genehmigten Dissertation.

The work is devoted to the modeling of acoustic waves in multi-layered structures sur-rounded 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 assump-tions. It is shown that the elimination of nonzero eigenvalues of the arising Helmholtz-like system can be achieved by introducing an additional term that causes the damping effect near the boundary. We also establish the well-posedness of the discretized problem and the convergence of Ritz-Galerkin solutions to the solution of the exact problem. Besides, we derive a domain decomposition schema for the numerical treatment of the problem. Finally, the results of 3D simulations are presented. The second part of the work presents a semi-analytical method for the fast character-ization of plane acoustic waves in multi-layered structures. The method identifies plane waves that can possibly exist in a given structure, determines their velocities, and com