Simple formulas for the dynamic response of parametrically excited slender and straight structures immersed in fluid

This work presents the development of a simplified mathematical formulation for the fast evaluation of the steady state response of slender structures under parametric excitation, considering also the interaction with a still surrounding fluid. The simplified formulation is obtained from a previous solution based on the multiple scales method. However, this previous solution requires a series of cumbersome integrals to be evaluated, rendering it non-attractive for widespread use in engineering design. The objective of the simplified solution is then to render it attractive as a design aiding tool for structural engineers. Along the work, many examples are shown comparing the proposed formulation with solutions obtained with the Finite Element Method in order to address the capability of the latter to correctly predict the amplitude of response of the structure. The results presented highlight this capability, and also provide a guided approach on how the formulation can be used for parametric investigations of the structure at hand.