Control of Chaotic Oscillation and Response Charaterisation in Duffing Oscillator Using Vibration Absorber

Abstract This work investigated the control of chaotic behavior of a harmonically perturbed DufTing Oscillator using

vibration absorber. The system of two degrees of freedom governing equations were simu Eated nu rner i~allyu sing classical

fourth order Runge-Kutta algorithm for a constant time step. The solution time history, phase plots and Poincare maps were

usd to validate tbe simulation. Essentially, the details of the' Poincare map were used numerically to determine the

periodicity ofDuffing oscil&r forspectmmof mass ratio at aconstant step of0.001. The time history, phase plots and the

Pomca~at mass ratio (p), absorber parameters (a,), and amplitude ofexcitation IF,) are in agreement with what is obtained

in open literature. The chaotic response of the Dufigdbsorbersystem at a, = I.!, F, =0.2 1: and, taken respectively. the

Duffmg and the absorber initiil conditions to be ( 1.0,O.O) and (0.0,0.0), this chaotic response was rendered periodic tor some

selected mass ratio (Eps1.0). Specifically, periods 1, 2 and 4 were obtained at p= 0.208; these periodic responses were

obtained at respective values ofa,=l. 1. a,=l.7803 and a,= 1.7595. In this work, eighty percent of the mass ratio selected did

ensure that the chaotic behaviour ofthe DuRutg-Absorber system is rendered periodic. This workdemonstrated the practical

utility ofvibration absorber as a chaotic oscillations control tool by the mass ratio approach; and having a recorded success of

about eighty percent.