A domain decomposition method for free vibration of circular cylindrical shells with discontinuity in thickness

This paper presents a new approach for the free vibration of circular cylindrical shells with sudden discontinuities in thickness, based on the domain decomposition and modified variational principle. The cylindrical shell is decomposed into N shell segments along the locations of the step variations. Continuity conditions along the interfaces between adjacent shell segments are primarily enforced with Lagrange multipliers, which then lead to the establishment of a modified variational functional through a procedure of identification of these Lagrange multipliers. To make the domain decomposition stable, least-squares weighted residuals of interface continuity equations scaled by weighted parameters are then added to the obtained functional. Double mixed series, i.e., the Fourier series and Legendre polynomials, are adopted as admissible displacement functions for each shell segment. Ritz procedure is finally employed to extract the natural frequencies. The present solution is found to be very stable for a large range of values of the weighted parameters. Numerical results derived from the proposed method show excellent agreement with those obtained from finite element method, but with far less computational effort. This study also examines the effects of step thickness ratios on the frequency parameters of stepped circular cylindrical shells. © 2012 American Scientific Publishers All rights reserved.