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16 August 2001 Nonlinear control of plate vibrations
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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 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.
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Osama N. Ashour and Ali H. Nayfeh "Nonlinear control of plate vibrations", Proc. SPIE 4327, Smart Structures and Materials 2001: Smart Structures and Integrated Systems, (16 August 2001);

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