Self Buckling Initial conditions

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SUMMARY

The discussion centers on the mathematical proof of self-buckling, specifically addressing the condition where the second derivative at x=0 equals zero, leading to the conclusion that A=0. The original poster references the Wikipedia page on self-buckling and expresses confusion regarding the application of Bessel functions in this context. A seasoned engineer notes that while the topic is mathematically intriguing, it lacks practical applications in real-world engineering scenarios.

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Vincent Isoz
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Hi

For a book I'm writing, i try to write a very very very detail proof of self-buckling.

I did it almost by taking inspiration of:

https://en.wikipedia.org/wiki/Self-buckling

But i really really don't get how we arrive to, that when, x=0 as we obviously must have:

\dfrac{\mathrm{d}^2 x}{\mathrm{d}x^2}(x=0)=0

that A=0? This last point i don't get it. I must do a stupid error using Bessel functions properties but since 3 weeks I'm trying and i fail... Any help would be greatly appreciated.

Thx
 
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While this topic is mathematically interesting, it has little practical application. In 50+ years as an engineer dealing with mechanics problems of all sorts, I have never seen anything close to this in real life, and I don't know of anyone who has. This may well be why you are not generating lots of answers.
 
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