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Comparative Accuracy of Shallow and Deep Shell Theories for Vibration of Cylindrical Shells

This paper investigates the limits and range of application of the shallow shell theory for vibration of singly curved cylindrical panels. The significance of neglecting tangential displacements in bending and twist in the Donnell-Mushtari-Vlasov shallow shell theory is examined. The Ritz stationary energy principle, with a class of geometrically oriented two-dimensional polynomial functions (p-Ritz method), is employed to determine the frequency parameters. A comparison of numerical results from the shallow and deep shell theories is presented. The paper concludes that the limits of the shallow shell theory are dependent on the aspect ratio and boundary condition. The conclusion regarding limitation for a cantilevered shallow shell available in the literature cannot be directly extended to other types of boundary conditions. For shells with unit aspect ratio, shallow shell solutions are practically accurate even for relatively large subtended angles, but the results could be otherwise for long shells. In general, the shallow shell theory is relatively accurate for shells with a subtended angle of not more than 40°.