A PERTURBATION METHOD FOR THE COMPLEX MODE THEORY OF LINEAR NON-CONSERVATIVE DYNAMIC SYSTEMS

摘要

The second order system of linear non-conservative dynamic equations cannot be decoupled by real mode theory unless some conditions are satisfied. The conventional method used in this case is so called complex mode theory in state space, but it is rather complicated and uneconomical in practical problems. In this paper, the perturbation method based on the real mode theory is utilized to solve the complex eigenpairs of such systems. The system eigenpairs are expanded into series forms corresponding to different order of magnitude and approximate equations of each order are then established. In virtue of the result that the zeroth order equations are those of corresponding system without damping whose modes are real and can be found by real mode theory, the higher order equations may be solved successively to obtain the modified complex eigenpairs up to any order needed. In order to improve the rate of convergence of the perturbation method, the damping matrix is divided into two parts: the first part can be diagonalized by real mode transformation and the second part is treated as small perturbated parameters. The multiple eigenvalue and gyroscopic eigenvalue problems are also discussed. At the end of this paper, two numerical examples are given.