Numerical techniques for wave propagation and scattering problems associated with anisotropic composites

The interaction of waves with anisotropic media is studied using numerical analysis. Two numerical techniques are developed and discussed. The first one is the hybrid finite element - T-matrix method for computing the far-field scattering response of elastic waves scattered by a single anisotropic scatterer embedded in an elastic medium. The internal fields within the boundary are computed by the finite element technique. The external fields are expanded by the wave function solution. With the use of the integral representation, a T-matrix is formulated. The hybrid method retains the most efficient characteristics of finite element method and T-matrix method for computation of the scattering problems. The validity of this method has been verified by comparing results for a spherical scatterer with calculations from exact analysis. Excellent agreement is shown.;The second technique is the finite element - eigenmode expansion method for computing the transmission and reflection characteristics of acoustic waves normally incident on a piezoelectric composite thin slab. Floquet modes are used to express the periodic field distributing in the infinite fluid medium. The composite slab is characterized by using the finite element analysis. A typical forced vibration problem is formulated by considering the pressure field as the exciting force acting on the slab. The advantages of the method are that the details of the modal information are given and the damping of the system is included in the computation. The reliability and validity of this technique is confirmed by comparison with the calculations from the exact solution. Exact agreement is found between the numerical results and the physical interpretation.;The possibility of the extension of both techniques to piezoelectric material problem has been suggested. It is concluded that these new approaches offer versatile analytical models for studying (1) the far-field scattering response of a single piezoelectric scatterer in elastic medium, and (2) the transmission and reflection characteristics of piezoelectric composites in fluid.