Dispersive waves in magneto-electro-elastic periodic waveguides

Magneto-electro-elastic (MEE) materials are attracting an increasing amount of scientific interest in physics, for their valuable potential in the functional management of mechanical-to-magnetoelectric energy conversions. The present paper focuses on heterogeneous MEE media - artfully realized by virtue of the periodic repetition of a multi-phase elementary cell - which represent promising solutions to passively control the propagation of multifield Bloch waves. Specifically, the linear continuum model governing the coupled free dynamics of a cellular non-dissipative MEE material is formulated for the unbounded three-dimensional domain. Then, the governing equations are specialized for a periodic layered waveguide with perfect inter-layer interfaces. The Floquet-Bloch decomposition is employed to analytically determine the uni-modular transfer matrix of the heterogeneous multi-layered cell. The related eigenproblem, governed by a palindromic characteristic polynomial in the Floquet multipliers, is solved in closed form to analyze the dispersion properties in the real-valued frequency domain and complex-valued wavenumber domain. Alternatively, a perturbation scheme is outlined to asymptotically approximate the exact eigensolutions. The dispersion spectra, composed of propagation and attenuation branches, are parametrically investigated for a two-layered periodic waveguide. The corresponding band structures are assessable a priori by leveraging the formal analogy with the stability analysis for non-autonomous dynamical systems. As main findings, slow-propagating quasi-shear-elastic waves and fast-propagating quasi-magneto-electric waves are found to dominate the low-frequency and high -frequency ranges, respectively, although some crossing points between the respective spectral branches can be detected. Quantitatively different but qualitatively similar behaviors of propagation and/or attenuation are observed for the quasi-shear-elastic waves and quasi-magneto-electric waves. Consequently, pass-pass, pass-stop and stop-stop bands of frequencies can be recognized and tuned by varying the key physical parameters. This rich spectral scenario opens the way for the functional customization of MEE-based metafilters or metapropagators, purposely designed to govern the transfer, localization, conversion, harvesting of energy across large frequency ranges.

Automated summary

This paper investigates the influence of heterogeneous multi-phase cells on the propagation of multifield Bloch waves in magneto-electro-elastic (MEE) materials. The dispersion properties are analyzed through analytical determination and perturbation methods. It is found that slow-propagating quasi-shear-elastic waves dominate the low-frequency range, while fast-propagating quasi-magneto-electric waves dominate the high-frequency range. The propagation and attenuation behaviors of these waves can be controlled by varying the physical parameters.