A one-dimensional theory is developed for modeling the analysis of beams containing piezoelectric sensors and actuators. The equations of motion and associated boundary conditions are derived for the vibrations of piezoelectrically sensored/actuated beams. The effect of coupling between longitudinal deflection and bending deflection is investigated. For the practical applications, in accordance with the proposed beam theory, a one-dimensional finite element formulation is presented. The proposed beam theory as well as the finite element approach can easily be used in developing a formal two-dimensional theory for piezoelectrically actuated composite plates and shells or other physical systems.
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