## 3 Analysis of Acoustic Vibration Transfer Characteristics of Coupled Systems  
### Structural Parameters of the Coupling System  
Next, through numerical simulations of the acoustic vibration transfer characteristics of the system in Figure 1, carry out a theoretical analysis of the sound pressure distribution pattern of the peripheral hydroacoustic field of the thin submerged cylindrical shell containing the internal complex coupled system, and the numerical correspondence between the sound pressure at the field points and the transferred power flow, the vibration level drop and the acoustic radiated power of the system. According to the general guidelines for vibration isolation design, Table 1 shows the basic parameter settings for the floating raft system. To avoid the chance of numerical analysis, three sets of parameter configurations are given here. Let the material of the thin cylindrical shell be steel (modulus of elasticity \(E=2.1\times 10^{11}\) Pa, Poisson's ratio \(\mu=0.28\), density \(\rho=7800\) kg/m\({}^{3}\), damping loss factor \(\xi=0.01\)), radius \(a=0.2\) m at the centre, length \(L=1\) m, thickness \(h=0.005\) m. The fluid outside the cylindrical shell has density \(\rho_{0}=1000\) kg/m\({}^{3}\) and sound velocity \(c_{0}=1500\) m/s. The excitation amplitude \(F_{1}=F_{2}=1N\). \begin{table}
\begin{tabular}{c c c c c} \hline \hline
**Parameters** & **Unit** & **Condition 1** & **Condition 2** & **Condition 3** \\ \hline Unit quality \(m_{1},m_{2}\) & kg & \(50,70\) & \(100,140\) & \(150,210\) \\ Upper vibration isolator re-stiffening \(k_{1},k_{2}\) & N/m\({}^{2}\) & \(10\times 10^{5}\times(1+0.1)\) & \(2\times 10^{5}\times(1+0.2)\) & \(1.3\times 10^{6}\times(1+0.15)\) \\  & \(1\times 10^{5}\times(1+0.1)\) & \(2\times 10^{5}\times(1+0.2)\) & \(1.3\times 10^{6}\times(1+0.15)\) \\ Upper vibration isolator spacing \(h_{1z},h_{1z},h_{2x},h_{1z}\) & m & \(0.06,0.1,0.06,0.1\) & \(0.1,0.15,0.1,0.15\) & \(0.2,0.3,0.2,0.3\) \\ Lower vibration isolator stiffness \(k_{R}\) & N/m\({}^{2}\) & \(1\times 10^{5}\times(1+0.1)\) & \(2\times 10^{5}\times(1+0.2)\) & \(2.6\times 10^{6}\times(1+0.15)\) \\ Lower vibration isolator spacing \(H_{x},H_{z}\) & m & \(0.18,0.35\) & \(0.36,0.7\) & \(0.5,1.05\) \\ Raft frame quality \(m_{R}\) & kg & \(100\) & \(200\) & \(300\) \\ Rotational inertia of unit \(1\)\(I_{x}\) & K\({}_{\mathrm{g}}\)-m\({}^{2}\) & \(1\) & \(1\) & \(1\) \\ Rotational inertia of unit \(2\)\(I_{z}\) & K\({}_{\mathrm{g}}\)-m\({}^{2}\) & \(1\) & \(1\) & \(1\) \\ Inertia of raft frame rotation \(I_{Rx}\) & K\({}_{\mathrm{g}}\)-m\({}^{2}\) & \(1\) & \(1\) & \(1\) \\ Inertia of raft frame rotation \(I_{Rx}\) & K\({}_{\mathrm{g}}\)-m\({}^{2}\) & \(1\) & \(1\) & \(1\) \\ \hline \hline \end{tabular}
\end{table} 
Table 1: Parameters of generator set, raft rack and vibration isolator. To simplify the calculation without loss of generality, the boundary conditions of the cylindrical shell are chosen to be simply supported at both ends. The simply supported boundary condition of a cylindrical thin shell is that which constrains its external normal direction and circumferential displacement at the z = 0 and z = L boundaries to 0, while leaving the axial displacement and the external normal deflection at the end face unconstrained.