PSI - Issue 84

Allan Larsen et al. / Procedia Structural Integrity 84 (2026) 1103–1110

1105

stranded cables and is responsible for the prevention of aeolian vibrations of overhead power lines at wind speeds above 7 m/s, IEEE (2015). Energy dissipation by fretting action is limited in contemporary highly tensioned hanger cables yielding damping levels of 0.0015 – 0.003 log. dec., thus allowing wind induced vibrations at high wind speeds. 2. Vortex induced (aeolian) vibrations Suspension bridge hanger cables as well as overhead power lines are prone to cross wind vortex induced vibrations if of sufficiently small mass and low damping. Vortex induced vibrations results when the frequency of the rhythmic vortex shedding along the span of the cable structure subjected to a wind flow coincides with one the natural frequencies of the cable thus establishing a resonance condition. The vortex shedding frequency is related to the cross-section dimension of the structure and the wind velocity through the Strouhal number = ⁄ , a constant depending on the cross-section shape. Detailed wind tunnel measurements of the response of a long flexible circular cylinder suspended to oscillate in its first cross wind bending mode, Birka (1993) reveals a characteristic bell shaped response versus wind speed curve indicating the onset of harmonic oscillations at a reduced wind speed = ⁄ = 5.0. For slight increases of the reduced wind speed the non-dimensional vibration amplitude ⁄ grows and the vortex shedding frequency locks-in with the structural frequency ⁄ = 1. Thus, = 1 ⁄ in the lock-in range. Beyond the lock-in range at high the harmonic vibrations of the structure cease and become irregular and of small amplitude. The vortex shedding frequency will again become proportional to the wind speed as predicted by the Strouhal relation = ⁄ .

= 0.2 = 0.18 = 0.15 −

Fig. 2. Measured vortex induced vibration response curve (left). Non-dimensional amplitude as function of Scruton number (right) Fig. 2 (left) displays the bell-shaped non-dimensional amplitude ⁄ vs non-dimensional wind speed ⁄ curve obtained from wind tunnel tests of a spring suspended section model of a hanger cable of the 1915 Çanakkale bridge, Fig. 3 (left). The onset wind speed for sizable response amplitudes (say larger than 10 % of the model diameter) is about ⁄ ≈ 5.0 corresponding to a Strouhal number = 0.2 marking entry of the lock-in range. The largest amplitudes are found at a Strouhal number = 0.18 or ⁄ ≈ 5.7 quoted in Eurocode EN 1991-1-4 as the critical wind speed for vortex shedding excitation whereas the lock-in range ends at = 0.15 or ⁄ ≈ 6.5. It is noted that the experiments of Brika and Laneville defines a slightly winder lock-in range ending at = 0.12. The amplitude of vortex induced vibrations of cables is governed by the mass of the cable and the damping often combined in a non-dimensional parameter the Scruton number = 2 2 ⁄ , where is the structural damping decrement, is the cable mass / unit length and is the density of air. Prediction of hanger cable amplitudes mostly rely on experimental data available in codes of practice. A dataset often applied for power line studies is due to Rawlins (1998) who fitted detailed wind tunnel test results by polynomials for easy use in calculations. The Rawlins response model curves for 1% and 5% turbulence is reproduced in Fig. 2 (right) together with more recent measurements obtained for the 1915 Çanakkale bridge cable section model, Larsen (2023) and a long elastic tube, Muggiasca (2018). It is noted that the Rawlins response curves appear to span the newer data quite well