## 4 Conclusions
\begin{tabular}{l l l l} \hline \(\overline{Q_{ij}^{k}}\) & Correlation stiffness coefficient & **T** & Transformation matrix \\  & The Angle between the principal direction & & \(Q_{ij}^{k}\) & Material coefficient of the \(k\) layer \\  & and the \(r\) direction & & \(G_{12}\), \(G_{13}\), \(G_{23}\) & Shear modulus \\ \(\mu_{12}\), \(\mu_{21}\) & Poisson's ratio & \(\overline{s}_{s}^{\prime}\) & Shear correction factor \\ \(N_{L}\) & Number of floors & \(Z_{k}\) & The base thickness of the \(k\) layer \\ \(Z_{k+1}\) & Upper surface thickness coordinates & \(T_{\rm P}\) & Total kinetic energy of the laminated plate \\ \(T_{\rm B_{s}}\) & Total kinetic energy of the NTH laminated & \(U_{\rm P}\) & Total potential energy of the laminated plate \\ \(U_{\rm B_{s}}\) & Total potential energy of the NTH laminated & \(U_{\rm P\text{-coupling}}\) & Coupling potential energy of laminated plate \\ \(U_{\rm B_{s}\text{-coupling}}\) & Coupling potential energy of the NTH & \(U_{SP}\) & Potential energy of boundary spring \\  & & \(W_{\rm P\text{-}\text{g}\text{n}}\) & Work done by the harmonic point force F \\ \(W_{\rm P\text{-}\text{g}\text{n}}\) & Material density of the \(k\) layer of laminates & \(\rho_{\rm B\text{-}\text{n}}^{k}\) & Material density of the \(k\) layer of laminated \\ \(\rho_{\rm P}^{k}\) & Material density of the \(k\) layer of laminates & \(\rho_{\rm B\text{-}\text{n}}^{k}\) & Material density of the \(k\) layer of laminated \\ \(U_{\rm stretch}\) & Tensile potential energy & \(U_{\rm bend}\) & Bending potential energy \\ \(U_{\rm s\text{-}\text{b}}\) & Bending coupled potential energy & \(f_{i}\) & Function of external load distribution \\ \(\mathbf{P}_{mn}\) & Two-dimensional unknown Fourier & \(\mathbf{Q}_{l}\) & One-dimensional unknown Fourier \\  & coefficient matrix & & coefficient matrix \\ \(\mathbf{K}_{\rm P}\) & Stiffness matrix of laminated plate & \(\mathbf{K}_{\rm B_{s}}\) & Stiffness matrix of the NTH laminated \\ \(\mathbf{M}_{\rm P}\) & Mass matrix of laminated plate & \(\mathbf{M}_{\rm B_{s}}\) & Mass matrix of the NTH laminated \\ \(\mathbf{C}_{\rm B_{s}\text{-}\text{g}\text{P}}\) & The coupling matrix between the NTH beam & \(\omega\) & Natural frequency \\ \(\Omega\) & Frequency parameter & \(M_{\rm P}\), \(N_{\rm P}\) & Truncation value of the laminated plate \\ \(M_{\rm b}\) & Truncation value of laminated curved beam & \(R_{\alpha}\) & of the middle surface \\ \(R_{\beta}\) & Mean radius of curvature in the \(\beta\) direction & \(L_{\alpha}\) & Medium surface \(\alpha\) direction length \\  & of the middle surface & & dimension \\ \(L_{\beta}\) & Medium surface \(\beta\) direction length & \(L_{z}\) & Middle surface \(z\) direction length dimension \\ \(\zeta\) & Damping value & \(H\) & Thickness of cavity \\ \(\phi\) & Apex angle of Spherical cavity & \(L\) & Length of cavity \\ \(\alpha\) & Cone apex Angle of cone sound cavity & \(U_{\rm C_{n}}\) & Total potential energy of cavity \(n\) \\ \(T_{\rm C_{n}}\) & Total kinetic energy of cavity \(n\) & \(W_{\rm wall}^{n}\) & The energy consumed by the cavity \(n\) \\ \(W_{\rm coupling}^{n}\) & The coupled potential energy of cavity \(n\) & \(W_{\rm sound}^{n}\) & The work done by a point source in cavity \(n\) \\ \(W_{\rm C_{1}-C_{2}}\) & Potential energy coupling between cavities 1 & \(\rho_{\rm C_{n}}\) & The density of acoustic media in cavity \(n\) \\ \(c_{n}\) & The speed at which sound waves travel in cavity \(n\) & \(j\) & Pure imaginary number \\ \(S_{r}\) & Area of the \(r\)-th acoustic wall & \(Z_{r}\) & Impedance value of the \(r\)-th acoustic wall \\ \(Q_{s}^{n}\) & Distribution function of point sound source & \(A\) & The amplitude of the point sound source \\  & in cavity \(n\) & \(k\) & The wave number of sound \\ \(\mathbf{K}_{\rm n}\) & Stiffness matrix of sound cavity \(n\) & \(\mathbf{M}_{\rm n}\) & Mass matrix of cavity \(n\) \\ \(\mathbf{C}_{\rm n}\) & Coupling matrix of sound cavity \(n\) & \(\mathbf{Q}_{\rm n}\) & Sound field source vector of cavity \(n\) \\ \(\mathbf{Z}_{\rm n}\) & Impedance matrix of the acoustic wall of & \(\mathbf{C}_{12}\), \(\mathbf{C}_{21}\) & Coupling matrix between cavities 1 and 2 \\  & cavity \(n\) & \(\mathbf{C}_{12}\), \(\mathbf{C}_{21}\) & Coupling matrix between cavities 1 and 2 \\ \(M_{c}\), \(N_{c}\), \(L_{c}\) & The truncation value of the cavity & & \\ \end{tabular}