Non-Axisymmetric Vibrations of Stepped Cylindrical Shells Containing Cracks

Abstract:

Based on the Donnell’s approximations of the thin shell theory, this paper presents solutions for the problem of free non-axisymmetric vibration of stepped circular cylindrical shells with cracks. The shell under consideration is sub-divided into multiple segments separated by the locations of thickness variations. It is assumed that at the jth step there exists a circumferential surface crack with uniform depth c_j . The influence of circular cracks with constant depth on the vibration of the shell is prescribed with the aid of a matrix of local flexibility. The latter is related to the coefficient of the stress intensity known in the linear fracture mechanics. Numerical results are obtained for cylindrical shells of stepped thickness containing cracks at re-entrant corners of steps. Shells with various combinations of boundary conditions can be analyzed by the proposed method. Furthermore, the influences of the shell thicknesses, locations of step-wise variations of the thickness and other parameters on the natural frequencies are examined. The results can be used for the approximate evaluation of dynamic parameters of cylindrical shells with cracks and flaws.

• Periodical: Advanced Materials Research (Volume 934)
• Pages: 136-142
• DOI: https://doi.org/10.4028/www.scientific.net/AMR.934.136
• Online since: May 2014
• Authors: Larissa Roots*
• Keywords: Crack, Cylindrical Shell, Non-Axisymmetric Vibrations, Step

References

[1] W. Soedel: Vibrations of Shells and Plates (Third Edition, Revised and Expanded, Marsel Dekker, N.Y. 2004).

[2] S. Timoshenko and S. Woinowsky-Krieger: Theory of Plates and Shells (McGraw-Hill, NY, Toronto, London 1959).

[3] L.H. Donnell: Beams, Plates, and Shells (McGraw-Hill 1976 (Engineering Societies Monographs Series).

[4] J. Lellep, L. Roots: Vibrations of cylindrical shells with circumferential cracks, WSEAS Transactions on Mathematics, 2010, 9, pp.689-699.

[5] R. Pellicano Francesco: Vibrations of circular cylindrical shells: Theory and experiments, Journal of.

[6] Sound and Vibration, 2007, 303, pp.154-170.