Free Vibration Analysis of Thin Circular Cylindrical Shell with Closure Using Finite Element Method

Vibration analysis of a thin circular cylindrical shell with closure is conducted using finite element method (FEM). Theoretically, shell vibrates in different axial modes, m; circumferential modes, n; and any of their combinations with corresponding modal frequencies. The present FEM results are verified by the results reported in the literature using various shell theories. The eigenvalues of the shell are extracted using block Lanczos and subspace iteration methods, in order to investigate their computational efficacy. Further, the effect of adding various types of closures at one end of the circular cylindrical shell such as flat, cone, and dome, on the modal frequencies are investigated. The two aspect ratios (length to radius ratio) of shell with closure, broad, and slender are considered for this study. The effect of the ratio of the thickness of the closure to the thickness of shell wall on the frequency is also investigated. For the shell with the closure, the vibration modes can be cylinder, closure, or combined cylinder and closure. The modal frequency of the cylindrical shell is significantly affected by the closure. The lowest frequency is observed in the flat type of closure in both the broad and slender cylindrical shells in comparison to the non-closure, dome, and cone type of the closures.