A numerical method to simulate the coupled oscillations of flexible structures in flowing fluids

A numerical method is developed to simulate the coupled phenomena in a fluid-flexible-structure system. Specifically, a two-dimensional panel method is used to calculate the hydrodynamic forces and a modal superposition method is adopted to solve the governing equation of an Eulerian beam. The stability boundary of a single flexible beam in a uniform flow is calculated and compared with previous results to verify the validity of the code. The flow-induced flapping of a single and two flexible bodies for S=1.0, U*=7.0 are investigated. For the flow-induced vibration of a single beam, the oscillation frequency is close to the secondary natural frequency of a cantilever. For two parallel flexible beams, they oscillate in phase when the non-dimensional separating distance H<0.25. When H>0.25, the out-of-phase mode occurs with a jump in frequency. When H>1, the interaction between the two beams decouples and the frequency and forces of each beam revert to behavior associated with a single beam in the same flow. Simulations of coupled-flapping of two tandem flexible structures proved that the drag acting on the upstream body is reduced while for that downstream drag is obviously increased when the structures are closely arranged. The numerical results obtained in the present work are qualitatively consistent with early experimental results.