A state-space approach for dynamic analysis of sliding structures

This study presents a numerical algorithm based on a state-space approach f or the dynamic analysis of sliding systems. According to the proposed schem e, the equations of motion for the base-isolated structure in both the stic k and slip phases are integrated into a single set of equations by treating the friction force as a Lagrange multiplier. The Lagrange multiplier is de termined, with additional conditions of equilibrium and kinematic compatibi lity at the sliding interfaces, via a simple matrix algebraic calculation w ithin the framework of state-space formulations. The responses can thus be obtained recursively from the discrete-time state-space equation using a on e-step correction procedure. In addition, the integration step size is main tained constant throughout the analysis. The effectiveness of the proposed scheme is confirmed through tramples of sliding systems, under conditions o f either free vibration or harmonic excitations, for which analytical solut ions are available. Additionally, the novel algorithm is compared with a co rrective 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 simplifyi ng the task, the proposed algorithm also enhances accuracy and efficiency. (C) 2001 Elsevier Science Ltd. All rights reserved.