Oscillation of bridges

Back to Suspension Bridges  Back to Bridges  Back to Home Page | Find Us on Facebook | Many thanks to Enviko Commercial

 Controlling oscillations Downloads of programs Effects of damping Effects of stiffness Effects of wind Exciting resonances Impulsive excitations Links about oscillation Oscillations of beams Oscillations of cables Oscillations of cable-stayed bridges Oscillations of towers Periodic excitations Oscillations Part 2

 The behaviour of a bridge is not fully specified by the static forces within it.  Any bridge can move. All the parts have both mass and elasticity, and can exchange energy between kinetic energy of the motion, and the strain energy of bending, stretching or torsion.   The bridge does not sit in a vacuum, doing nothing. It experiences the wind, and it experiences the live loads caused by traffic. These two facts have a profound effect on bridge design. Even the steps of pedestrians can affect a light, flexible foot-bridge. Consider, for example, a heavy train going on to the bridge. The stable shape of the bridge with the train is very slightly different from the shape without it, because the need to change the stresses means a change of strains as well. After the deflection, the bridge is in a lower state of energy than before. Where has the extra energy gone? Clearly, for the bridge to have changed its shape, it must have moved, so it must have had kinetic energy. This page is concerned with that movement, and the form it takes. Oscillations of Towers The picture to the left represents a side view of one tower of a suspension bridge before the suspended parts have been added.  The left hand bar represents the static situation. The right hand shape (exaggerated) reminds us that the tower can oscillate. In principle there could be higher modes, the next mode having a node near the top, but these modes have higher frequencies and smaller amplitudes. The oscillations can be a serious problem before the bridge has been completed, especially when the two legs have not yet been joined by a cross member at the top, or lower down. Like any other massive elastic object, the tower will have a natural resonant frequency. Energy transferred from the wind will tend to excite this resonance. Furthermore, because the towers are not streamlined, it is possible for them to shed vortices downstream. These tend to occur on alternate sides of an obstacle, making for an oscillatory situation. This can be observed with a flapping flag or even with the rope slapping against the flag-pole. This picture shows a vertical cantilever made of foam plastic, being bent by a fan. The second picture shows the effect of oscillation. Tall metal chimneys are usually provided with helical strakes, which affect the flow in such a way that the vortices do not occur. The helical shape makes the system work well whatever the direction of the wind. Flutter has been known to affect the wings of high-speed aircraft, though this is now unusual, as the phenomenon is well understood and the technology is mature.

 Oscillations of Cables The picture below represents the first five modes of oscillation of a hanging cable, such as an empty clothes line or a cable of an incomplete suspension bridge.   In the fundamental mode at the top, the oscillation would require large changes in the length of the cable, so this mode is strongly suppressed. The main mode is therefore the second harmonic, with a node in the middle. This has important consequences for the behaviour of suspension bridges. The millennium bridge in London has eight parallel cables, spaced away from the deck. Had some been curved inwards, so that they were closer to the deck at the centre, the fundamental horizontal mode might have been somewhat suppressed. Having little depth, it has little resistance to vertical movement also. Moving  Demonstration  Download  for  Cables Click here to download (or run in place) a simple movie (48 Kbytes) simulating oscillations of a stretched cable and a hanging cable.