Eigensensitivity Analysis for Asymmetric Nonviscous Systems

摘要

THE eigensensitivities of mechanical systems with respect to structural design parameters have become an integral part of many engineering design methodologies including optimization, structural health monitoring, structural reliability, model updating, dynamic modification, reanalysis techniques, and many other applications. Fox and Kapoor [1] computed the derivative of each eigenvector as a linear combination of all of the undamped eigenvectors. Later, Adhikari and Friswell [2] and Adhikari [3] extended the modal method to the more general asymmetric systems with viscous and nonviscous damping, respectively. Nelson [4] presented a method, which requires only the eigenvector of interest by expressing the derivative of each undamped eigenvector as a particular solution and a homogeneous solution. Later, Friswell and Adhikari [5] extended Nelson's method to symmetric and asymmetric systems with viscous damping. Recently, Adhikari and Friswell [6] extended Nelson's method to symmetric and asymmetric nonviscously damped systems. Fox and Kapoor [1] also suggested a direct algebraic method to calculate the eigensensitivity for symmetric undamped systems by solving a nonsingular linear system of algebraic equations. Lee et al. [7] derived an efficient algebraic method, which has a compact linear system with a symmetric coefficient matrix for symmetric systems with viscous damping. Later, Guedria et al. [8] extended the algebraic method to general asymmetric viscous damped systems. Chouchane et al. [9] reviewed the algebraic method and extended their method to the second-order and high-order derivatives of eigensolutions. Li et al. [10] extended the algebraic method to symmetric and asymmetric nonviscously damped systems. Xu and Wu [11] proposed a new normalization and presented a method for the computation of eigensolution derivatives of asymmetric systems with viscously damping. Recently, Mirzaeifar