Amplitude‐dependent modal viscous damping for distributed stick–slip systems

Abstract An accurate damping model serves as the foundation for reliable structural analysis. One of the primary sources of structural damping is the stick–slip mechanism caused by interfacial friction. Structural damping is usually represented by the modal damping ratio, and the modal equivalent viscous damping ratio (EVDR) of a stick–slip system is crucial in structural dynamic modeling. To date, an accurate yet simple prediction method for modal amplitude‐dependent EVDR that considers the distribution characteristics of the stick–slip mechanism remains unavailable. In the present study, the modal EVDRs of a distributed stick–slip system (DSSS) extended from a single degree‐of‐freedom stick–slip system were calculated using the modal energy equivalence method. The correlation between the stick–slip parameters and the modal damping behavior was investigated at various amplitude levels on the basis of the assumption of equal stick–slip parameters. A two‐parameter damping model represented by a single stick–slip damping model was developed to capture the amplitude dependence of the frictional EVDR. Furthermore, a practical prediction method based on the stick–slip parameters was proposed for the modal EVDR of the fundamental and higher‐order modes. The seismic analysis of two illustrative structures with nonuniform and uniform interstory stiffness demonstrated the effectiveness and applicability of the proposed method in predicting the modal EVDR of the DSSS. The proposed equivalent linear viscous damping system is suitable for the quick prediction of structural dynamic responses.