A finite element algorithm for solution of the natural vibration problem of electroelastic bodies with passive external electric circuits, interacting with a quiescent fluid

Abstract

In this paper we consider a mathematical statement of the problem on natural vibrations of piecewise-homogeneous electroelastic bodies with passive external electric circuits (shunting circuits) of arbitrary configuration and interacting with a quiescent fluid. The behavior of the piezoelectric body is described using the equations of electrodynamics of deformable electroelastic media in the quasi-static approximation. The motion of an ideal fluid in the case of small perturbations is considered within the framework of the acoustic approximation. Small strains in a thin plate are determined using the Reissner – Mindlin theory. The numerical solution is developed using the finite element method. The proposed algorithm is based on the approach, in which the global stiffness matrix generated with the aid of the ANSYS software package is decomposed into required constituents. The system of governing equations is constructed using the developed algorithm, which is realized in the FORTRAN language. Complex eigenvalues of the examined system are defined from the solution of the non-classic modal problem using the Mueller method. A thin plate with piezoelectric element located on the free surface of a layer of a quiescent fluid of finite size is considered as an example.