Vibration Control for Liènard Systems

Abstract

Self-excitations can be dangerous in many nonlinear systems and can produce catastrophic failures, that is a sudden and complete failure that cannot be put right. We extend the nonlocal vibration control to the suppression of the self-excited vibrations of the Liènard system. We introduce a non local control force that yields a third order non-linear differential equation and use a nonlocal active control to mitigate the amplitude peak in the self-excitations. The nonlocal parameters can be carefully adjusted, in order to avoid undesirable behavior and dynamical nonlinear excitations.  We consider the effects of changing the nonlocal parameters on the stability and the value of the response of the system under control. We demonstrate that our method can successfully improve the self-excitation active control, studying a Liènard system through the (AP) asymptotic reduction method. A nonlocal force can be used to suppress self-excitations and put under control the oscillator behavior.