Lattice vibrational waves in cubic crystal plates

Abstract

An investigation is given of the lowest symmetric (extensional) and the lowest antisymmetric (flexural) mode of waves in a cubic crystal plate bounded by two planes of symmetry. The investigation was carried out using the continuum theory of anisotropic elasticity, and also using a simple cubic lattice model. Particular attention was given to the change of the character of both the extensional and flexural mode, which takes place as the wave length is decreased from infinity down to values of the order of the plate thickness. Both modes tend to become surface modes whenever surface waves are possible along the direction of propagation. However, some essential differences were observed, regarding this transition from bulk modes to surface modes, between materials which propagate Rayleigh surface waves and those which propagate generalized Rayleigh surface waves. © 1965 Springer-Verlag.