Tuned Mass Dampers for Structures with Bilinear Hysteresis

Abstract

A design method of tuned mass dampers (TMDs) for structures with bilinear hysteresis subject to harmonic excitation is proposed. Conventional TMDs fail to control a bilinear structure as the equivalent natural frequency of the structure diverges from the TMD natural frequency at the higher level of excitation. The basic concept is to implement bilinearity to TMDs to keep the structural equivalent natural frequency and the TMD equivalent natural frequency tuned even when the structure yields. The proposed bilinearity of TMDs is similar to the structural bilinearity, but the initial yielding displacement is set several times larger by the amplitude ratio of the TMD to the structure. This amplitude ratio is derived from perturbation solutions of modes of the single-degree-of-freedom structure/TMD system. Numerical studies show that the proposed method gives consistent reduction of structural responses at any level of excitation. The steady-state responses subject to harmonic excitation are calculated by a frequency domain technique based on equivalent linearization.