Active damping of nonstationary vibrations of a rectangular plate under impulse loading

Abstract

The behavior of a double-layer (metal-piezoceramics) rectangular plate under nonstationary electromechanical loading is studied. It is assumed that the mechanical load versus time law and the area of its application are specified. The electric signal applied to solid electrode coatings of the piezolayer reduces the amplitudes of mechanically induced vibrations of the plate. Two approaches to determining the profile of the electric signal are considered – the first is focused on minimizing the plate strained state, and the second approach deals with suppressing forced vibrations with an account of minimizing power input for forming a control action. The Kirchhoff-Love generalized hypotheses are used for simulating electromechanical vibrations. The boundary problem solution was derived using the Laplace integral transform in time and separation of variables. To assess the effectiveness of the approaches suggested, the plate vibrations were investigated when the piezolayer was in the direct piezoelectric effect mode. The numerical and analytical results were validated by comparison with finite element solutions. The paper also describes the method of solving the problem of restoring the time dependence of the mechanical load based on known values of the difference of potentials between open piezolayer electrodes, which occur due to bending vibrations of the bimorph plate.