In this article an analytical model for the vibration of an elastic plate-cylindrical shell structure with complex boundary conditions and coupling conditions is constructed, in which the six displacements for the plate and shell structures are represented simultaneously by the composite Fourier series method. The boundary conditions and coupling conditions are modelled respectively. By setting four types of uniform coupling springs along their conjunctions, the mechanical coupling effects for the plate-shell structure are completely considered. Ultimately, the Hamilton's principle is employed to derive the characteristic equation for the structural system. On this basis, an approach of combining the rigid body theory and the composite Fourier series method is proposed to model a general dynamic model of a floating raft isolation systems based on an elastic plate-cylindrical shell structure with multi-excitation sources, and the isolation performance and the power transfer characteristic are investigated. What's more, the mechanism of the finite continuous floating raft vibration isolation is revealed from the viewpoint of energy. At the same time, the influence of the types of excitations, the positions and number of mounts, as well as different parameters of the system on vibration isolation are investigated, which provides an effective technical mean to the design of the floating raft isolation system.
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