Self Buckling Initial conditions

[Vincent Isoz]

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

 

[Dr.D]

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.