PSI - Issue 84

Allan Larsen et al. / Procedia Structural Integrity 84 (2026) 1103–1110 1109 blue and identifies a peak response at the free end of the model of ⁄ ≈ 0.48 occurring a non-dimensional wind speed ⁄ ≈ 44. The rain-wind curve is compared to the similar bell-shaped curve of vortex-induced vibrations obtained from tests with the model shown in Fig. 2 (left) displaying a peak amplitude ⁄ ≈ 0.26 at a non-dimensional wind speed ⁄ ≈ 5.7. Comparison of the two response curves in Fig. 7 (left) clearly demonstrates that the excitation provided by rain-wind is much stronger than that of vortex shedding.

Fig. 7. Non-dimensional model vibration amplitudes as function of the non-dimensional wind speed (left), logarithmic abscissa axis. Non dimensional amplitude as function of Scruton number (right), logarithmic ordinate. The bell shape of the ⁄ vs ⁄ curve the rain-wind vibrations, Fig. 7 (left), may suggest the existence of a lock-in range for rain-wind vibrations as is the case of vortex induced vibrations. However, it should be remembered that the water film running down the model is subject to the shear forces of the wind and is expected to be blown off the surface at some wind speed. This action will re-establish the surface conditions of the dry model and thereby end the galloping range. It is noted from Fig. 7 (left) that the model vibration amplitudes are significantly reduced at a non-dimensional wind speed ⁄ ≈ 90 corresponding to an upper wind speed of the galloping range of about 22 m/s. The measured magnitudes of the non-dimensional amplitude ⁄ as function of the Scruton number is shown in Fig. 7 (right). Four repeat tests were run for each individual Scruton number which displays some variation likely because the Ghosenol surface treatment was partly washed off model surface during each run and had to be re-applied. The maximum amplitude envelope was fitted by a curve for application in design calculations. Comparison of the rain-wind vibrations (blue) to the Rawlins curve (red) representing vortex induced vibrations emphasizes that the excitation provided by rain-wind is much stronger than the excitations due to vortex shedding. An important observation to be kept in mind when designing dampers for mitigation of hanger cable vibrations. Fitting helical strakes composed of circular cross section rope having a diameter of 10% of the cable model mitigated the rain-wind vibrations by preventing the continuous water film forming along the sides of the cylinder. The shape of the ⁄ vs ⁄ curve, Fig. 7 (left), may also shed some light into the frequency of vibration or wind speed of a hanger cable subjected to rain-wind vibrations. Video recordings of the galloping oscillations of the 1915 Çanakkale bridge hanger shown in Fig. 6 (left) establishes the vibration frequency as 2.7 Hz corresponding to the 5 th eigenmode. Assuming that the hanger cable is to vibrate in the mode receiving the largest excitation occurring at ⁄ ≈ 44 the corresponding wind speed is estimated as 12.5 m/s in agreement with on-site observations made at the time of the video recording. The rain-wind model tested has almost the same diameter and vibration frequency as the prototype hanger cable. However, the length and mode shape of the model are clearly different. The implications of these differences are not known in detail, but it is speculated that a very long cable exposed to natural rain may accumulate water slightly differently than the shorter model wetted by spray nozzles. The difference in mode shape, sinusoidal versus linear along the length will certainly affect the maximum amplitude. Commonly known mode shape correction procedures indicate that model amplitudes should be multiplied by a factor 2 - 3 to be representative of the prototype.