An Analytical Study of the Nonlinear Flexural Vibration of Thin Circular Cylindrical Shells

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Abstract
The nonlinear flexural vibration property of thin circular cylindrical shells with simply supported ends is analytically studied. The deflection mode is assumed so as to satisfy the continuity of the circumferential displacement in the large deflection theory and consists of the driven mode and its companion mode. The governing equations are derived by using HAMILTON'S principle. For the approximate solution of the nonlinear equation and its stability analysis, the method of averaging is used. The steady solution of the driven mode has the resonance curve of the softening type, and becomes unstable with the appearance of the companion mode at the region of the resonance. The values of the structural damping and the exciting force are effective for the stability of thesteady solution. In this unstable region the vibration of circumferentially traveling wave mode is stable. The present analytical results offer a satisfactory explanation to the available experimental observation.

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