具有不完全特征向量系的状态向量摄动的快速算法

Sensitivity of state vector of a defective system

对具有不完全特征向量系的n自由度一般黏性阻尼的线性振动系统,针对当系统参数进行局部小修改,即产生摄动变化时模态分析工作复杂的问题,本文根据广义特征向量及伴随矩阵理论,提出并构造了一个求解状态向量摄动问题的快速算法。在已知原始解(摄动前)的基础上,只需逐个代入递推计算,无需解大型方程组便可求出状态向量或特征向量的摄动量。数值算例证明了此方法的有效性。

A fast method of calculatin based on the theory of generalized e expressed by a linear combination of obtained original g the state vector derivatives of a defective system is presented igenvector and adjoint matrix. The state vector derivatives are generalized eigenvectors, and the expansion coefficients can be by a recursion algorithm instead of solvin system. The numerical example is given to g large-scale equations based on eigensolutions of prove the efficiency of the method.