Control of chaotic oscillation and response characterisation in duffing oscillator using vibration absorber

Abstract

"This work investigated the control of chaotic behavior of a harmonically perturbed Duffing Oscillator using vibration absorber. The systems of two degrees of freedom governing equations were simulated numerically using classical fourth order Runge-Kutta algorithm for a constant time step. The solution time history, phase plots and Poincare maps were used to validate the simulation. Essentially, the details of the' Poincare map were used numerically to determine the periodicity of Duffing oscillator for spectrum of mass ratio at a constant step of 0.001. The time history, phase plots and the Poincare at mass ratio (µ), absorber parameters (αa), and amplitude of excitation (Fo) are in agreement with what is obtained in open literature. The chaotic response of the Duffing-Absorber system at αa= 1.1, Fo = 0.21: and, taken respectively. The Duffing and the absorber initial conditions to be (1.0,0.0) and (0.0, 0.0), this chaotic response was rendered periodic for some selected mass ratio (0≤µ≤1.0) Specifically, periods 1, 2 and 4 were obtained at µ= 0.208; these periodic responses were obtained at respective values αa=1.1, αa=I.7803 and αa= 1.7595. In this work, eighty percent of the mass ratio selected did ensure that the chaotic behaviour of the Duffing-Absorber system is rendered periodic. This work demonstrated the practical utility of vibration absorber as a chaotic oscillations control tool by the mass ratio approach; and having a recorded success of about eighty percent. "