Effects of geometrical nonlinearity on the performance of bidirectional tuned mass dampers

Abstract

AbstractThis research work focuses on the presentation of a novel model for considering the effects of geometrical nonlinearity in the response of bidirectional tuned mass dampers (TMDs). A new form of nonlinear equations of motion is derived. Unlike the conventional linear model, herein, the equations of motion are coupled in two orthogonal directions. The response of the novel nonlinear equations is obtained and compared to the typical linear equations and it is shown that the linear ones are not accurate enough to model the response of the multidirectional TMDs. Perturbation analysis is done to assess the response of TMD system under two internal resonance cases. In the proposed model, phenomena such as jump and energy transfer can take place. The effects of excitation amplitude, damping ratios, and frequency detuning parameters are investigated on the jump and energy transfer phenomena. According to the proposed nonlinear equations, the performance of the bidirectional TMDs depends on the excitation amplitude. Moreover, in some cases, by considering the nonlinear terms in the bidirectional motion equations of TMDs, their performance is improved. However, the nonlinear terms may affect the performance of TMDs negatively, which leads to a very high amplitude of the responses in the main controlled structure under seismic and harmonic excitations.