Flow-induced vibration of an Euler-Bernoulli beam

Flow-induced vibration of a fixed-fixed elastic cylinder with a large aspect ratio (≈ 58) is considered. The structural vibration is modelled by the Euler-Bernoulli beam theory, and the normal mode method is used to analyze the structural response. The flow field are resolved using a finite element method and the flow-induced forces are thereby calculated. Altogether two different cases are examined, one at resonance and another at off-resonance. Results thus obtained are compared with experimental measurements and a discrete-parameter model [a two-degree-of-freedom (2-d.o.f.) model] analysis. The comparison shows that, while the 2-d.o.f. model gives reasonable prediction of the mid-span vibration displacements for the resonant and off-resonant case, the present method yields the span-wise multi-mode response of the cylinder similar to that observed experimentally. Based on these results, a correction formula is derived to estimate the span-wise vibration from the 2-d.o.f. model result. Correlation results are also presented to show that fluid-structure interactions mainly affect the phase relation between the fluid forces and the corresponding vibration of the cylinder. Such influences have different effects along the cylinder span.