Driving Trajectories of Multistable Systems to Desirable Modes with Parametric Excitations

In this work, switching of vibrations between different modes of a class of multistable systems with parametric excitations is studied. An intermittent control method without altering the underlying dynamics of the system or its coexisting attractors is proposed. When an orbit meets a proximity constraint with the desired orbit, the control action is applied intermittently in the time domain. This control input is operated by perturbing one of the attractors with an impulsive force, thereby switching the system response to the other attractor. The stability of the method is analyzed theoretically, and its effectiveness is verified by numerical results. Additionally, the influences of neighborhood boundary on the amplitude and duration of control inputs in unconstrained and constrained intermittent control methods are also analyzed.