Free vibrations of an elastic square cylinder in a cross-flow

Flow field and structural vibration of a square cross-section cylinder in a uniform cross-flow were measured simultaneously. The measurement is compared with that obtained for a circular cross-section cylinder of the same hydraulic diameter in an effort to understand the effect of fixed and moving flow separation points on fluid-structure interactions. While a single hot-wire was used to measure the velocity, the dynamic strains associated with the lateral and longitudinal bending displacements of the cylinder were simultaneously measured using optical fibre Bragg grating (FBG) sensors. It is found that a violent vibration occurs at the resonance where the vortex shedding frequency coincides with the third mode natural frequency of the fluid-structure system, irrespective of the cross section of a cylinder. Evidently, the instability is not affected by whether the flow separation point is fixed or not. However, the vibration amplitude of the square cylinder doubles that of the circular cylinder even though the flexural rigidity of the square is larger. This is attributed to the occurrence of galloping in the square cylinder case, which provides additional energy for the resonance. Using an auto-regressive moving average modelling technique, the effective damping factor, including structural and fluid damping, was deduced from the measured strain signals. It is observed that the effective damping factor corresponding to the third mode natural frequency of the fluid-structure system is smaller than that corresponding to the first or second mode natural frequency.