多参数结构特征二阶灵敏度

提出了一种有效计算多参数结构特征值与特征向量二阶灵敏度矩阵--Hessian矩阵的方法.将特征值和特征向量二阶摄动法转变为多参数形式,推导出二阶摄动灵敏度矩阵,由此得到特征值和特征向量的二阶估计式.该法解决了无法用直接求导法计算特征值和特征向量二阶灵敏度矩阵的问题.数值算例说明了该算法的应用和计算精度.

Second-Order Sensitivity of Eigenpairs of Multiple Parameter Structures

A method for computing the second-order sensitivity matrix of eigenvalues and eigenvectors of the multiple parameter structures,i.e.the Hessian matrix,was presented. The second-order perturbations of eigenvalues and eigenvectors were transformed into the multiple parameter forms, and the second-order perturbation sensitivity matrices of eigenvalues and eigenvectors were developed. Using these formulations, the efficient methods based on the second-order Taylor expansion and second-order perturbation were obtained to estimate the changes of eigenvalues and eigenvectors when design parameters changed. The method avoided direct differential operation thus reducing the difficulty for computing the second-order sensitivity matrices of eigenpairs. A numerical example was given to demonstrate the application and the accuracy of the proposed methods.