结构动力学中具有重特征值的灵敏度分析

为了计算重特征值情形的特征向量导数,推广Nelson's方法被广泛采用,其中有些已被认为在某些情形下是错误的.本文利用数学定理和新的灵敏度定义给出特征值和特征向量导数的精确解.该方法数学上严格,无论是否存在重特征值均适用.为了实际应用,还讨论了用低阶特征值确定近似解的可能性,算例验证了本文方法.

Exact Solution of Eigenvalue and Eigenvector Derivatives and Its Application in Structural Dynamics

To compute eigenvector derivatives with repeated eigenvalues, several extended Nelson's methods have been developed. Some of these methods have been pointed out that they may fail in some cases. To deal with those difficulties under repeated eigenvalues circumstances, the developed formulas have been used to calculate sensitivities and discuss the case where repeated eigenvalues are present in this paper. The exact solution of derivatives of eigenvalue and eigenvector is presented by utilizing the mathematical theorem and new definitions of sensitivities. This algorithm is rigorous mathematically and suited for both distinct and multiple eigenvalues cases. The new technique is powerful, easy to implement and simple in its conception. For practical application, the probability of determining approximate solution by using lower order eigendata is discussed. Examples that demonstrate the algorithm are presented.