## 1 Introduction
[17] employed the dipole strain gradient elasticity theory and fractional derivatives to study thermal shock problems. The influence of the Lorentz force induced by an external magnetic field on the propagation of elastic waves has significant theoretical and practical value for understanding and controlling the wave behavior. In 1963, [PERSON] and [PERSON] [18] approached this problem by combining the linear elastic theory with linearized electromagnetic theory, analyzing the motion of plane waves in a uniform static magnetic field and examining the vibration of a free infinite elastic plate under the influence of Lorentz forces. In 1966, [PERSON] and [PERSON] [19] studied the propagation of elastic waves in uniform electromagnetic solids, by focusing on the reflection and transmission of magnetoelastic shear waves under three different initial stress states. In 1988, [PERSON] and [PERSON] [20] utilized [PERSON]'s electromagnetic theory to investigate the propagation of elastic waves in a uniformly isotropic electroelastic half-space. In 1996, [PERSON] et al. [21] considered the modulation effect of external magnetic fields and studied the propagation of elastic waves in electromagnetic and thermal elastic half-spaces. In 1990, [PERSON] et al. [22; 23] investigated the reflection and transmission of magnetoelastic transverse waves in self-enhancing media. Since the late 20 th century, the mechanics of electromagnetic elastic solids have been studied more widely and extensively. In 2002, [PERSON] et al. [24] derived a solution for the free vibration of linearly anisotropic, electromagnetic elastic multilayer rectangular plates. In 2003, [PERSON] [25] applied the finite element method to study the free vibration problem in solid magnetoelectric cylinders. In the same year, [PERSON] et al. [26] used the state vector analysis method to study the free-vibration problem of multilayer magnetoelectric elastic plates, and their calculation results were consistent with those of [PERSON] et al. [24]. Control of elastic wave propagation by an external magnetic field has significant theoretical and practical value; thus, the effect of an externally applied magnetic field on the propagation of elastic waves in conductive solids has received widespread attention. For example, between 2006 and 2010, [PERSON] et al. [27; 28; 29] studied the reflection of waves in electromagnetic thermoelastic solids by introducing the Lorentz force and applying generalized thermoelastic theory. Based on the research of [PERSON] [30], in 2007, [PERSON] et al. [31; 32] applied the space state vector and transfer matrix method to derive the dispersion equation in electromagnetic elastic solids and studied the reflection and transmission problems of elastic waves in multilayer electromagnetic elastic structures. In 2015, [PERSON] et al. [33, 34] applied viscoelastic theory and generalized thermoelastic theory, introduced the Lorentz force, and studied the reflection and transmission problems of SH waves at the interface of two inhomogeneous viscoelastic solids. In 2018, [PERSON] et al. [35] applied the fractional order theory and generalized thermoelastic theory, introduced the Lorentz force, and investigated the two-dimensional electromagnetic-thermal elasticity coupling problem. Recent research on the influence of an external magnetic field on the propagation of elastic waves by introducing the Lorentz force includes the work of [PERSON] et al. [36] in 2020, who considered prestresses and studied the propagation problem of plane waves in thermoelastic half-spaces with temperature and porosity. [PERSON] [37] utilized the Lord-Shulman generalized thermoelastic theory to derive a controlling equation for rotating orthogonal anisotropic magnetothermal elastic half-spaces and studied the reflection problem of elastic waves on stress-free adiabatic surfaces. [PERSON] et al. [38] discussed various reflection wave propagation characteristics in semi-infinite, uniform, and isotropic magnetothermal elastic media. In 2023, [PERSON] et al.