Keywords: coupled problems, piezoelectric bodies, voids, Cowin-Nunziato theory, acoustic loads, external electric circuits, finite element method, dynamic analysis.

In the present work for modelling piezoelectric porous materials and transducers a new mathematical model is suggested, which generalizes the model of the piezoelectric medium with damping properties and the Cowin-Nunziato model of the elastic medium with voids. Using this model for piezoelectric bodies with voids or pores, the effective moduli of porous piezocomposite ceramics can be defined more precisely.

In the new generalized Cowin-Nunziato model the field functions of mechanical displacements, electric potential and the function of the porosity changes are considered. On the basis of this model we have obtained the formulations for the generalized continual statements of piezoelectric bodies with voids or pores. For numerical analysis we have obtained the finite element approximations of the problems for piezoelectric bodies with voids in the expanded and reduced forms.

The finite element technologies for piezoelectric device modelling with acoustic loads and external electric circuits are also considered. Note that in this case for the coupled acousto-poro-piezoelectric problem we consider an acoustic medium with dissipation and obtain the coupled finite element systems with symmetric saddle matrices.

A set of algorithms, which use the symmetrical saddle matrices to create and solve the finite element (FE) equations, is proposed for static and dynamic acousto-poro-piezoelectric problems. Thus the Newmark method without velocity and acceleration node values is used for the step-by-step time integration scheme and a modified Cholesky decomposition method is used for a linear system solver. All procedures that we need in the FE manipulations (the degree of freedom rotations, mechanical and electric boundary condition settings, etc.) are provided in a symmetrical form. The FE evaluation of the natural frequencies of the compound electroelastic bodies with voids are investigated. The schemes presented use FE block matrices, where different matrix blocks are related to different field variables.

In this generalized Cowin-Nunziato model the more precise technique for effective moduli calculation of porous piezocomposites includes the following stages:

• Determination of the porous piezocomposite material characteristic by an effective moduli method from the finite element solutions of five special static piezoelectric problems for the representative volume of the 3-3 connectivity structure;
• Comparison of the basic characteristics determined from the calculated effective moduli with the corresponding values obtained from experiments and practical design formulae;
• Fitting the values of the material properties responsible for the change in porosity properties, minimizing the differences of the selected characteristic parameters of porous piezoceramics, obtained using the effective moduli method and as a result of the experimental data evaluation.

The efficiency of the proposed model and finite element approximations is verified using the analysis of a focusing spherical device from porous piezoceramics emitting ultrasonic waves in the surrounding acoustic medium.

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