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

In vibratory systems, linear and nonlinear vibration absorbers can be used to suppress 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. Comparison of the effects of attached nonlinear absorber on a nonlinear system with that of a linear one, under the resonance cases is performed. The stiffness of the main system and the absorber are considered to be cubically nonlinear, whereas the behavior of the dampers is supposed to be linear. Using multiple time scales (MTS) method, approximate solution of the nonlinear equations of motion is obtained. It is concluded 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, effective reduction in the vibration amplitude can be achieved using a nonlinear absorber.