Pendulum vibration absorber with a nonlinear viscous damping mechanism

Simple pendulum vibration absorbers, as one of the most common models of absorbers, experience nonlinear behaviors in the large amplitude of oscillations, and under such conditions, they are not effective enough and are more prone to lose their stability. To overcome some of these drawbacks, a complementary damping mechanism including two nonlinear elements is introduced. Alongside the ordinary linear viscous damper, a damping mechanism is also utilized to control the oscillations of the dynamic structure exposed to the excitation forces more intense than the ones considered in the optimization. In other words, they make this system more robust and stable in the face of excitations stronger than the presupposed conditions. The complementary elements of this mechanism are proposed to offer an appropriate approximation of various likely models which can be used as practical nonlinear damping mechanisms. The steady-state solutions of the nonlinear governing equations are achieved with pinpoint precision with the help of the harmonic balance method and more precise approximations of trigonometric functions. To enhance the impacts of this mechanism, optimization is performed for a compound objective function in addition to the conventional one. This study explains how such mechanisms are capable of contributing to the higher robustness and stability of pendulum vibration absorbers under a wider range of excitation intensities. The performance of this absorber is also studied for an N-story shear structure as a multidegree of freedom (MDOF) system.