THE EFFECT OF PURE SHEAR ON THE REFLECTION OF PLANE WAVES AT THE BOUNDARY OF AN ELASTIC HALF-SPACE

This paper is concerned with the eect of pure shear on the re ection from a plane boundary of innitesimal plane waves propagating in a half-space of incompressible isotropic elastic material. For a special class of constitutive laws it is shown that an incident plane harmonic wave propagating in the considered plane gives rise to a surface wave in addition to a re ected wave (with angle of re ection equal to the angle of incidence) although its amplitude may vanish at certain discrete angles but is independent of the state of deformation. Re ected wave amplitude is exactly equal to one in this case. For a second class of constitutive laws similar behavior is found for certain combinations of angle of incidence, material properties and de- formations, but additional possibilities also arise. In particular, there may be two re ected waves instead of one re ected wave and a surface wave. Here surface wave amplitude depends upon the pure shear and the re ected wave amplitude is not equal to one in general. The dependence of the amplitudes of the re ected, and surface waves on the angle of incidence, the states of deformation is illustrated graphi- cally.