Question: Solving the Bending Vibration of Euler-Bernouli Beam

Hello

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

Y(x)=A*sin(a*x)+B*cos(a*x)+C*sinh(a*x)+D*cosh(a*x)

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:

Y(0)=Y(l)=0

Y''(0)=Y''(l)=0

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.

Beam_vibration.mw Transverse_vibration_of_beams.pdf

Any help would be appreciated

Kind regards

Jacob