New method to evaluate the rate of convergence for two-dimensional system involving friction damper

Abstract

The performances of the two-dimensional system involving friction damper acquire highly sophisticated understanding both in steady-state and transient-state since the inherent strong nonlinearity associated with force-velocity characteristics, which highlightings the necessity to investigate the rate of convergence during transient-state. In this paper, we propose a numerical model of a two-dimensional system comprising friction damper and calculate the responses during transient-state with highly accurate slip/stick transition times and positions. We introduce the distances between two adjacent sticking points belong to two consequent orbits to describe the evolvements of responses during transient-state. We reveal that the distances are close to be logarithmically proportional to the cycle numbers during transient-state and oscillate around some sufficiently tiny value during steady-state. We establish a criterion of the nearness of approach to the steady-state by observing the critical cycle number i0 determined by the slope rate and intercept and employ it to evaluate the rate of convergence during transient-state. We consider several representative cases and utilize the new method to see how the rate of convergence is affected by constant normal load and present an approximation for the optimized constant normal load for the system with fastest rate of convergence.