Finite Element Analysis of Thin Circular Cylindrical Shells

Abstract

Free vibration finite element (FE) analysis of thin circular cylindrical shells is investigated. The circular cylindrical shell can vibrate in different modes and theoretically infinite modes are possible. The axial mode, m and circumferential mode, n, in any of their combinations define the modes and the corresponding modal frequencies. The shell elements are used to model the thin circular cylindrical shells. The eigenvalues of the shell are extracted using block Lanczos iteration method. Detailed mesh convergence studies are performed for different height or length to radius (H/R) ratios. Importantly, selection of
appropriate FE mesh size criteria based on the perimeter and height of the circular cylindrical shell, as well as thickness to radius (h/R) ratio are shown for various boundary conditions. The modal frequencies of the cylindrical shell are investigated for different boundary conditions such as clamped-clamped (C-C), clamped-free (C-F), and simply-supported - simplysupported (S-S). The effects of height to radius (H/R) ratio and thickness to radius (h/R) ratio on the modal frequencies of the cylindrical shells are also studied. For all the considered boundary conditions, the modal frequencies of the cylindrical shells increase with higher circumferential mode number and also with the increase in the h/R ratio. The modal frequencies are observed to be the lowest in the case of the C-F boundary condition of the shell.