Characterization of Acoustic Waves in Multi-Layered Structures

The work is devoted to the modeling of acoustic waves in multi-layered structures surrounded by a fluid and consisting of different kinds of materials including piezoelectric materials and composite multilayers. It consists of three parts. The first part describes the modeling of an acoustic sensor by the finite element method. The existence and uniqueness of a time-harmonic solution are rigorously established under physically appropriate assumptions. The convergence of Ritz-Galerkin solutions to the exact solution is proved. The second part of the work describes a semi-analytical method for the fast calculation of dispersion relations for plane acoustic waves in multi-layered structures. The software implementing this approach is presented. The third part investigates a number of issues of the homogenization theory for linear systems of elasticity. The limiting equations are rigorously derived by the two-scale method and an error estimate is established. For the case of laminated structures, an explicit formula for the elasticity tensor of the homogenized material is derived.