Enhanced vibration control using non-reciprocal piezoelectric beam having sensing and actuating bimorph: Spectral element formulation

Abstract

A unique strategy of low-frequency wideband vibration control by harnessing the concept of feedback control between the piezoelectric bimorph sub-cells which are acting as sensors and actuators is conceptualized in this paper. In the unit cell, voltages from the sensing bimorph are fed back to actuate another bimorph through operational amplifier-based gain circuits. The prime novelty of the paper is the non-trivial formulation of the spectral element of the non-reciprocal piezoelectric beam (NRPB), having electro-mechanically coupled sensing and actuating bimorph in the unit cell, derived from the exact solution of the governing differential equations. The analytical formulation employing the spectral element method enables the elementary assembling of the NRPB units to simulate different boundary conditions and various configurations arising due to the alteration of the position of the sensing and actuating bimorph. The direct frequency responses for various configurations are obtained for a cantilevered and a simply-supported beam with varying feedback gain. The feedback gain induced damping to the system, hence sharp peaks and drops are flattened. Most promisingly, the amplitude of the displacement response for the entire frequency range can be brought down below its corresponding static deformation with the application of positive gain for certain configurations. Hence, the proposed system could potentially be used for application in the field of vibration and acoustics.