Resonance, stability and chaotic vibration of a quarter-car vehicle model with time-delay feedback

This paper examines dynamical behavior of a nonlinear oscillator with a symmetric potential that models a quarter-car forced by the road profile. The primary, superharmonic and subharmonic resonances of a harmonically excited nonlinear quarter-car model with linear time delayed active control are investigated. The method of multiple scales is utilized to obtain first order approximation of response. We focus on the influence of delay in the system. This naturally gives rise to a delay deferential equation (DDE) model of the system. The effect of time delay and feedback gains of the steady state responses of primary, superharmonic and subharmonic resonances are investigated. By means of Melnikov technique, necessary condition for onset of chaos resulting from homoclinic bifurcation is derived analytically. We describe a method to identify the critical forcing function and time delay above which the system becomes unstable. It is found that proper selection of time-delay shows optimum dynamical behavior. The accuracy of the method is obtained from the fractal basin boundaries.