Active Vibration Control for A Bilinear System with Nonlinear Velocity Time-delayed Feedback

The primary resonance, stability and design methodology of a piecewise bilinear system under cubic velocity feedback control with a designed time delay are investigated. Through combining multi-scale perturbation method with Fourier expansion, the effects of time delay on dynamics behaviours are explored. Subsequently, the linearization of average equations obtained from analytical multi-scale method is applied to obtain the corresponding characteristic function, and thus stability boundaries can be determined. In order to obtain the desired vibration control performance, appropriate gain and time delay of feedback are chosen based on the frequency response function and stability conditions. Lastly, the assessment of the influences of the feedback parameters on vibration transmissibility is given. Results show that both feedback gain and time delay are significant factors for altering dynamics behaviours and improving effectiveness of controller.