## 3 Influence Analysis of Stiffeners on Lamb Wave Propagation Law  
### Finite Element Simulation Model  
The ABAQUS finite element simulation software has obvious advantages in solving non-stationary nonlinear problems. This paper uses ABAQUS software to study the influence of stiffeners on the propagation law of Lamb wave. In the actual situation, when the impact source signal arrives at the receiving sensor, the signal propagation paths through the stiffeners are diverse. The two-dimensional finite element model cannot reflect this feature. According to the parameters of fan-ring shaped high-stiffened panel of sealed bulkhead of manned spacecraft, this paper establishes a three-dimensional model. The schematic diagram of model is shown in Figure 4, recorded in a Cartesian coordinate system, and the origin is the geometric center of the flat side. The model is an aluminum panel measuring 500 mm \(\times\) 500 mm \(\times\) 3 mm, and has three stiffeners in the radial direction and the circumferential direction respectively. The stiffener's height and thickness are 22 mm and 4 mm, respectively. The radial spacing is 108 mm, the circumferential spacing is 3.2\({}^{\circ}\), the inner arc radius is 1955 mm and the outer arc radius is 2295 mm. The mesh cell shape is set to a hexahedron with the mesh size of 1 mm. The material parameters of the stiffened panel are shown in Table 1.  
Figure 4: The schematic diagram of model (absorbing layers are not shown). The interference of boundary reflection waves increases the difficulty of analysis. Establishing a large model can solve this problem, but it will cause too much simulation calculation. Some scholars have found that adding several layers of Rayleigh damping coefficient increasing material to the outer edge of the structure constitutes the absorbing layer, which can effectively suppress the reflected waves of the ultrasonic guided waves at the edge of the structure. This method has been verified to be suitable for finite element simulation of ultrasonic guided waves [47]. In this paper, Equation (15) is used to calculate the Rayleigh damping coefficient of each layer of material:  
\[C_{n}=C_{\max}\frac{n\cdot l}{L}, \tag{15}\]  
where \(n\) is the serial number of the absorbing layer, \(C_{n}\) is the Rayleigh damping coefficient of the \(n\)-th layer material, \(C_{\max}\) is the maximum Rayleigh damping coefficient, \(l\) is the length of each absorbing layer, and \(L\) is the total length of the absorbing layer. Therefore, \(L\)/\(l\) is the number of layers of the absorbing layer. In this paper, \(C_{\max}\) is taken as \(5\times 10^{6}\), \(L\) is taken as 40 mm, and \(l\) is taken as 2 mm, and a total of 20 layers of absorption layer. The Rayleigh damping coefficient of each layer of material is calculated by Equation (15), and the remaining material parameters are the same as those of the stiffened panel. The load is a 20 \(\upmu\)s superimposed sine wave with a frequency of 50 kHz to 500 kHz spaced 1 kHz, acting on the stiffened side point (0,0,3) in the negative direction of the \(Z\)-axis in the form of concentrated force. The load expression is shown in Equation (16). \[y(t)=\left\{ \begin{array}{ll}\sum\limits_{f_{1}=50k}^{500k}\mathrm{A}\sin(2 \pi f_{1}t)&0\leq t<t_{0}\\ 0&t\geq t_{0}\end{array} \right., \tag{16}\]  
where \(t_{0}\) is 20 \(\upmu\)s.  
The time domain and frequency domain characteristics of the load are shown in Figure 5.  
On the flat side of the stiffened panel, the origin is centered, the x-axis is the positive direction, and the counterclockwise is the positive direction. With a radius of 230 mm, a receiving point is set every 30\({}^{\circ}\) in the range of \(-90^{\circ}\) to \(90^{\circ}\). There are 7 receiving points. The serial number is shown in Figure 4. The straight paths from point 1, point 4 and point 7 to the origin pass through two stiffeners. The straight paths from point 2, point 3, point 5 and point 6 to the origin pass through three stiffeners.