Modal analysis of piezoelectric bodies with voids. I. Mathematical approaches

In the present paper the finite element method for the solution of the eigenvalue problems for piezoelectric bodies with voids is considered. The porosity change properties are taken into account according to Cowin-Nunziato model. The vector-matrix formulations of the modal piezoelectric problems for media with voids are given. The finite element approximations of the continual equations are carried out and the finite dimensional eigenvalue problems are obtained in the expanded and in the various reduced forms. Algorithmic features of the boundary conditions account for electrode surfaces and the surfaces contacting with rigid stamps are discussed. The finite element eigenvalue problems for practically important electric resonance and antiresonance frequencies are obtained. As a numerical example the focusing spherical ultrasonic piezoelectric emitter fulfilled from porous piezoceramics is considered. With the use of Cowin-Nunziato model the effective moduli of the porous piezoceramic material are defined precisely. The results, which we obtain, show a good optimal agreement with the experimental data. The resonant frequency behavior modelling for free and loaded on acoustic media piezoelectric transducer is realized. (C) 2009 Published by Elsevier Inc.