High-frequency Rayleigh waves in materials with micro-structure and couple-stress effects

A well-known deficiency of the classical theory of elasticity is that it does not predict dispersive Rayleigh-wave motions at any frequency. This contradicts experimental data and predictions of the discrete particle theory (atomic-lattice approach) for high frequencies. The present work is intended to explore whether the elastic couple-stress theory with micro-structure can overcome the deficiency of the classical theory. Our analysis shows indeed that Rayleigh waves propagating along the surface of a half-space are dispersive at high frequencies, a result that can be useful in applications of high-frequency surface waves where the wavelength is often of the micron order. Provided that certain relations hold between the various micro-structure parameters entering the theory employed here, the dispersion curves of these waves have the same form as that given by previous analyses based on the atomic-lattice theory. In this way, the present analysis gives means to obtain estimates for micro-structure parameters of the couple-stress theory. Besides the Rayleigh-wave results reported here, basic theoretical results for the kinetic energy and momentum balance laws in micro-structured media with couple-stress effects are derived and presented.