Modal Energy Equivalence Method for Calculating Amplitude-Dependent Viscous Damping of Distributed Stick–Slip Systems

The stick–slip mechanism caused by interfacial friction is one of the primary sources of structural damping, with its damping contribution commonly quantified by the equivalent viscous damping ratio (EVDR). To date, no method is available to calculate the amplitude-dependent modal EVDR of a multi-degree-of-freedom system with a distributed stick–slip mechanism. This study presented a novel method named the modal energy equivalence method (MEEM) to calculate the amplitude-dependent EVDR for normal modes of a distributed stick–slip system (DSSS). Based on a generalized single-degree-of-freedom stick–slip system, the analytical expression for the amplitude-dependent EVDR was developed in modal coordinates by applying the energy balance principle. The seismic analysis results indicated that the MEEM could effectively capture the three-stage amplitude dependence of modal EVDR and provide accurate response estimates over a wide amplitude range for the DSSS. Finally, for practical applications of the MEEM, the Rayleigh damping was determined with multi-modal EVDRs using the linear least squares method, and its effectiveness was validated based on the responses from the equivalent analysis.