Anisotropy and dispersion of elastic waves in periodically multilayered anisotropic media

Abstract

The propagation characteristics of elastic waves in general periodically multilayered media formed by alternate arrangement of two or more arbitrarily-anisotropic materials are comprehensively studied. Combining with the state-space formalism for obtaining the wave solutions to the constituent layers, the Floquet-Bloch theorem for providing the periodic relations between neighboring unit cells, the method of reverberation-ray matrix (MRRM) is employed to derive the general dispersion equations of the periodically multilayered anisotropic media. By solving the dispersion equations in cases of all possible sorts of wavenumber components, the complete anisotropic and dispersion characteristics of elastic waves can be provided. By numerical examples, the slowness and the phase velocity curves are provided to summarize the innovative anisotropic characteristics of elastic waves in three coordinate planes. The effects of the anisotropic parameters on the slowness/phase velocity curves have also been discussed. Moreover, all kinds of dispersion curves including the frequency-related and phase velocity-related curves along the directions perpendicular, parallel, and oblique to the layering are provided to reflect the general dispersion characteristics of elastic waves from various viewpoints. It is found that the innovative anisotropy characteristics of elastic waves in the periodically multilayered anisotropic media include that the slowness curves have periodicity in the thickness direction and the least positive period decreases with the increasing of frequency. As the frequency becomes big enough, the slowness/phase velocity curves show interactions between the modes within the overlapping neighboring periods. The common dispersion characteristics of elastic waves along various directions include the symmetry of wavenumber, the asymptotic of the wavelength and the phase velocity curves to the frequency lines corresponding to zero wavenumber, as well as the cutoff property of the phase velocities of the lowest three basis modes. The waves in oblique directions are special in that the mode transition and repulsion due to the zone folding effect of periodicity along thickness as well as the cutoff property of higher-than-third-order overtones along layering are simultaneously in effective.