The propagation of shear horizontal surface acoustic waves (SHSAWs) in an inhomogeneous magnetoelectro-elastic (MEE) half-space with 6-mm symmetry is studied. By virtue of both the direct approach and Strohformalism, the dispersion relations corresponding to two general cases of material properties variation are obtained. In the first case, it is assumed that all material properties involving the MEE properties and density vary similarly in depth, whereas, the second case considers identical variation for the MEE properties, which differs from the variation of the density. The non-dispersive SHSAW velocities pertinent to the homogeneous MEE media are obtained under eight different surface electromagnetic boundary conditions as the limiting cases of the current study. The dispersion curves corresponding to eleven inhomogeneity profiles of practical importance are presented in an effective dimensionless format, and the effects of different types of inhomogeneity functions describing the composition of the functionally graded magneto-electro-elastic (FGMEE) half-space on the dispersion relation are discussed.

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Classical continuum theory (CCT) provides a mathematical model to study the mechanical response of materials under external effects. In the context of CCT, there is no material length scale, and a solid body is sub-dividable into an infinitesimal element with the same behavior as the bulk material, disregarding the fact that all materials are made of building blocks and have microstructures in different length scales. The lack of material characteristic length-scale in CCT prevents it from recognizing any size-effect. Additionally, even order material property tensors associated with this theory can only characterize the centrosymmetric behavior

Propagation of shear horizontal surface acoustic waves (SHSAWs) within a functionally graded magneto-electro-elastic (FGMEE) half-space was previously presented (Shodja HM, Eskandari S, Eskandari M. J. Eng. Math. 2015, 1–18) In contrast, the current paper considers propagation of SHSAWs in a medium consisting of an FGMEE layer perfectly bonded to a homogeneous MEE substrate. When the FGMEE layer is described by some special inhomogeneity functions – all the MEE properties have the same variation in depth which may or may not be identical to that of the density – we obtain the exact closed-form solution for the MEE fields. Additionally, certain special inhomogeneity functions with monotonically decreasing bulk shear wave velocity in depth are considered, and the associated boundary value problem is solved using power series solution. This problem in the limit as the layer thickness goes to infinity collapses to an FGMEE half-space with decreasing bulk shear wave velocity in depth. It is shown that in such a medium SHSAW does not propagate. Using power series solution we can afford to consider some FGMEE layers of practical importance, where the composition of the MEE obeys a prescribed volume fraction variation. The dispersive behavior of SHSAWs in the presence of such layers is also examined.