A periodic, Fourier series solution is presented for the nonlinear dynamic response of an impulsively loaded, elastic cylindrical shell. This result has been obtained by a new application of the quadratic form of Newton’s method; in this modification the frequency is considered to be the basic independent variable, and analytic corrections are obtained when solutions of the linear variational equations are nonperiodic. The solution presented here is shown to consist of a slowly varying function modulating a rapidly varying function, and is compared with results obtained by direct numerical integration.

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