## 3 Reflection of Elastic Wave  
Contrary to traditional interface conditions, for the microstructure solids considered in this paper, the continuous interface conditions are expressed respectively, indicating that the displacement, normal displacement gradient, monopole force, and dipole force are continuous at the interface. Clearly, these interface conditions are entirely different from those of the classical elastic solids. In this case, because the region above the boundary is a vacuum and is under the influence of an external magnetic field, the interface conditions can be expressed as  
\[\mathbf{P}+\mathbf{\eta}=0, \tag{27a}\] \[\mathbf{R}=0, \tag{27b}\]  
where \(\mathbf{P}\) represents the unipolar force, and \(\mathbf{R}\) represents the dipole force. Owing to the perturbation in the external magnetic field, expressed as \(\mathbf{H}=H_{0}\mathbf{e}_{z}\), and the induced magnetic field, symbolized as \(\mathbf{h}=(-H_{0}\
abla\cdot\mathbf{u})\mathbf{e}_{z}\), according to [PERSON]'s equation, and as depicted in Figure 1, the Maxwell stress tensor can be reformulated as  
\[\eta_{yy}=\mu_{0}\big{(}H_{y}h_{y}+H_{y}h_{y}-H_{y}h_{y}\big{)}=0,\ \eta_{yx}=\mu_{0}\big{(}H_{y}h_{x}+H_{x}h_{y}\big{)}=0,\ \eta_{yz}=\mu_{0}\big{(}H_{y}h_{z}+H_{z}h_{y}\big{)}=0, \tag{28}\]  
in essence, Maxwell stress vanishes at the boundary. When an incident wave strikes the interface, four distinct types of reflected waves emerge in the elastic medium, as depicted in Figure 1, namely reflected P wave, reflected SV wave, reflected P-type surface waves (i.e., SP waves), and reflected S-type surface waves (i.e., SS waves). Based on [PERSON]'s law, the apparent wave numbers for all waves, both the incident and reflected, remained consistent at the interface. Specifically, they are equal to  
\[\sigma_{SV}\sin\beta_{1}=\sigma_{P}\sin\beta_{2}=\xi, \tag{29}\]  
\(\beta_{i}(i=1,2)\) signifies the incidence and reflection angles of SV waves and P-waves, as depicted in Figure 1.  
Let the potential functions of the incident P-wave and the incident SV wave be:  
\[\varphi^{I}=A_{0}\exp{i[\sigma_{P}(x\sin\beta_{2}-y\cos\beta_{2})-\omega t]}, \tag{30a}\]  
Figure 1: Reflection of elastic waves. \[\psi^{I}=B_{0}\exp i[\sigma_{SV}(x\sin\beta_{1}-y\cos\beta_{1})-\omega t], \tag{30b}\]  
the potential functions of the reflected P wave and the reflected SV wave are  
\[ \begin{array}{c}\varphi^{R}=A_{1}\exp i[\sigma_{P}(x\sin\beta_{2}+y\cos\beta_ {2})-\omega t]\\ +C_{1}\exp(i\sigma_{P}x\sin\beta_{2}-\gamma_{SP}y-i\omega t),\end{array}  \tag{31a}\] \[ \begin{array}{c}\psi^{R}=B_{1}\exp i[\sigma_{SV}(x\sin\beta_{1}+y\cos\beta_ {1})-\omega t]\\ +C_{2}\exp(i\sigma_{SV}x\sin\beta_{1}-\gamma_{SS}y-i\omega t),\end{array}  \tag{31b}\]  
among them, \(\sigma_{SS}^{2}=\gamma_{SS}^{2}-\xi^{2}\), \(\sigma_{SP}^{2}=\gamma_{SP}^{2}-\xi^{2}\). \(\sigma_{P}\), \(\sigma_{SV}\), \(\sigma_{SP}\), and \(\sigma_{SS}\) are the wavenumbers of the reflected P-wave, the reflected SV wave, the reflected SP wave, and the reflected SS wave, respectively. The equations presented in \(A_{0}\) and \(B_{0}\) represents the amplitudes of the incident waves. Similarly, \(A_{1}\) and \(B_{1}\) denote the amplitudes of the reflected P and SV waves, respectively, whereas \(C_{1}\) and \(C_{2}\) signify the amplitudes of the reflected SP and SS waves, respectively. We introduced \(A_{1}/A_{0}\), \(B_{1}/A_{0}\), and \(C_{1}/A_{0}\), \(C_{2}/A_{0}\) represent the ratios of the amplitudes of the reflected P-wave, SV waves, SP waves, and SS waves respectively to the amplitude of the incident P wave.