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Modified Slender Body Theory for a Structure of Variable Cross-Section

We consider the hydrodynamic force acting on a slender structure with a variable (in general, time-dependent) circular cross-section. The structure is embedded in a nonuniform ambient flow-field of a perfect fluid. Exact analytical expressions for the cross-sectional loading exerted on the slender structure are presented. The newly found nonlocal terms can lead to a resonant interaction between the nonuniformity of the ambient flow-field and the longitudinal variation of the cross-section.