任意位置含振子圆板非轴对称振动的积分方程方法研究  

INTEGRAL EQUATION METHOD ON NON-AXISYMMETRIC VIBRATION OF CIRCULAR PLATES CARRYING OSCILLATORS AT ARBITRARY POSITIONS

作　　者：王卫东[1] 程泉[1] 许明田[2] 

机构地区：[1]山东大学土建与水利学院,济南250061 [2]山东大学能源与动力工程学院,济南250061

出　　处：《机械强度》2009年第3期481-486,共6页Journal of Mechanical Strength

基　　金：山东省中青年科学家科研奖励基金资助项目(2006BS0512)~~

摘　　要：运用特殊函数论和富里叶级数理论,采用由贝塞尔函数组成的平方可积空间上的一类完备正交函数系构造圆板的格林函数;应用积分方程和广义函数论,给出在圆板的任意位置带有弹性振子的耦合系统动态特性的积分方程方法。计算实践表明该方法不仅算法简捷、收敛速度快、计算精度高,而且能从整体上对系统的动态特性加以研究,从而为这类结构的优化设计和安全性评估提供有效的途径。A new method for the free vibration of circular plates with non-axisymmetrie oscillators is presented by combining the method of integral equations and the Fourier series method in structure mechanics. Basing on the theory of integral equation and Fourier-Bessel function, the Green＇ s function of the circular plates is constructed by the Besscl function of the first kind. Then the eigenvalue problem of free vibration of circular plates is transformed into the problem of integral equation by using superposition theorem. And then the eigenvalue problem of integral equation is transformed into a standard eigenvalue problem of a matrix with infinite order. In the calculating practice, the Q--R algorithm is used by replacing the matrix of infinite order with the square matrix of finite order according to the required precision. The advantages of this method are its briefness, its high precision and its extensiveness. Moreover, this method makes it possible for us to consider the dynamic features of circular plates with additional linear system as a whole. It can also provides a useful tool for the optimal design of systems.

关 键 词：振动 固有频率 积分方程 正交函数系 格林函数 圆形板 

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