Analysis of Floquet Waves in Periodic Multilayered Isotropic Media with the Method of Reverberation-Ray Matrix

The in-plane elastic waves in periodically multilayered isotropic structures, which are decoupled from the out-of-plane waves, represented mainly by frequency–wavenumber spectra and occasionally frequency–phase velocity as well being studied predominantly for periodic bi-layered media along perpendicular to thickness direction existing research. This paper investigates their comprehensive dispersion characteristics arbitrary directions entire (low high) frequency ranges, including frequency–wavelength, wavenumber–phase velocity, wavelength–phase spectra, surfaces slowness curves with fixed frequencies, spectra. Specially, completely reflect propagation of all directions. First, method reverberation-ray matrix (MRRM) combined Floquet theorem is extended derive equation general structures means elastodynamic theory materials state space formalism layers. correctness derivation numerical stability both low high particularly its superiority over transfer (MTM) within ranges near cutoff verified several examples. From these demonstrations octal- media, provided summarized. It found that although frequencies associated dimensionless wavenumber ql=nπ (n an integer) always demarcation between pass stop bands case incident wave, but this not exist oblique wave due coupling two modes waves. compared counterpart body infinite obtained Christoffel now have periodicity direction, consistent configuration structures. higher a smaller minimum positive period more properties additional modes.