The time-domain modal superposition method of linearly damped systems with added mass

The total mass matrix cannot satisfy the requirement of orthogonality for linearly damped systems with added mass. Traditional modal superposition method will be not be directly used for calculating time-domain responses. In order to calculate the responses, a real domain modal superposition method based on simplified damping matrix and a complex domain modal superposition method based on state space method are constructed, respectively. The numerical examples show that the calculation results of these two methods are approximately equal. Then the dynamic responses of the linearly damped system with different distributions of added mass are analyzed. As the number of storey with added mass decreases, the lateral resistance of the structure increases. The added mass should be prioritized at the bottom storey.