In this thesis, two-dimensional waves of finite amplitude inelastic materials of harmonic type are considered. After specializingthe basic equations of finite elasticity to these materials,attention is restricted to plane motions and a new representationtheorem (analogous to the theorem of Lamé in classical linearelasticity) for the displacements in terms of two potentials is derived.
The two-dimensional problem of the reflection of an obliquelyincident periodic wave from the free surface of a half-space composedof an elastic material of harmonic type is formulated. The incidentwave is a member of a special class of exact one-dimensional solutionsof the nonlinear equations for elastic materials of harmonictype, and reduces upon linearization to the classical periodic "shearwave" of the linear theory.
A perturbation procedure for the construction of an approximate solution of the reflection problem, for the case where the incident wave is of small but finite amplitude, is constructed. Theprocedure involves series expansions in powers of the ration of the amplitude to the wavelength of the incident wave and is of the so-calledtwo-variable type. The perturbation scheme is carried farenough to determine the second-order corrections to the linearized theory.
A summary of results for the reflection problem is provided,in which nonlinear effects on the reflection pattern, on the particledisplacements at the free surface and on the behavior at large depthin the half-space are detailed.
