Free- and Forced-Vibration Characteristic Analysis of a Double-Layered Cylindrical Shell with General Boundary Conditions

The double-layered cylindrical shell represents a key structural configuration for underwater vehicles, where its vibration behavior remains a primary concern in engineering design and analysis. This study develops a spectral element method (SEM) for dynamic modeling of multi-component shell systems by extending the vibrational governing equations of conical shells. The methodology is validated through finite element method (FEM) case studies on both conical shells and double-layered cylindrical configurations. Parametric investigations examine ribbed substructures and solid rib plates within the cylindrical shell assembly, while artificial spring techniques model arbitrary boundary conditions—with validation against classical benchmarks confirming their effectiveness for elastic constraints. Numerical demonstrations reveal the following: rib and plate thickness variations exhibit a negligible impact on low-frequency vibrational responses; the natural frequency sensitivity peaks when the elastic boundary stiffness approaches the inherent dynamic stiffness of the shell’s base configuration, while extreme stiffness values approximate clamped or free boundary conditions with engineering significance. The proposed SEM framework demonstrates a superior computational efficiency and accuracy compared to conventional FEM approaches. These findings deliver practical guidance for marine structural engineering, particularly in the boundary condition specifications and performance optimization of composite shell systems.