Vibration reduction and stability study of a dynamical system under multi-excitation forces via active absorber

Abstract

An active vibration absorber for suppressing the vibration of the nonlinear system when subjected to external and parametric excitations forces will be studied. The aim of this paper is to study the effect of the nonlinear controller on the vibrating system. The approximate solutions up to the second order are derived using the method of multiple scale perturbation technique near the primary, principal parametric and internal resonance case. The stability of the solution is investigated using both phase plane methods and frequency response equations. The effects of different parameters on the vibration of the system are investigated. The reported results are compared to the available published work. Key words: Active control method, perturbation method, stability, resonance.