Optimal Placement of Piezoelectric Element on a Plate Interacting With a Fluid Layer

Abstract

In this paper, we determine the optimal location of the piezoelectric element on the upper surface of a plate, interacting with a layer of a quiescent fluid of finite size. As a quantity, allowing us to evaluate the operating efficiency of a piezoelectric element in damping a single specified mode of structure vibrations, we take the electromechanical coupling coefficient. It is calculated based on the values of the natural frequencies of the system, obtained for the two characteristic performance modes of an electric circuit (open and short circuit modes). The behavior of the piezoelectric element is described by the equations of electrodynamics of deformable electroelastic media in the framework of the quasi-static approximation. The motion of an ideal fluid in the case of small perturbations is considered in the framework of the acoustic approximation. Small strains in a thin plate are determined using the Reissner – Mindlin theory. The numerical implementation of the problem is carried out using the finite element method. The obtained results made it possible to identify situations, where the optimal location of the piezoelectric element can be determined without considering the effect of the fluid.

Keywords: natural vibrations, ideal fluid, optimization and finite element method