Free vibration of cantilevered cylinders : effects of cross-sections and cavities

This study investigates the influence of a cavity on the natural frequencies and mode shapes of a homogeneous, isotropic, elastic solid cylinder. Cavities of different shapes and sizes are often found in engineering applications to provide access, reduce weight and to cut cost in production. As a result, detailed quantitative solutions to this class of problem will be of great interest to engineering practitioners. In this study, a highly efficient and accurate numerical algorithm is proposed to examine the vibrations of elastic solid cylinders with a deep cavity. The technique uses the exact theory of three-dimensional elasticity in conjunction with the Ritz form of minimum energy principle to derive the governing eigenvalue equation. Within the context of three-dimensional elasticity, displacement functions composed of a set of twodimensional lateral surface functions and one-dimensional longitudinal functions are defined for each displacement component. The orthogonality inherent in these functions has resulted in well form eigen value matrices which can be manipulated and solved with ease. The technique yields upper-bound natural frequencies and three-dimensional deformed mode shapes for a wide range of elastic hollow cylinders with an arbitrary cross section. Most of the results presented herein are believed to be new to the existing literature. © 1995 Springer-Verlag.