Vibration Analysis of a Nonlinear System with a Nonlinear Absorber under the Primary and Super-harmonic Resonances (TECHNICAL NOTE)

Abstract   In vibratory systems, linear and nonlinear vibration absorbers can be used to suppress the primary and super-harmonic resonance responses. In this paper, the behavior of a nonlinear system with a nonlinear absorber, under the primary and super-harmonic resonances is investigated. The stiffnesses of the main system and the absorber are cubically nonlinear and the dampers are linear. Multiple time scales method is used to obtain approximate solution of the nonlinear equations of motion. Results show that at primary resonance, a linear absorber can suppress the peak amplitude of the system better than a non-linear one. But under super-harmonic resonance, the vibration amplitude can be more effectively reduced by adding a nonlinear absorber to the vibrating system.