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. In this work, various reduced order finite element models for the prediction of passive reduction of structural vibration by means of shunted piezoelectric system are presented. The problem consists of an elastic structure with surface-mounted piezoelectric patches. The piezoelectric elements are connected with resonant shunt circuits in order to damp specific resonant frequencies of the structure. An efficient electromechanical finite element formulation for the dynamic analysis of the problem is first recalled. Different strategies to solve the problem using a modal reduction approach are then proposed. These strategies are based of the use of two original projection bases: (i) the combined basis formed by both the short-circuited and open-circuited modes, and (ii) the coupled basis formed by the electromechanical modes that take into account the effect of the inductances of the electrical shunts circuit. Various results are presented in order to validate and illustrate the efficiency of the proposed new finite element reduced order formulations.

NEW REDUCED ORDER FINITE ELEMENT FORMULATIONS FOR VIBRATION ATTENUATION USING PIEZOELECTRIC SHUNT DAMPING