Vibration suppression of a dynamical system to multi-parametric excitations via time-delay absorber

The aim of this work is to control the dynamic system behavior represented by a beam at simultaneous primary and sub-harmonic resonance condition, where the system damage is probable. Control is conducted via time delay absorber to suppress chaotic vibrations. A comprehensive investigation of the effect of the time delay on the control of a beam when subjected to multi- parametric excitation forces is presented. Multiple scale perturbation method is applied to obtain the solution up to the second order approximation. Different resonance cases are reported and studied numerically. Stability of the steady state solution for the selected resonance case is investigated applying Rung–Kutta fourth order method and frequency response equations via Matlab 7.0 and Maple11. Time delay absorber is effective like ordinary one within a specified range of time delay. The delay time is an important factor in selecting the absorber. The effects of the different parameters of the absorber on the system behavior are studied numerically. The reported results are compared with the available published work.