The nonlinear dynamics of long, slender cylinders for moderately large deformations are studied by projecting the solution along the set of eigenmodes of the linear problem. The resulting set of nonlinear ordinary differential equations is truncated on the basis of bandlimited response. The efficiency of the method is due to the derivation of asymptotic solutions for the linear problem in its general form, by using the WKB method. Applications for the dynamics of risers, including the effects of nonlinear fluid drag and geometric nonlinearity demonstrate the features of the method.

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