积分方程方法求解任意位置含集中质量圆板的振动特性  

STUDY ON FREE VIBRATION OF CIRCULAR PLATE WITH CONCENTRATED MASS 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(南校区)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：《机械强度》2009年第5期832-836,共5页Journal of Mechanical Strength

基　　金：国家自然科学基金(No.50775132);山东省中青年科学家科研奖励基金(No.2006BS0512)资助项目~~

摘　　要：针对任意位置带有集中质量的圆形板结构的自由振动问题,运用特殊函数论和傅里叶级数理论,采用由第一类贝塞尔函数组成的平方可积空间上的完备正交函数系构造圆形板结构的静力学格林函数,将带有附加质量的圆形板结构的非轴对称自由振动问题转化为积分方程特征值问题,进而应用积分方程理论,将其转化为无穷阶矩阵的标准特征值问题,给出分析在任意位置带有集中质量的圆形板结构动态特性的积分方程方法。数值计算结果表明方法的正确性和有效性。The free vibrations of circular plate with arbitrary number of concentrated mass at arbitrary positions is analysed by using integral equation method. A set of complete systems of orthogonal functions, which is constructed by Bessel functions of the first kind, is used to construct the Green＇ s function of circular plates firstly. Then the eigenvalue problem of free vibration of circular plate carrying concentrated mass at arbitrary positions is transformed into the problem of integral equation by using the superposition theorem and the physical meaning of the Green＇ s function. And then the eigenvalue problem of integral equation is transformed into a standard eigenvalue problem of a matrix with infinite order. Numerical examples are presented.

关 键 词：振动 圆形板 集中质量 固有频率 积分方程方法 正交函数系 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]