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The ability of a single piezoelectric patch with a single negative capacitance shunt for the multimodal vibration damping is used in this work to drastically reduce the acoustic radiation of a vibrating plate. With a geometry fixed, the elastic properties can be controlled using the resistance and the negative capacitance of the shunt: using a value of the negative capacitance close to the instability domain of the circuit, the stiffness can be placed in the softening region of the system, while the resistance tunes both the stiffness and losses. By means of an optimal design, several modes with non-zero electromechanical coupling factors can be simultaneously damped. As a consequence at these frequencies the acoustic radiation of the plate is drastically decreased. The results open prospects to tackle the vibration and acoustic problems in an industrial context.

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