Investigation and optimization of nonlinear pendulum vibration absorber for horizontal vibration suppression of damped system

Abstract

Nonlinear pendulum vibration absorber is investigated in this paper to control resonance peak of linear primary system with horizontal vibrations subjected to forced and motion excitations. Pendulum vibration absorbers have been utilized as tuned mass damper for many years, but by this knowledge, nonlinear analysis of this problem has not been investigated anywhere. Harmonic balance (HB) method is used to solve nonlinear differential equations and analyze the stability of their results. Optimum damping and natural frequency ratios are derived by minimizing the maximum steady-state response of primary system with numerical optimization. The presented analysis shows that the pendulum absorber design based on linear model resulting in a small area around the original frequency for vibration absorption. For linear pendulum design, with a small deviation from the linear range, the amplitude of initial system greatly increased, and its performance will fall sharply. But if the design is based on a nonlinear pendulum with larger amplitude of motion, the resulting design will have a higher accuracy. In this paper, responses with inferior periods are inspected beside main period one. Different methods are used for optimized nonlinear pendulum. Finally, system robustness and chance of bifurcation will be predicted. Copyright © 2015 John Wiley & Sons, Ltd.