Vibroacoustic analysis of revolving shells in an acoustic half-space using the Chebyshev spectral approach

A Chebyshev spectral approach is developed for the vibroacoustic analysis of revolving shell structures submerged in an acoustic half-space. The method couples dynamic modeling of shell vibrations with the Helmholtz boundary integral formulation, employing the half-space Green’s function to evaluate radiated sound pressure for both soft and rigid boundary conditions. To address the higher accuracy requirements for singular integrals introduced by high-order Chebyshev polynomials, an adaptive numerical integration strategy is implemented. The approach is validated through numerical examples involving a single spherical shell, a cylindrical shell, and a coupled conical–cylindrical–spherical shell, with results compared against analytical solutions, literature data, and commercial software. Detailed convergence, accuracy, and computational efficiency studies using the spherical shell benchmark confirm the effectiveness of the proposed method. This framework provides an efficient and robust tool for vibroacoustic analysis of complex shell structures in underwater acoustic environments. In addition, the study reveals that significant circumferential modal coupling occurs at shallow submersion depths, leading to pronounced frequency shifts and energy redistribution among modes. These effects manifest as distinct changes in both the displacement and radiated sound pressure spectra, especially for lower circumferential wavenumber modes.