Complete dispersion characteristics of elastic waves in periodically multilayered arbitrarily-anisotropic media

Abstract

In the previous researches, the dispersion property of periodically layered media (PLM) is mainly represented by the frequency-wavenumber spectra. Here this paper studies the complete dispersion characteristics of elastic waves along arbitrary direction in space in periodically layered arbitrarily-anisotropic media (PLAM) by the comprehensive frequency-related dispersion surfaces and their profiles. The present model deems that the wave components in the thickness and layering directions are both variable quantities and considers their interrelation effect. For obtaining the general propagation characteristics of Floquet-Bloch waves, firstly the partial waves in the constituent layers of triclinic materials are described by the state-space formalism. Secondly, considering the traveling within the constituent layers, the multiple scattering at the interfaces and the periodicity across the unit cell of these partial waves, the dispersion equation is derived by the method of reverberation-ray matrix (MRRM), which is further solved by the golden section and bisection methods in combination. Finally, numerical examples are provided to verify the analysis method and to illustrate the comprehensive frequency-related dispersion surfaces and their profiles on four typical sections. On the basis of these numerical results, the general and complete band and dispersion characteristics of the Floquet-Bloch waves in general PLAM are summarized in detail. It is discovered that with respect to the thickness-directed components of wave quantities, the dispersion surfaces and curves reflect the band characteristic of Floquet-Bloch waves on the frequency axis due to the repeated configuration (periodic condition) along the thickness, and the wave repulsion between neighboring orders of modes and the wave coupling between different kinds of modes (Primary and Shear modes) generally contribute to the formation of frequency bands. It is also found that with respect to the layering-directed components of wave quantities, the dispersion surfaces and curves indicate the cutoff property and the continuously-propagating characteristic of Floquet-Bloch waves as the frequency below and above the cutoff frequencies, respectively, which are caused separately by the multiple scattering of waves at interfaces and by the wave conversion between neighboring orders of modes subjected to the Snell’s law due to infinitely expanding configuration along the layering.