Nonlinear control of plate vibrations

A nonlinear active vibration absorber to control the vibrations of plates is investigated. The absorber is based on the saturation phenomenon associated with dynamical systems with quadratic nonlinearities and a two-to-one internal resonance. The technique is implemented by coupling a second-order controller with the plate's response through a sensor and an actuator. Energy is exchanged between the primary structure and the controller and, near resonance, the plate's response saturates to a small value. Numerical results are presented for a cantilever rectangular plate. Modal analysis is used to solve for the plate displacement. Finite-element methods are used to extract the eigenmodes of the system. A numerical study is conducted to optimize the location of the actuators on the structure to maximize its controllability. In this regard, the control gain is maximized for the PZT actuators. Furthermore, a more general method is introduced, which is based on a global measure of controllability for linear systems.