On the reflection of elastic waves incident on the boundary of a diatomic half-space (Q1098667)

The paper examines reflection of a plane longitudinal wave incident upon the surface of a half-infinite space the material of which is elastic, and the particles include two atoms of different thermomechanical properties. After establishing the constitutive equations of the constituents, equations of motion are solved by appeal to four quasi- potential functions. Satisfaction of the boundary conditions yields the characteristic equations of the problem which - in contrast to the conventional case, and in agreement with observations - indicates dispersion of waves. An example involving relaxed bonds between the constituents is examined and illustrated by graphs.