A state-space approach for dynamic analysis of sliding structures

Abstract

This study presents a numerical algorithm based on a state-space approach for the dynamic analysis of sliding systems. According to the proposed scheme, the equations of motion for the base-isolated structure in both the stick and slip phases are integrated into a single set of equations by treating the friction force as a Lagrange multiplier. The Lagrange multiplier is determined, with additional conditions of equilibrium and kinematic compatibility at the sliding interfaces, via a simple matrix algebraic calculation within the framework of state-space formulations. The responses can thus be obtained recursively from the discrete-time state-space equation using a one-step correction procedure. In addition, the integration step size is maintained constant throughout the analysis. The effectiveness of the proposed scheme is confirmed through examples of sliding systems, under conditions of either free vibration or harmonic excitations, for which analytical solutions are available. Additionally, the novel algorithm is compared with a corrective psuedo-force iterative procedure for seismic response analysis of a FPS-supported five-story building. The novel algorithm is more systematic and easy to implement than conventional approaches. Moreover, by simplifying the task, the proposed algorithm also enhances accuracy and efficiency.