Modified modal methods for calculating eigenpair sensitivity of asymmetric damped system

Many 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