Switching between coexisting stable periodic solutions by impulsive forces with an application to a vibrating plate

Single-degree-of-freedom nonlinear mechanical systems under periodic excitation may possess coexisting stable periodic solutions. Depending on the application, one of these stable periodic solutions is desired. We propose two algorithms to design an impulsive force that will bring the system from an undesired to a desired stable periodic solution. Both algorithms have a variant that requires only limited information about the applied force. We illustrate our method for a single-degree-of-freedom model of a rectangular plate with geometric nonlinearity, which takes the form of a monostable forced Duffing equation with hardening nonlinearity.