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Calming Effects against Cable Vibration
Cable-stayed bridges have been built in increasing numbers since 1950, particularly for medium to long-span bridges and are now used where previously a truss or suspension bridge might have been the first choice. But despite the number of cable-stayed bridges being built, there are still elements of the technology that cause concern to engineers, such as the effects of cable vibration phenomena. Even newly-built cable-stayed bridges have experienced quite severe vibrations. Several cable vibration mechanisms have been identified and characterized, the four most common phenomena being vortex shedding, galloping, parametric excitation (deck/pylon and cable interaction), and wind and rain-induced vibrations. Excessive cable vibrations have been observed on numerous other bridge structures and preventative design measures and excitation mechanisms are often debated. But the use of highly-sophisticated dynamic evaluations and countermeasures can be counterproductive, because of the complexity of the physical phenomenon of cable vibration and the fact that even today not all vibration mechanisms are fully understood.
When airflow is forced around an object, vortices are shed off the object; consecutive vortices from opposite sides of the object produce alternating perpendicular forces. If the frequency of the alternating forces matches any of the natural frequencies of the cable, vibrations may occur. Galloping is a phenomenon that occurs because of aerodynamic instability, where the airflow creates uplift forces around an unsymmetrical cross-section. Galloping may occur on cables if the airflow hits at an angle such that the effective aerodynamic shape of the cable is an elliptical cross section. Cables with an ellipticity of 2.5 in combination with low structural damping have been observed to be susceptible to galloping instability. Ellipticity is defined as the maximum width divided by the minimum width of the cross-section; therefore a circle would have an ellipticity of 1. An ellipticity of 2.5 corresponds to an angle of inclination of the cable of 25°, which can typically occur on long-span cable stayed bridges. The formation of ice on the cable can also change the cross-section of a stay cable to induce galloping. Cable vibration may also occur as a result of vibrations of the bridge deck or the pylon, which are transferred through the anchorages into the cables. Deck and pylon vibration can occur because of aerodynamic effects or periodic traffic loads, such as trains and trucks. If the natural vibration frequencies of the structure are close to the natural frequencies of the cable stays in combination with low damping, parametric excitation may occur. One particular phenomenon that produces large amplitudes of cable vibration is wind and rain-induced vibration. Rainwater forms rivulets under the influence of the airflow around the cable, which then changes the aerodynamic cross-section of the stay cable in such a way that it is susceptible to vibrations. Once the cable starts vibrating, the rivulets start to oscillate at the same frequency as the cable. One point to note is that such vibrations have never been reported during heavy winds, suggesting that the rivulets get blown off as the wind speed increases.
The short-term consequence of cable vibration is complaints from bridge users; the long-term consequence may be reduced safety factors or even failures of complete cables due to a rapid accumulation of bending fatigue stress cycles at the anchorages.
Various countermeasures are available; the use of a helical rib on the outside of the cable surface is particularly effective against wind-rain induced vibration. The fillet helps to prevent the formation of the coherent water rivulets, which are responsible for the cable vibrations and therefore mitigates the excitation at its source. Other cable surface treatments include dimples and longitudinal grooves. If the natural frequencies of the structure are close to those of the cable stays, cross-ties can be installed to shift the natural frequencies of the cable stays and to avoid any possible interaction of deck and pylon with the stay cables. Designers should check that certain modes of cable vibration are not exaggerated by attaching only one cross-tie at the half or third point of the cables, for example. The use of cross-ties can also be an effective method for suppressing other types of cable vibration. Supplemental devices can be used to add damping to the cable - hence achieving sufficient total damping as an efficient measure against cable vibrations. If the cable begins to vibrate, with the movement of the cable at the position where it is attached to the damping device, energy is dissipated through the damper to stabilize the cable. Structural elements have a certain level of inherent (internal) damping, which is typically of the order of 0.9 to 1.8% logarithmic decrement for individually protected tensile elements inside a flexible stay pipe. However, inherent damping is often insufficient to prevent cable vibrations and therefore supplemental damping might be required. Typical devices for cables are so-called 'rubber doughnuts', mechanical dampers and hydraulic dampers. The theoretical maximum supplemental damping is independent of the particular type of damping device and only a measure how much damping a 'perfect' damper could provide. The key parameter is the distance at which the damper is placed as a percentage of the total length of the stay cable. Dampers are generally placed at 2% to 2.5% of the cable length, which results in a value of roughly 6% to 8% damping, which is sufficient for most applications.
'Rubber doughnut' damping devices are so-called because they are doughnutshaped, they generally consist of a proprietary internal damping device, which is typically positioned at the end of a steel guide pipe. High-damping rubber devices have proven to be a suitable countermeasure against cable vibration, even on extremely long span bridges, such as the Tatara Bridge in Japan, with its main span of 950m and maximum cable length of 450m. There are many other damping devices available on the market, such as hydraulic, electromagnetic and mechanical dampers. Although these can provide an appropriate solution, engineers should consider site conditions, construction tolerances and maintenance requirements when deciding which to install.
A proprietary BBR solution is the mechanical friction dampers, which require minimal maintenance; they operate in the same way as car brakes, being virtually maintenance-free and working for years without maintenance. Proprietary BBR friction dampers can be used as internal dampers, where they are installed inside the steel guide pipe or externally, attached to the free length of the cable using a damper housing and external brace.
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