用动态子结构法求结构固有频率的函数逼近解

FUNCTION APPROACHING SOLUTION OF FINDING NATURAL FREQUENCY OF STRUCTURE BY DYNAMIC SUBSTRUCTURE METHOD

本文利用精确的动力凝聚、变频变换代替定频变换，按双协调条件建立一个刚度矩阵和质量矩阵含有特征值参数的特征方程．在求解结构的固有频率时，首先研究了特征值与特征值参数的函数关系，并运用切比雪夫多项式来逼近此非线性函数；再用牛顿法求解非线性方程，得出其固有频率；最后用本方法计算了两个实例．所得结果同精确解和实验结果进行了比较，误差在工程允许范围之内．

By means of the accurate dynamic condensating method,bicompactible conditions and variable frequency transformation a characteristic equation with stiffness and mqss matrix containing eigen parameter is obtained. In the solution of the natural frequencies of the whole structure, the functional relationship between the eigenvalue and eigenvalue parameter is dealt with and the chebyshev interpolation polynomial is used to approach the non linear function. Then the natural frequencies of each mode are obtained by using the Newton method to solve the non-linear equations.