An Analytical Solution for Free Vibration Research of Coupled Rectangular Plate–Cylindrical Shell Structures

Shell structures with built-in plates are widely used in engineering. This paper presents a unified analytical method for the dynamic stiffness model of coupled plate–shell structures, considering the effect of internal plates on the vibration characteristics of the assembled system. The coupled structure is decomposed along the plate–shell interface. Using Gorman’s superposition method and structural symmetry, the boundary displacement solution of the full structure is simplified to a quarter-structure problem. The dynamic stiffness matrices of substructures are derived and assembled to establish the analytical model. Numerical examples are conducted to investigate the dynamic behaviors of the coupled system, and the convergence and accuracy of the proposed method are verified against numerical simulations. Furthermore, a test rig is established for a rectangular plate–cylindrical shell structure, and modal experiments are carried out. The measured natural frequencies and mode shapes agree well with theoretical predictions. The proposed method provides a general theoretical approach for the vibration analysis of plate–cylindrical shell coupled structures.