MATHEMATICAL-MODELING OF WAVE-PROPAGATION IN ANISOTROPIC MEDIA

A generally anisotropic (21 constants) plate of infinite extent immersed in two fluid half-spaces is subjected to an infinite harmonic longitudinal plane wave of arbitrary frequency originating in the upper fluid half-space and propagating at an arbitrary angle of incidence. The mathematical modeling of the interaction between the plate and the incident wave gives rise to an analytical expression for each of the reflection (R) and the transmission (T) coefficients. The displacement fields in the fluid half-spaces and the plate are fully described, and therefore all stresses and strains are known. Graphs of \R\ and \T\ vs. frequency are presented. Consequently, lamb-like modes can be identified equally through the investigation of either R or T. The conservation of energy principle (\R\2 + \T\2 = 1) is verified graphically. Also, slowness curves corresponding to different rotations of the plate elastic tensor for quasi-longitudinal and quasishear waves are presented. This study is very general in nature and can be easily specialized to particular cases of geometries and wave propagations. The numerical analysis was done through the use of VAXIMA/MACSYMA-a symbolic computation software package permitting parametric study of otherwise intractable mathematical expressions.