This article investigates the propagation behaviour of horizontally polarized shear waves in a layered composite structure. In the considered model, a functionally graded piezoelectric material layer is sandwiched between corrugated piezomagnetic layer and elastic substrate. Method of separation of variables is used to obtain the displacement components in all three mediums. Dispersion relation has been established in the determinant form for the two cases, magneto-electrically open case and magneto-electrically short case. Effects of material gradient (of functionally graded piezoelectric material layer), corrugation parameters and layer width are distinctly marked and represented graphically. This study finds its application towards manufacturing and optimization of piezoelectric sensors and transducers. Also, the obtained result may be utilized for acquiring a better performance in surface acoustic wave devices.