Passive structural vibration reduction by means of shunted piezoelectric patches is addressed in this article. The concept of topology optimization, based on the solid isotropic material with penalization method, is employed in this work to optimize, in terms of damping efficiency, the geometry of piezoelectric patches, as well as their placement on the host elastic structure. The proposed optimization procedure consists of distributing the piezoelectric material in such a way as to maximize the modal electromechanical coupling factor of the mechanical vibration mode to which the shunt is tuned. An original finite element formulation, suitable to any elastic structures with surface-mounted piezoelectric patches, is proposed to solve the electromechanical problem. Numerical examples validate and demonstrate the potential of the proposed approach for the design of piezoelectric shunt devices.
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