Complex Modal Superposition Method For Non-proportional Damping Of Linear Systems

On the base of the state place formulations, the thesis discusses systematically the free vibration and the force vibration of damped multi-story liner system. According to the theory, aiming at principally the effect of ground motion that earthquake causes,this thesis analyze non-proportional damped structure theoretically, raising an approach that calculate the displace of every story and between-store by complex mode shapes spectrum splice. Meanwhile verifying it's calculation precision through comparison with exact solution. In addition, deducing the response style of stable state when system is forced by two different methods, meanwhile contrasting with the especial condition of the general form that is affected by earthquake ground motion , and gaining the same conclusion. At last, this thesis deduces the solution of free vibration that is affected by random initial displace and velocity.