Critical examination on in-plane inertias for vibration characteristics of cylindrical shells

There has been a common assumption that neglects the in-plane inertia or rotary inertia of a cylindrical shell to yield analytical and numerical solutions of the vibration characteristics. This assumption can largely simplify some derivation processes and result in a unified governing equation, nevertheless, precondition and justification of this assumption have not been examined yet. Presented herein is a critical examination on the in-plane inertia and rotary inertia for breathing vibration of the cylindrical shell. Analytical solutions are presented based on Donnell's shell theory and the first-order shear deformation theory, respectively, in which simply-supported, clamped and free ends of the cylindrical shell are considered. Finite-element analyses about breathing modes and vibration characteristics are conducted to confirm the validity of present solutions. Furthermore, the mechanisms of some phenomenons are interpreted. It is shown herein that the influences of ignoring the in-plane and rotary inertias on natural frequencies of the cylindrical shell depend on the breathing modes, principally by the number of waves in the circumferential direction of the breathing modes. The in-plane inertia along the axial direction has a very limited effect on natural frequencies compared with those along the radial and circumferential directions. There are large relative differences by using the functions of beam-like modes to calculate the vibration characteristics of the cylindrical shell with clamped or free ends under the cases of lower number waves.