## 2 Materials and Methods  
As shown in Figure 1, the 1D PC plate is made of silicon, whose material parameters are as follows: mass density \(\rho=2332\) kg/m\({}^{3}\), shear wave velocity \(v_{\rm t}=5840.9\) m/s, and elastic constant C\({}_{44}=79.56\) GPa. Each unit cell contains four layers, whose characteristic length is \(t_{1}\)-\(t_{4}\), where \(t_{1}+t_{3}=2a/3\) and \(t_{2}+t_{4}=a/3\). The lattice constant is \(a=9\) mm, the height of pile \(h_{1}=3\) mm and \(h_{2}=4.2\) mm. The above geometric parameters remain unchanged in the discussion of this paper. Two additional geometrical parameters are defined as \(p=(t_{1}-t_{3})/(t_{1}+t_{3})\) and \(q=(t_{2}-t_{4})/(t_{2}+t_{4})\). Since the values of \(t_{1}\)-\(t_{4}\) are positive, both parameters range from [\(-1\),\(1\)], which forms a closed parameter space. A virtual 3D parameter space can be formed by these two parameters plus the wave vector, where WPs can be investigated.  
When the Shear horizontal (SH) guided waves propagate in the 1D PC plates, the governing equation is expressed as:  
\[-\rho\omega^{2}U_{2}=T_{12,1}+(\text{C}_{44}U_{2,3})_{\,3}, \tag{1}\]  
where the subscripts \(1\), \(2\), and \(3\) represent the coordinates \(x\), \(y\), and \(z\), \(U_{2}\) is the displacement vector along the y-direction, C\({}_{44}\) is the elastic constant, and \(T_{12}\) is the stress tensor component.  
Based on the Bloch-Floquet theorem, the displacement in PC plates is given as:  
\[\mathbf{u}(\mathbf{r},t)=\mathbf{u_{k}}(\mathbf{r})e^{i(\mathbf{k}\cdot \mathbf{r}+\omega t)}, \tag{2}\]  
where \(\mathbf{r}=(x,y,z)\) is the position vector and \(\mathbf{k}=(k_{x},\,k_{y},\,k_{z})\) is the Bloch wave vector. Since the 1D PC plates are periodic in the \(x\) direction, one unit cell is considered. We substitute  
Figure 1: The synthetic Weyl points in 1D PC plates. (**a**) The unit cell consists of four layers. (**b**) Dispersion curves with different \(p\) and \(q\) values (**c**) Bulk dispersions plotted for bands \(1\) and \(2\) with the wave vector plus two structural parameters.  
Equation (2) into (1) and discretize the model with sufficient elements. The eigenvalue equation in the finite element method (FEM) framework is:  
\[(\mathbf{K}(\mathbf{k})-\omega(\mathbf{k})^{2}\mathbf{M})\mathbf{u}=0, \tag{3}\]  
in which \(\mathbf{K}\) and \(\mathbf{M}\) stand for stiffness matrix and mass matrix. The band structures for the 1D PC plates can be obtained by scanning the points of the Brillouin zone.  
Using the frequency domain study of COMSOL software 5.6, the TS and the RP can be calculated. For TS, the simulation model is shown in Figure 2. A uniform harmonic shear displacement is applied on the left side of the PC plate and the perfectly matched layers (PMLs) are used to avoid reflection. The energy density spectrum normalized by the flat panel is defined as:  
\[I=\frac{\sqrt{{v_{2x}}^{2}+{v_{2z}}^{2}}}{\sqrt{{v_{1x}}^{2}+{v_{1z}}^{2}}} \tag{4}\]  
in which \(v_{1x}\) and \(v_{1z}\) stand for the displacement of the receive point with PC plate, while \(v_{2x}\) and \(v_{2z}\) stand for the displacement of the receive point with flat panel.  
For the RP calculation, the left PML layer is replaced with a hard boundary condition. With the same excitation, the RP can also be obtained from the rigid boundary.