Objective A semi-analytical method coupling the energy variational principle with non-negative acoustic intensity (NAI) is developed to analyse submerged stiffened combined shells, addressing near-field energy exchange and truncation artifacts that may arise in wavenumber-domain filtering.
Method A Rayleigh–Ritz model of a stiffened conical-cylindrical-spherical shell with internal bulkheads is constructed using Chebyshev polynomials and circumferential Fourier series. Penalty springs couple the substructures, and fluid loading is introduced through the boundary element method and an energy-equivalent mapping. NAI is calculated using a generalized eigenvalue decomposition of the Hermitian part of the area-weighted radiation impedance matrix. Convergence is examined, and dry and wet modal frequencies are compared with finite element results and published data, respectively. Spatial distributions of active, supersonic and non-negative acoustic intensity are also compared.
Results For the reported cases, the maximum absolute relative errors are 4.58% for dry modes and 4.71% for wet modes. The computation time per frequency is reduced from approximately 51.6 s for FEM/BEM to approximately 8.3 s. At 63, 136 and 241 Hz, the NAI distributions contain no alternating positive and negative values and reveal differences between vibration amplitude and radiation contribution. They also avoid the stripe artifacts introduced by wavenumber-domain filtering in the compared supersonic intensity calculation.
Conclusion The method supports vibro-acoustic analysis and identification of radiation contribution distributions for submerged axisymmetric stiffened combined shells, providing a computational tool for acoustic optimization.
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