## 3 Numerical Results and Discussion
### Steady-State Response Analysis
Figure 16 provides sound pressure response curves at observation points in the coupling system among the composite laminated rotationally stiffened plate and the spherical-cylindrical cavities under the monopole point source or point force excitation. The boundaries of the composite laminated rotationally stiffened plate are SSSS, the number of stiffness \(n\) is 1, and the coupling system's geometric parameters are: \(R_{1}\) = 0.4 m, \(R_{2}\) = 1.2 m, \(\phi_{1}\) = 30\({}^{\circ}\), \(\phi_{2}\) = 90\({}^{\circ}\), \(L\) = 1.8 m, \(h_{\rm p}\) = 0.02 m, \(\theta\) = 90\({}^{\circ}\), \(R_{\rm b1}\) = 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 angles are [0\({}^{\circ}\)/90\({}^{\circ}\)], the material of the laminated beam is steel, and the acoustic cavity is filled with air. The point sound source is located at (0.72 m, 0.26 m, 0.56 m) within spherical cavity 1, and the point force is located on the surface of the stiffened plate at (0.34 m, 0.72 m). Observation point 1 is located within the spherical cavity at (0.26 m, 0.99 m, 0.24 m), and observation point 2 is located within the cylindrical cavity at (0.96 m, 0.53 m, 1.15 m). As shown in Figure 16, the sound pressure response curves obtained using the present method are in good agreement with the finite element method results. In this section, using the example of the coupling system between the composite laminated rotationally stiffened plate and the spherical-cylindrical cavity, we have studied the impact of the amplitude of a point source or point force excitation on the sound pressure response of the coupling system between the composite laminated rotationally stiffened plate and the cavity. Figure 17 illustrates the sound pressure response curves at various observation points of different amplitudes of the point source or the point force excitation. In this example, the relevant parameters of the coupled system between the composite laminated rotationally stiffened plate and spherical-cylindrical cavity are the same as in Figure 16. The amplitudes (\(A\)) of the point source or the point force excitation are set to 1 kg/s\({}^{2}\), 2 kg/s\({}^{2}\), and 3 kg/s\({}^{2}\). The point source is located at (0.65 m, 0.32 m, 0.44 m) within the spherical cavity, and the point force is applied on the surface of the stiffened plate at (0.50 m, 0.50 m). Observation point 1 is within the spherical cavity at (0.45 m, 0.56 m, 0.40 m), and observation point 2 is within the cylindrical cavity at (0.75 m, 0.35 m, 0.60 m). As shown in Figure 17, variations in the amplitude of the point force or point source excitation lead to vertical shifts in the sound pressure response amplitude, and this effect increases with the increasing amplitude of the external point source excitation. Figure 15: Sound pressure response curves at observation points within the lower cylindrical acoustic cavity 2 for different thicknesses of the composite stiffened plate when excited by a point sound source in upper cylindrical cavity 1. To validate whether the computed results obtained by the present method of the coupled system between the composite laminated rotationally stiffened plate and the conical-cylindrical cavity correspond to those obtained with the finite element method, Figure 18 presents the sound pressure response curves at various observation points of the single monopole point source or point force excitation. The boundaries of the composite laminated rotationally stiffened plate are set to SSSS; the number of stiffeners \(n\) is 1. The coupling system's geometric parameters are: \(R_{1}\) = 0.6 m, \(R_{2}\) = 1.2 m, \(R_{3}\) = 1.8 m, \(\alpha\) = 30\({}^{\circ}\), \(L\) = 2 m, \(h_{\rm p}\) = 0.02 m, \(\theta\) = 90\({}^{\circ}\), \(R_{\rm b1}\) = 1.5 m, \(b_{1}\) = 0.06 m, and \(h_{\rm 1}\) = 0.04 m. The material of the laminated plate is graphite epoxy resin, with layer angles of [0\({}^{\circ}\)/90\({}^{\circ}\)], and the material of the laminated beam is Q235 steel.