Abstract: In this paper， the analytical model of the vibration characteristics for the composite double-layer spherical shell and annu? lar plate coupled structure under different boundary conditions is constructed using the spectral geometry method based on the firstorder shear deformation theory， and the boundary conditions of the coupled structure are simulated by the artificial virtual spring technique. The coupling relationship between the sub-structures is simulated by arranging the coupling spring simulator according to the connection relationship. The Hamiltonian principle is applied to derive the characteristic equations of the composite doublelayer spherical shell and annular plate coupled structure， and the inherent characteristics and steady-state response of the coupled structure are solved. The results obtained are compared with the results of finite element method to verify the correctness of the cal? culations. The effects of geometric parameters， material parameters on the vibration response of the composite double-layer spheri? cal shell and annular plate coupled structure are analyzed.