Hello there!(adsbygoogle = window.adsbygoogle || []).push({});

So here's my problem, while you solve the Euler Bernoulli beam Equation by separation of variables, how do I have to prove the separated function of space are orthogonal? If so, are hyperbolic sines and cosines orthogonal when you have a product or a linear combination of them?

The pde is- [; u_{tt}+\alpha^{2} u_{xxxx} = o ;] where [; \alpha ;] is a constant that is material dependent. The separated function of space is [; F(x) = \sum_{n=1}^{\infty} [cosh(\beta_{n}x)-cos(\beta_{n}x)]-[sinh(\beta_{n}x)-sin(\beta_{n}x)] ;] where [; \beta_{n} ;] is some constant.

**Physics Forums | Science Articles, Homework Help, Discussion**

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

# Solving higher order PDE's

Loading...

**Physics Forums | Science Articles, Homework Help, Discussion**