Complex modal methods for analysis of random earthquake response of shear type structures with horizontally translational and rotational base

The random earthquake response of multi-layer shear type structure with horizontally translational and rotational base is studied systematically. The dynamic equations are established. According to the fact that the first mode contributes as the main part of the total motion, the vibration sharp of the structure is developed and approximated to the first mode shape. Then, according to the situation that the mass matrix is non-symmetry and damping matrix is non-classical, the complex mode theory is used to decouple the equations and to derive the exact solutions of random earthquake response of structural displacement, velocity and acceleration. A calculating example is given. The method can be used to analyse the non-stationary random earthquake response.