonaxial symmetric vibration of circular and annular plates attached with substructures as a whole,thus providing an effective way for the optimal design and safety evaluation of structures of this kind.

关 键 词：振动 固有频率 积分方程 正交函数系 圆形板 环形板 格林函数 

分 类 号：O327[理学—一般力学与力学基础] O175.5[理学—力学]