Flexible structures within a non-uniform inflow may undergo complex vortex-induced vibrations (VIV) containing multiple frequencies and vibration modes. Therefore, the critical question arises on whether and how a flexible cylinder's structural response and fluid forces undergoing multi-frequency vibrations resemble or differ from mono-frequency vibrations. Therefore, we experimentally studied the problem of dual-frequency VIV of a stepped flexible cylinder, viz., a large-aspect ratio flexible cylinder consisting of two segments with different diameters and rigid cylinder forced vibration experiments. The results show that the maximum in-line (IL) and cross-flow (CF) displacements and the frequency ratio of the stepped cylinder separated by individual frequency resemble those of a uniform cylinder vibrating in the uniform flow at a single frequency. In addition, it is found that forced vibration results from rigid cylinders undergoing multi-frequency IL and CF motion can improve the prediction of the multi-frequency flexible cylinder VIV, provided the amplitudes and phases, as well as the true reduced velocity Vr for each of the dual frequencies match, especially when .
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