To model piezoelectric porous materials, a new mathematical model is suggested which is a generalization of the model of the piezoelectric medium with damping properties and the Cowin - Nunziato model of elastic media with voids. In the new generalized Cowin - Nunziato model, the field functions of mechanical displacements, electric potential and function of the porosity change are considered. Based of this model, formulations of the generalized continual problems for piezoelectric bodies with voids or pores are obtained. For numerical analyses, obtained the finite element approximations and algorithms with symmetric saddle matrices are obtained. Using this model for piezoelectric bodies with voids or pores, the effective moduli of porous piezocomposite ceramics can be determined more precisely. The efficiency of the proposed model and finite-element approximations is verified by analyzing a focusing spherical device of porous piezoceramics emitting ultrasonic waves in a surrounding acoustic medium.
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