Efficiency of modal analysis to compute the seismic response of dam - Foundation systems with non - Proportional damping

In a finite element model of typical dam - foundation - reservoir systems, the presence of heterogeneous material properties for the dam and the foundation produces a combined damping matrix that is non-proportional to the mass and/or the stiffness matrices of the system. In this case, the undamped real free-vibration modes cannot uncouple the damping forces such that the classical mode superposition method using real modes is not applicable. This paper presents comparative analyses of recent coordinate reduction procedures that have been developed to compute the response of linear systems with non-proportional damping. The comparisons are based on the numerical efficiency and the accuracy of the displacement, acceleration and stress response, and on the distribution of the damping energy in the system.