In the present work we analyze wave propagation in piezoelectric layered structures with special emphasis on semiconductor layered systems. The mathematical and physical formulation of the problem is stated according to the phenomenological theory of continuous media. The general solution of the system of equations for a piezoelectric material with cubic symmetry is given. The boundary conditions for mechanical displacements and elastic stresses, as well as the electrical quantities, are analyzed. The problem is split into two coupled system of second order ordinary differential equations: one for the displacement v1(z) and the electric potential ψ(z), and the other for the two remaining mechanical displacements v2(z) and v3(z). The dispersion relations are expressed through determinants because of their complexity, and the dispersion curves are numerically obtained. The obtained results, in the form of propagating waves along the structure, are discussed.
In this paper effective material properties of randomly distributed short fiber composites are calculated with a developed comprehensive tool for numerical homogenization. We focus on the influence of change in volume fraction and length/diameter aspect ratio of fibers. Two types of fiber alignments are considered: fiber orientations with arbitrary angles and parallel oriented fibers. The algorithm is based on a numerical homogenization technique using a unit cell model in connection with the finite element method. To generate the three-dimensional unit cell models with randomly distributed short cylindrical fibers, a modified random sequential adsorption algorithm is used, which we describe in detail. For verification of the algorithm and checking the influence of different parameters, unit cells with various fiber embeddings are created. Numerical results are also compared with those from analytical methods.
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