In order to solve the vibration and acoustic characteristics of spherical shell in light fluid environment, based on Jacobi-Ritz-spectral BEM, a unified analysis formula for acoustic vibration of spherical shell under arbitrary boundary conditions is established. Based on the First-order shear deformation theory (FSDT) and domain decomposition method (DDM), the theoretical model of spherical shell structure is established. The improved Jacobi polynomial is innovatively used to construct the displacement tolerance function of the spherical shell. Based on the spectral Kirchhoff-Helmholtz integral formula, the theoretical model of the acoustic fluid outside the spherical shell is established. The special form of Jacobi polynomial Chebyshev polynomial is used to describe the excitation sound pressure on the spherical shell segment, so as to ensure that the generalized coordinates of the structure can be perfectly matched with the acoustic boundary element nodes. In addition, the integration along the meridian of the shell is used to control the movement of the fluid, which simplifies the surface integration. The CHIEF method is used to solve the problem of non-unique solution of acoustic variables of rotary structure. Compared with the published literature, numerical simulation results and experimental results, the proposed method has higher calculation accuracy. In addition, based on this method, the influence of boundary conditions, geometric dimensions and other factors on the acoustic and vibration characteristics of spherical shells is discussed, which accumulates data for analyzing the acoustic and vibration behavior of spherical shells.
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