What is the exact mathematical reason behind the Tacoma narrow bridge collapse ? I have googled about the collapse , but I didn't get a correct reason and a mathematical model.
2026-03-27 14:21:40.1774621300
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Tacoma Narrows bridge collapse : mathematical explanation.
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The old physics textbook explanation in terms of 'resonant frequency' is disputed by closer analysis and simulation. In addition to the extensive discussion at Wikipedia
http://en.wikipedia.org/wiki/Tacoma_Narrows_Bridge_(1940)#Cause_of_the_collapse
there are some articles by P.J. McKenna challenging the (then) standard account as due to incorrect approximation of the equations:
https://www.maa.org/sites/default/files/pdf/upload_library/22/Ford/McKenna1-18.pdf
http://www.math.utah.edu/~gustafso/tnarrows/
Kristen Moore (McKenna's PhD student at the time he wrote his article) has several publications on this subject at her webpage
I assume you are referring to the failure of the Tacoma bridge in 1940.
It is difficult to provide a detailed reply here (and IANAExpert), but this was a classic case of aeroelastic flutter, a harmful and self-reinforcing interaction between a structure and a fluid. Structural dynamicists study such problems.