The existence of pure surface modes in elastic materials with orthorhombic symmetry

A pure surface mode in a semi-infinite elastic body with a traction-free boundary is a progressive harmonic surface wave in which the displacement is everywhere co-planar with the wave and surface normals. When the elastic material has orthorhombic symmetry, with one of the 2-fold symmetry axes normal to the bounding plane, there are generally only two directions in which a pure surface mode may propagate, but additional directions appear when the transmitting material has higher symmetry. It is shown that for all the possibilities arising in this way the positive definiteness of the strain energy is a sufficient condition for the existence of a unique pure surface mode. The properties of pure modes in elastic materials belonging to the orthorhombic, tetragonal, hexagonal and cubic systems are discussed with particular reference to conditions under which the motion has the same features as a Rayleigh wave.