A study on friction-tuned mass damper: harmonic solution and statistical linearization

Abstract

Tuned mass dampers (TMDs) have been a popular vibration control device used primarily for suppressing wind-induced oscillations in tall structures and have recently also been used for controlling vibrations due to seismic excitations. A nonlinear damper consisting of a TMD with a nonlinear dry (pure) friction damping at the interface between the primary structure and the TMD is analyzed in this paper. This nonlinear damper has potential for control of vibration but has not received much attention by researchers. In particular, the nonlinear behavior of the system has not been explored in detail so far. A periodic solution for the response of the structure-friction TMD (FTMD) system modeled as a two-degree-of-freedom system is obtained under harmonic excitation using harmonic balance based on a method of averaging. To consider more realistic random excitations, a statistical linearization method is used to replace the nonlinear friction by an equivalent viscous damping. Numerical simulations have demonstrated that the linearized solutions for both the harmonic and the random cases are accurate enough. The periodic and statistical linearized solutions are used to analyze dynamic characteristics of structure-FTMD system. As expected in a nonlinear system, the frequency response function (FRF) of the displacement response of the structure for the structure-FTMD system is dependent on the level of excitation. For a given level of excitation, an optimum friction coefficient has been found to exist which corresponds to the least root-mean-square value of the displacement response of the primary mass.