Modified modal methods for calculating eigenpair sensitivity of asymmetric damped system

Abstract

SUMMARYMany real systems such as moving vehicles on roads, missiles following trajectories and ships in sea water have asymmetric mass, damping and stiffness matrices. Eigen-sensitivity analysis methods for the symmetric damped system cannot be used in the asymmetric damped case. Therefore, a method for calculating eigenpair sensitivity of the asymmetric damped system is needed. To do this, a modal method employing a modal superposition idea was recently developed. Since the accuracy of the modal method is dependent on the number of modes used in calculation, the modal method needs higher eigenvectors to guarantee the accuracy. In large-scale systems, however, only a few lower modes are generally considered for the dynamic analysis. Hence, if the modal method is used to obtain the eigen-sensitivity of the large-scale system, the significant errors could not be avoided due to the lack of the information of higher modes. In this paper, the modified modal methods for computing the sensitivities of the eigenpairs of asymmetric damped system using a few lowest sets of modes are proposed. Numerical example shows that the proposed methods achieve better calculating efficiency than the previous modal method.

Simultaneous iterative method for the derivatives of several eigenpairs of unsymmetric damped systems

“…This example is a gyroscopic system rotating with high speed and has a lumped mass in the centre of the beam, which is from [19].…”

Approximate method for eigensensitivity analysis of a defective matrix

“…Refs. [39,40] extended the method to a non-self-adjoint system with simple eigenvalues based respectively on the linear eigenvalue problem of twice order and on the quadratic eigenvalue problem, both of which can calculate the first-order eigenvector derivatives. Up to now, we have not found any work on the study of approximate method for eigensensitivity analysis of a defective matrix.…”

Second-order sensitivity of eigenpairs in multiple parameter structures

“…Lim and Junkins [6] discussed eigenvector derivatives; Liu et al [7] presented an accurate method for computing eigenvector derivatives for free-free structures. Moon et al [8] proposed a modified modal method for calculating the eigenpairs sensitivity of symmetric damped systems. Gong and Xu [9] , Maddulapalli et al [10] , and Choi et al [11] developed the methods for modal sensitivity analysis of the modified structure or product design selection.…”