Nonlinear Forced Vibrations of Infinitely Long Cylindrical Shells.
COLUMBIA UNIV NEW YORK DEPT OF CIVIL ENGINEERING AND ENGINEERING MECHANICS
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Large amplitude forced vibrations of infinitely long, thin cylindrical shells are determined, using generalized coordinates which are the infinie sequence of normal modes of linear shell theory. The perturbation procedure employed gives solutions consisting only of a finite number of terms, so that arbitrary truncation of the infinite series in terms of the modes is avoided. As reported previously, unusual types of response are possible, in which the nodal lines of the applied sinusoidal pressure in space and of the radial displacement do not agree. Amplitude-frequency relations for regular and unusual responses are obtained. Numerical coefficients occurring in these relations are tabulated. It is demonstrated that the unusual responses exist only for sufficiently small values of a nondimensional parameter which increases with the ratio of critical damping. The unusual solutions become unstable, or do not exist, when the parameter exceeds cut-off values derived in the text. The situation is illustrated by a sequence of examples with varying values of damping. Author