Time-domain numerical continuation of periodic orbits for harmonically forced hysteretic nonlinear systems with Iwan joints

Abstract

Coulomb sliders are used widely in order to model frictional interfaces. In many applications, the nonlinear Frequency Response Functions (FRFs) of these systems is desired, but it is extremely computationally expensive to use time-domain integration methods to compute the steady-state response. The nonlinear force and stiffness of these devices depends on the position of sliders, and the implicit nature of the slider positions makes these systems hysteretic and therefore non-trivial to address using conventional continuation methods. This paper proposes a novel numerical method, dubbed ”Hysteresis Identification via Reversal Points or (HIRP)” that can compute the steady-state harmonically forced response of frictional nonlinear systems. For this purpose, a quasi-static algorithm is introduced which can evaluate the state of sliders at any time based on the reversal points over a period. This reduces the number of state variables needed in the continuation routine by at least an order of magnitude. The method has been tested by computing the harmonic response of a hysteretic system with multiple Coulomb sliders. The method is evaluated on multi-degree of freedom systems with Iwan joints, demonstrating that the method can be a valuable tool for predicting the nonlinear, steady-state response of hysteretic systems.