This study revealed the wave behavior of SH waves when the magnetic path is closed or opened, providing important implications for understanding the propagation rules and applications of SH waves in periodically structured systems. On the other hand, [PERSON] et al. [10] studied the propagation of SH waves in occasionally layered piezoelectric materials based on a perfect alternate structure of piezoelectric films and polymer films. They obtained the phase velocity equation, discussing the filtering effect of this structure and the impact of volume fraction and shear modulus ratio of piezoelectric layers and polymer layers on the phase velocity. This study provides important insights for designing new piezoelectric phonon crystal devices. [PERSON] et al. [11] studied the propagation of elastic waves in a phonon crystal containing piezoelectric and magnetic encapsulation bodies based on magnetic-electric elastic coupling while regarding the electric and magnetic fields as quasi-static. Their research has significant value for piezoelectric/piezomagnetic composite materials in microwave technology, promoting a deeper understanding of the properties of this composite material and its applications in related fields. Electromagnetic composite materials have multiple properties that have received extensive attention in electromagnetic fields. In recent decades, many scholars have dedicated themselves to studying electromagnetic composite materials' mechanical and electrical properties. For example, [PERSON] et al. [12] studied the problem of an infinite two-dimensional anisotropic piezoelectric-piezomagnetic medium containing elliptical pores. Subsequently, [PERSON] et al. [13] extended this method to the free vibration problem of an infinite-length anisotropic-supported piezoelectric-piezomagnetic laminate and provided numerical examples for a single-layer piezoelectric plate, a two-layer piezoelectric-piezomagnetic laminate, and a four-layer piezoelectric-piezomagnetic laminate. [PERSON] et al. [14] solved the problem of a three-dimensional anisotropic functional gradient piezoelectric-piezomagnetic rectangular laminate under the combined action of mechanical and electrical loads. They applied the variational principle to transform the problem of combined mechanical and electrical loads into an individual load problem. These research results provide necessary theoretical support for applying electromagnetic composite materials. In elastic dynamics, various mathematical methods are employed to study the propagation of SH waves. [PERSON] et al. [15] utilized the stiffness matrix method and the transmission matrix method to investigate the transmission of SH waves through infinite/semi-infinite piezoelectric/piezoelectric and periodic composite materials. [PERSON] et al. [16]studied the propagation of SH waves through piezoelectric/piezomagnetic plates using constant differential equations and the stiffness matrix method. They discussed the impact of film thickness on the phase, group, and first-mode magnetic-mechanical coupling factor. [PERSON] et al. [17] employed the coupled stress elastic indeterminacy theory to investigate the mechanical behavior of materials. They obtained the global solution for crack problems through integral transformation and the Wiener-Hopf technique. [PERSON] et al. [18] used complex and potential functions to study the scattering of plane harmonic waves via multiple elliptical cavities in a water-saturated soil medium. [PERSON] et al. [19] proposed a double orthogonal polynomial series method, which can be used to design and optimize multi-layer piezoelectric voltage-magnetic material transducers. Lamb waves and surface waves hold great importance in research as unique waves. [PERSON] et al. [20] studied the propagation of Lamb waves in a functional gradient piezoelectric-piezomagnetic material plate, considering the continuous change in material parameters along the thickness direction.