SH wave propagation along a periodic grating surface with grooves in a magneto-electro-elastic substrate

This paper investigates the shear horizontal wave (SH wave) propagation along the periodic grating surface with grooves in a magneto-electro-elastic (MEE) substrate. The theoretical derivation is given for an arbitrary surface profile. Based on the Bloch-Floquet theorem and by using the Taylor-Mclaurin's series as well as the orthogonality condition of the wave modes, the mechanical, electric and magnetic boundary conditions at the profile surface are first transformed into the equivalent boundary conditions at the reference surface, and then further converted into an infinite set of linear homogeneous equations, whose determinant determines the dispersion relation. In the numerical examples, rectangular grooves are considered and the coupled-mode approximation is applied for truncating the infinite series. Numerical examples are presented for a magneto-electro-elastic (80% PZT4 and 20% CoFe2O4) composite. The results show that a band-gap occurs at the resonance frequency. With the increase of the wave-number, both the frequency and the wave velocity are reduced.