Jerk Dynamics and Vibration Control for the parametrically excited van der Pol system

Abstract

In parametrically excited van der Pol system, dangerous vibrations can be controlled and governed by Jerk dynamics. We choose a non-local force for the vibration control and a third or-der nonlinear differential equation (jerk dynamics) is necessary for the control method implementation. Two slow flow equations on the amplitude and phase of the response describe the oscillator motion and we are able to check the control strategy performance. The stability and response of the system is connected to the feedback gains. The dangerous excitations amplitude peak can be reduced adequately picking feedback gains. The new method is successfully checked by numerical simulation