## 3 Numerical Results and Discussion
### Steady-State Response Analysis  
This section investigates the sound pressure response of the coupled system between the composite laminated rotationally stiffened plate and the cylindrical-cylindrical, spherical-cylindrical, and conical-cylindrical acoustic cavities under the point source or point force excitation. Figure 14 shows the sound pressure response curves at various observation points for the coupling system between the composite laminated rotationally stiffened plate and the cylindrical-cylindrical acoustic cavity under monopole point source or point force excitation. The boundaries of the composite laminated rotationally stiffened plate are SSSS, the number of stiffeners is \(n=1\), and the coupling system's geometric parameters are as follows: \(R_{1}\) = 0.4 m, \(R_{2}\) = 1.2 m, \(L_{1}\) = 0.5 m, \(L_{2}\) = 1 m, \(h_{\text{p}}\) = 0.02 m, \(\vartheta\) = 90\({}^{\circ}\), \(R_{\text{b1}}\) = 0.8 m, \(b_{1}\) = 0.06 m, and \(h_{1}\) = 0.04 m. The material of the laminated plate is graphite epoxy resin, the layer angle is [0\({}^{\circ}\)/90\({}^{\circ}\)], the material of the laminated beam is steel, and the medium in the acoustic cavity is air. The point source is located at (0.69 m, 0.50 m, 0.38 m) within cylindrical cavity 1, and the point force is applied on the surface of the stiffened plate at (0.29 m, 0.93 m). Observation point 1 is located at (1.05 m, 0.34 m, 0.30 m) within cylindrical cavity 1, and observation point 2 is located at (0.96 m, 0.53 m, 0.55 m) within cylindrical cavity 2. From Figure 14, it can be observed that the response curves obtained by the present method are in good agreement with the finite element simulation results. In the coupling system among the composite laminated rotationally stiffened plate and the cylindrical-cylindrical acoustic cavities, when the source excitation of the point sound and observation points are not in the same cavity, the sound pressure response of the coupled system will be influenced by the thickness (\(h_{\text{p}}\)) of the composite stiffened plate among the two cavities. To investigate how the thickness of the composite stiffened plate affects the mechanism, Figure 15 provides sound pressure response curves at observation points within the lower cylindrical acoustic cavity 2 for various thicknesses of the composite stiffened plate when excited by the source of point sound in the upper cylindrical cavity 1. Here, \(h_{\text{p}}\) = 0 m indicates that there is no composite stiffened plate between the two cavities. The relevant factors of the composite laminated rotationally stiffened plate and the cylindrical-cylindrical acoustic cavity are the same as in Figure 14. The point sound source is located at (0.53 m, 0.51 m, 0.32 m) within cylindrical cavity 1, observation point 1 is located at (0.73 m, 0.45 m, 0.49 m) within cylindrical cavity 2, and observation point 2 is located at (0.36 m, 0.65 m, 0.38 m) within cylindrical cavity 2. Figure 14: (a) Sound pressure response of observation point 1 under the point sound source. (b) Sound pressure response of observation point 2 under the point force. Sound pressure response curves at various observation points for the coupled system between the composite laminated rotationally stiffened plate and the cylindrical-cylindrical acoustic cavity under the monopole point source or point force excitation. From Figure 15, it can be observed that the sound pressure response curve's amplitude at the same observation location declines as the thickness of the composite stiffened plate increases; there is a substantial difference in the sound pressure response with and without the composite stiffened plate. This result indicates that the composite stiffened plate in the coupling system has a specific influence on noise reduction, and this impact rises with the increasing thickness of the stiffened plate.