The fundamental and second periods of transverse oscillation of a cylinder containing a flowing fluid are theoretically determined for the approximate solution of two, coupled, nonlinear partial differential equations describing the transverse and longitudinal motion. The calculations indicate that the existence of the fluid transport velocity reduces all cylinder natural periods of oscillation and increases the relative importance of non-linear terms in the equations of motion. Accordingly, in many cases of practical interest the linear analysis is shown to be severely limited in its applicability. Curves are presented that will assist one to estimate both the accuracy of the linear period and the approximate nonlinear period in selected examples. A new approximate solution method is utilized that permits accurate and efficient calculation of the nonlinear period. This method can be applied to the period determination of additional cylindrical models not examined herein; the method appears to be semi-generally applicable to the periodic solution of weakly nonlinear systems.

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