Elastodynamics. Linear theory

Description

This present volume (Volume II) of "Elastodynamics" is devoted to an exposition of the dynamical theory of linear isotropic elasticity. The plan and the scope of this treatise includes a thorough discussion of the fundamental theorems concerning elastodynamics and various mathematical methods of solutions and their applications to a class of problems in one, two, and three dimensions. The uniqueness and reciprocal theorems are presented and applied. The solutions by means of potentials, singular solutions, complex function technique, methods of integral equations, and integral transforms are explored. Free and forced vibrations of bodies, of finite and infinite extent, having boundaries that are plane, cylindrical (circular, elliptic), ellipsoidal, and spherical shapes are discussed in some detail. Both initial- and boundary-value problems, including displacement traction and mixed boundary conditions, are solved. The book closes with a chapter on diffraction theory. Various tables and graphs displaying frequencies, displacement, and stress fields should be useful to practitioners. Originally it was our intention to include accounts of anisotropic, imhomogeneous elastic, and thermoelastic solids, and lattice dynamics. Unfortunately, owing to length limitations, this project had to be abandoned.