Free vibration of circular cylindrical shells with discrete circumferential stiffnesses

Abstract

Gears with thin rims are broadly applied in aircraft and light-weighted applications. This study will derive the governing equations of cylindrical shells with discrete circumferential stiffnesses based on Hamilton's principle and Flügge shell theory. To derive the governing equations, the discrete circumferential stiffnesses which are displacement coupled are handled as external forces and expressed by Dirac delta function. The circumferential modal function contains multiple components of different circumferential wave number for the existence of discrete stiffnesses. The Galerkin method is adopted to discretize the governing equations. The natural frequencies and vibration modes are studied. The effects of different stiffness, the ratio of thickness and length to radius, number of discrete stiffnesses on natural frequencies and mode shapes are also investigated in this study.