DETERMINATION OF MACROSCOPIC ELECTROMECHANICAL CHARACTERISTICS OF 1-3 PIEZOCERAMIC POLYMER COMPOSITES BY A CONCENTRIC TUBE MODEL

An axisymmetric concentric tube model of a piezoelectric rod and a concentric elastic tube is used to characterize 1-3 piezoelectric/elastic composites macroscopically. The model is based on the following assumptions: the wavelength of mechanical waves is large compared to the distance between adjacent rods, displacements follow the separable static solutions for tubes, the electric field is constant, and displacements are continuous across the interface between the rod and the tube. With average displacements of and total forces on the surfaces as the mechanical degrees of freedom, and with charge and potential at the ends of the rod as the electrical degrees of freedom, the relation between the electromechanical degrees of freedom is given in matrix formulation. The formulation resembles the use of element stiffness matrices in the finite element method. A recursive numerical scheme for combining the matrix for the tube and the piezoelectric rod into one for the composite piezoelectric rod is used to directly identify the majority of the e-set of constitutive constants for 1-3 composites. The remaining constitutive constants are estimated from a cubes model, to allow inversion of the d-g-, and h-sets and calculation of other characteristics.