Impulsive Steering Between Coexisting Stable Periodic Solutions With an Application to Vibrating Plates

Abstract

Single-degree-of-freedom (single-DOF) nonlinear mechanical systems under periodic excitation may possess multiple coexisting stable periodic solutions. Depending on the application, one of these stable periodic solutions is desired. In energy-harvesting applications, the large-amplitude periodic solutions are preferred, and in vibration reduction problems, the small-amplitude periodic solutions are desired. We propose a method to design an impulsive force that will bring the system from an undesired to a desired stable periodic solution, which 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.