Dynamic Reliability-Based Seismic Optimal Design of Structures with Tuned Mass Damper

Abstract

This paper presents a dynamic reliability-based optimization technique for the seismic design of structures with tuned mass damper (TMD). Firstly, the governing equation of multi-degree-of-freedom structure with TMD is established. Then, the main structure is unfolded by the first mode. Considering that the damping is non-classical and the total main structure and TMD system is un-symmetric, the complex modal analysis is adopted to uncouple the governing equation and the analytical solutions of stochastic seismic response under the Kanai-Tajimi spectrum loading are obtained. Taking the ratio between the first-order modal displacement standard deviation of the structure with TMD and the one without TMD as the objective function, the dynamic reliability of the TMD system displacement as the constraint, the optimal design parameters of the TMD system are obtained through the penalty function method. A 10-story building with TMD system illustrates the proposed dynamic reliability-based optimization method. It is believed that such an optimization technique provides an effective tool for the seismic design of structures with TMD.