An Approximate Method for Non-Proportionally Damped Systems with Many Degrees of Freedom

[摘要] The paper presents an approximate method of counting real solutions of non-proportionally damped systems with many degrees of freedom. Resolving a modal damping matrix into a diagonal matrix and a off-diagonal matrix, determining two perturbation equations respectively, we can get the approximate real solution. Two examples have given process of calculating the free vibration in the equation of the motion of the high-rise building system and the forced vibrations in a simple spring-mass system. We can also obtain the solution for the non-proportionally damped system with very big damping coefficients if the diagonal elements of normal modal damping matrix occupy a dominant position. The solution obtained by the new method is in very good agreement with the solution obtained by the numerical method.

[关键词] non-proportional damping;real modal;many degrees of freedom;perturbation technique