Swaying of footbridges
...Целый взвод слизнули воды,
Как корова языком,
Потому что у природы
Есть такой закон природы --
Колебательный закон !
...Повторяйте ж на дорогу
Не для кружева - словца,
А поверьте, ей же Богу,
Если все шагают в ногу --
Мост об-ру-ши-ва-ет-ся !
I thought that the basic physics of foot bridge swaying was well understood, but it turns out that the textbook explanations are grossly incorrect, and what causes this swaying is not really known!
...In 2000, the footbridge across the Thames River opened for public use and immediately experienced an unexpectedly large lateral oscillation-a “wobble”-that forced its closing and eventual retrofitting. Synchronous lateral excitation is the explanation commonly given for the wobble by several physicists in the field of nonlinear systems. This explanation is at best partial and at worst completely incorrect.
...Let’s start with an observation by John Macdonald involving the Clifton Suspension Bridge in Bristol, UK. The dominant lateral vibration of the Clifton bridge was at 0.5 Hz. The middle span of the London bridge also had its first lateral mode at 0.5 Hz, with a second lateral mode of approximately equal amplitude at 1.0 Hz. In contrast, average walking frequency is about 1 Hz. In other words, the average walker took four steps, two with the right foot and two with the left, for every left-right cycle of the first lateral mode of the Millennium Bridge. So even if the walkers were in phase with the bridge’s motion, that would not have amplified the bridge’s first lateral mode unless a nonlinear mechanism was at work.
...An explanation that has nothing to do with synchronous lateral excitation is that the walkers adjusted neither their frequency nor their phase but their balance due to the bridge’s lateral motion. Macdonald suggested that as a balance strategy walkers adjusted the width of their steps in response to the lateral motion of the bridge. And as the bridge’s lateral motion increased in amplitude, in some instances, the walkers’ lateral adjustment increased, thus providing the necessary driving term proportional to the bridge’s lateral motion. That balance response can either amplify or dampen the bridge’s motion, depending on the natural frequency of the bridge and the frequency of the walkers’ steps. The wobble is a wonderful example of an unresolved physics problem. http://ptonline.aip.org/journals/doc/PHTOAD-ft/vol_63/iss_3/8_1.shtml?bypassSSO=1
PS: Macdonald J. H. G.(2009) Lateral excitation of bridges by balancing pedestrians. Proc. R. Soc. A 465:1055-1073 http://www.physics.ohio-state.edu/~wilkins/writing/PDF/bridgewobble.pdf
http://www.physorg.com/news148707380.html
http://www2.eng.cam.ac.uk/~den/PEDESTRIAN_EXCITATION.pdf
Как корова языком,
Потому что у природы
Есть такой закон природы --
Колебательный закон !
...Повторяйте ж на дорогу
Не для кружева - словца,
А поверьте, ей же Богу,
Если все шагают в ногу --
Мост об-ру-ши-ва-ет-ся !
I thought that the basic physics of foot bridge swaying was well understood, but it turns out that the textbook explanations are grossly incorrect, and what causes this swaying is not really known!
...In 2000, the footbridge across the Thames River opened for public use and immediately experienced an unexpectedly large lateral oscillation-a “wobble”-that forced its closing and eventual retrofitting. Synchronous lateral excitation is the explanation commonly given for the wobble by several physicists in the field of nonlinear systems. This explanation is at best partial and at worst completely incorrect.
...Let’s start with an observation by John Macdonald involving the Clifton Suspension Bridge in Bristol, UK. The dominant lateral vibration of the Clifton bridge was at 0.5 Hz. The middle span of the London bridge also had its first lateral mode at 0.5 Hz, with a second lateral mode of approximately equal amplitude at 1.0 Hz. In contrast, average walking frequency is about 1 Hz. In other words, the average walker took four steps, two with the right foot and two with the left, for every left-right cycle of the first lateral mode of the Millennium Bridge. So even if the walkers were in phase with the bridge’s motion, that would not have amplified the bridge’s first lateral mode unless a nonlinear mechanism was at work.
...An explanation that has nothing to do with synchronous lateral excitation is that the walkers adjusted neither their frequency nor their phase but their balance due to the bridge’s lateral motion. Macdonald suggested that as a balance strategy walkers adjusted the width of their steps in response to the lateral motion of the bridge. And as the bridge’s lateral motion increased in amplitude, in some instances, the walkers’ lateral adjustment increased, thus providing the necessary driving term proportional to the bridge’s lateral motion. That balance response can either amplify or dampen the bridge’s motion, depending on the natural frequency of the bridge and the frequency of the walkers’ steps. The wobble is a wonderful example of an unresolved physics problem. http://ptonline.aip.org/journals/doc/PHTOAD-ft/vol_63/iss_3/8_1.shtml?bypassSSO=1
PS: Macdonald J. H. G.(2009) Lateral excitation of bridges by balancing pedestrians. Proc. R. Soc. A 465:1055-1073 http://www.physics.ohio-state.edu/~wilkins/writing/PDF/bridgewobble.pdf
http://www.physorg.com/news148707380.html
http://www2.eng.cam.ac.uk/~den/PEDESTRIAN_EXCITATION.pdf