Coupled vibro-acoustic analysis of submerged double cylindrical shells with stringers, rings, and annular plates in a symplectic duality system

Abstract

A wave propagation analysis model of a submerged double cylindrical shell with stringers, rings, and annular plates is established in a symplectic duality system, accounting for acoustic-structure coupling. First, the vibration problem of the double cylindrical shell with stringers is introduced into the symplectic duality system by the Hamiltonian function. The wave propagation parameters and wave shape matrices with symplectic orthogonal relations are obtained by solving a symplectic eigenvalue problem. Then, according to the wave propagation relations, the wave amplitudes are derived by accounting for unknown forces, moments, and pressures induced by the rings, annular plates, and fluid. Finally, the vibration and acoustic responses are obtained through the wave shape matrices and wave amplitudes. In this study, the wave propagation parameters and wave shape matrices are calculated in the symplectic dual space, and the axial thickness discontinuity induced by the rings and annular plates is addressed through the cutting of the wave propagation path. Consequently, the convergence is not affected by the number of rings and annular plates, and the method achieves higher calculation accuracy and efficiency compared with the modal superposition method based on analytical beam functions. The parameter analysis indicates that proper combinations of the number and thickness of the annular plates can significantly reduce the vibro-acoustic responses for the same total mass of the annular plates, while changing the number of rings and stringers cannot. When the inner and outer cylindrical shells lose the same mass, altering the thickness of the outer shell has a greater impact.