The book is concerned with the theory of transverse isotropic elastic wave propagation within the framework of the linear theory. The author studies transient wave motion in two and three-dimensional unbounded and semibounded solids for which explicit exact results can be derived.
In chapter 1 the elasto-dynamic basic equations are given and the range of variation of the elasticity constants is examined for transversely isotropic materials (hexagonal crystals) under the condition of hyperbolicity, i.e. the possibility of wave motion. Chapter 2 is devoted to the wave front due to a point source which lends itself to a solution in the form of an envelope to a plane wave solution of the characteristic differential equation of the system. The conditions on the elasticity parameters which insure the existence of inflection points on the slowness curve are derived, leading to a classification of the wave front shape and to other propagational phenomena. In chapter 3 an explicit solution for the two-dimensional anisotropic elastic wave Green tensor based on integral transform methods is obtained. Further the gaps in the wave field behind the leading front are investigated. For the three- dimensional case explicit results are given along the symmetry axis. In chapter 4 the surface motion problem of a point loaded two-dimensional halfspace (Lamb’s problem) is completely solved for the full range of hexagonal crystals. The corresponding three-dimensional problem is treated in chapter 5 where the epicenter motion due to the sudden application of a (buried or surface) point load is considered.
The book is written from the viewpoint of the applied mathematician and is of interest for scientists and engineers in crystal acoustics, crystal optics, magnetogasdynamics, dislocation theory, seismology ad fibre wound composites. It is an up to date monograph based on the author’s and other contributions and distinguished by a concise, clear and exhausting representation. Detailed studies are facilitated by numerous references.