Free Vibration of Rotationally Restrained Stepped Open Cylindrical Shells: New Analytical Solutions

Abstract The rotationally restrained stepped open cylindrical shells are typical components utilized in the aeronautic, astronautic, and marine fields for their merits in light weight and designated structural enhancement. Nonetheless, few analytical free vibration studies have been reported by reason of the challenges in dealing with the high-order partial differential equations incorporating the complex joining and boundary conditions. In the present work, we make a first successful attempt to solve such issues by developing a novel analytical solution scheme with an integration of the symplectic superposition method and the subdomain division technique. The frequencies are acquired by rigorous derivations without assuming displacement forms. The stepped open cylindrical shells subjected to three rotationally restrained boundaries under two stepped thickness directions are considered to exhibit the versatility of the proposed solution scheme, and all the free vibration solutions show excellent agreement with their counterparts from the literature or the commercial software. Moreover, sufficient parametric analyses on the crucial design variables have been conducted on the basis of the analytical solutions, and the findings may reduce the structural analysis procedure of stepped open cylindrical shells.