## Abbreviations
\([A_{\text{FN}}]\) dynamical matrix for the fluid-structure coupled system  
\([A^{S}]\) reduced dynamical matrix for the structure  
\([\mathbf{\Lambda}^{S}]\) random reduced dynamical matrix for the structure  
\([A^{S}]\) dynamical matrix for the structure  
\([A^{Z}]\) dynamical matrix associated with the wall acoustic impedance  
\([C]\) random reduced coupling matrix between the internal acoustic fluid and the structure  
\([D]\) reduced damping matrix for the internal acoustic fluid  
\([\mathbf{D}]\) damping matrix for the internal acoustic fluid  
\([D^{S}]\) reduced damping matrix for the structure  
\([\mathbf{D}^{S}]\) damping matrix for the structure  
\(\mathbf{D}\) degrees of freedom  
\(\mathbb{F}\) vector of discretized acoustic forces  
\(\mathbb{F}^{S}\) vector of discretized structural forces  
\(G_{ijkl}(0)\) initial elasticity tensor for viscoelastic material  
\(G_{ijkl}(t)\) relaxation functions for viscoelastic material  
\(\mathbf{G}\) mechanical surface force field on \(\partial\Omega_{S}\)  
\([\mathbf{G}]\) random matrix  
\([\mathbf{G}_{0}]\) random matrix  
\([K]\) reduced \"stiffness\" matrix for the internal acoustic fluid  
\([\mathbf{K}]\) \"stiffness\" matrix for the internal acoustic fluid  
\([K^{S}]\) reduced stiffness matrix for the structure  
\([\mathbf{K}^{S}]\) stiffness matrix for the structure  
\([M]\) reduced \"mass\" matrix for the internal acoustic fluid  
\([\mathbf{M}]\) random reduced \"mass\" matrix for the internal acoustic fluid  
\([M]\) \"mass\" matrix for the internal acoustic fluid  
\([M^{S}]\) reduced mass matrix for the structure  
\([\mathbf{M}^{S}]\) mass matrix for the structure  
\(\mathbb{P}_{\alpha}\) internal acoustic mode  
\([P]\) matrix of internal acoustic modes  
\(Q\) internal acoustic source density  
\(Q_{E}\) external acoustic source density  
\(\mathbf{Q}\) random vector of the generalized coordinates for the internal acoustic fluid  
\(\mathbf{Q}^{S}\) random vector of the generalized coordinates for the structure  
\(\mathbf{p}\) random vector of internal acoustic pressure DOF  
\(\mathbb{P}\) vector of internal acoustic pressure DOF  
\(\mathbf{U}\) random vector of structural displacement DOF  
\(\mathbb{U}_{\alpha}\) elastic structural mode \(\alpha\)  
\([\mathcal{U}]\) matrix of elastic structural modes  
\(Z\) wall acoustic impedance  
impedance boundary operator for external acoustic fluid  
\(\delta\) dispersion parameter  
\(\varepsilon_{kh}\) component of the strain tensor in the structure  
\(\omega\) circular frequency in rad/s  
\(\rho_{0}\) mass density of the internal acoustic fluid  
\(\rho_{E}\) mass density of the external acoustic fluid  
\(\rho_{S}\) mass density of the structure \(\sigma\) stress tensor in the structure \(\sigma_{ij}\) component of the stress tensor in the structure \(\sigma_{ij}^{\text{elas}}\) component of the elastic stress tensor in the structure \(\tau\) damping coefficient for the internal acoustic fluid \(\partial\Omega\) boundary of \(\Omega\) \(\partial\Omega_{E}\) boundary of \(\Omega_{E}\) equal to \(\Gamma_{E}\) \(\partial\Omega_{S}\) boundary of \(\Omega_{S}\) \(\Gamma\) coupling interface between the structure and the internal acoustic fluid \(\Gamma_{E}\) coupling interface between the structure and the external acoustic fluid \(\Gamma_{Z}\) coupling interface between the structure and the internal acoustic fluid with acoustic properties \(\Omega\) internal acoustic fluid domain \(\Omega_{E}\) external acoustic domain \(\Omega_{S}\) structural domain