Modal decomposition of multi-degree-of-freedom structure with non-proportionally distributed rate-independent linear damping

Rate-independent linear damping benefits low-frequency structures by mitigating excessive displacement without increasing the floor acceleration response under severe ground motions. The advantage of rate-independent linear damping in controlling low-frequency structures is attributed to its constant loss stiffness, which ensures high damping in low-frequency components while maintaining low high-frequency damping forces. In this study, a modal decomposition method was developed for a base-isolated structure containing rate-independent linear damping distributed non-proportionally to the stiffness. Because the response of a single-degree-of-freedom system containing rate-independent linear damping can be well-approximated by a linear viscous damping system having the same eigenvalues, the behavior of the rate-independent linear damping system can be evaluated via the response-spectrum approach. In the proposed modal analysis method, separated modal responses of a base-isolated structure were employed to demonstrate how rate-independent linear damping can achieve a displacement control effect similar to that of linear viscous damping with a low floor acceleration response. Compared with conventional frequency analyses, the proposed method was found to accurately predict the dynamic responses of a rate-independent linear damping system.