Distributed structural control using multilayered piezoelectric actuators

Equations of motion are developed for a multilayered symmetric beam consisting of a substructure and four added layers of piezoelectric material. Timoshenko beam theory is used to develop the equations. The external circuits to which the piezoelectric layers are connected are included in the model. The beam structure is modelled as a distributed parameter system, while the external circuit elements are discrete elements, therefore the resulting model is of the combined system. Additionally, the mechanical energy dissipation mechanisms within the structure as well as an external dissipation mechanism are included in the model.; The resulting system of partial differential equations of the combined system are cast in state space form. Using the Ritz-Galerkin method, the equations are also discretized. Two piezoelectric materials are evaluated in conjunction with using the external electronic circuits to add passive damping. Piezoceramic materials are shown to add significant amounts of passive damping in modes of the structure to which the external circuits are tuned.; Two rate feedback control laws designed to add active damping to the structure, the first limited to local feedback, and the second based on global feedback, are implemented numerically. The results show that giving the control forces applied to the beam a spatial variation with respect to the length of the beam, which can vary with time, yields damping ratios higher than similar control strategies where the spatial variation of the control forces is fixed with respect to time. The control strategies applied to the structure resulting in higher damping ratios in the higher modes. It was observed that the higher modes of a structure could achieve critical damping using the active control strategy presented here.