INTERFACIAL WAVES IN AN INEXTENSIBLE ELASTIC COMPOSITE

The composite considered here is formed by welding together two semi-i nfinite bodies, made of different transversely isotropic elastic mater ials, each inextensible along the symmetry axis. It is known from prev ious work that a small-amplitude wave can propagate along the plane in terface only when the directions of inextensibility in the constituent bodies coincide. The case chosen for detailed study in the present pa per is that in which the common direction is parallel to the interface : this is mathematically the simplest and physically the most interest ing situation. The secular equation governing the speed of propagation is derived and reformulated by a matrix method which yields a necessa ry and sufficient condition for the existence of an interfacial wave a nd a proof that whenever such a wave exists it is unique. The domain o f existence of interfacial waves is seven-dimensional, the coordinates being the angle between the directions of propagation and inextensibi lity and six dimensionless combinations of the material constants. Fou r of the combinations relate to one of the constituent materials and t he others to both. The bimaterial combinations and the quotient of two of the others effectively control the set of directions in which an i nterfacial wave can travel. Some representative cases are discussed nu merically.