I need to solve the Bending Vibration of Euler-Bernouli Beam Problem and I keep getting stuck. I start with a fairly straight forward fourth order differential eq. Using the dsolve command gives me the general solution
Maple insist on using e^(x)+e^(-x) instead on sinh and cosh - but it's the same. So far so good.
My specific problem is a clamped-pinned beam of length l - so my boundary conditions are (correct me if I'm wrong here):
In the clamped end at x=0: Y(0)=0, Y'(0)=0
In the pinned end at x=l: Y(L)=0, Y''(0)=0
Using both the dsolve(ode,ics) and a dsolve(ode) and then solve(ics) both results in the trivial solution Y(x)=0 - which is wrong - I know there is a tan(a*l)-tanh(a*l) solution.
To get a easier and well documented example to solve by hand, I also tried with a simply supported beam. Boundary conditions are then:
Same result - only the trivial solution Y(x)=0 and If you solve it by hand you get a sin(a*l) solution.
What am I doing wrong? Is it syntax error on my part or what?
I have attached both my maple doc and a pdf with a walkthrough of the correct solution.
Any help would be appreciated