Euler-Bernoulli beam equation, implicit scheme

Hi,

 I am trying to simulate the motion of an Euler-Bernoulli beam (clamped-free) using finite differences. Using the explicite scheme works, but the time step condition is a bit too restrictive for my case (I need real-time computations at 44kHz sampling frequency)

Hence, I try to use an implicite schemes. The problem is then that the oscillation of the beam is damped (no damping terms are included in my motion equation for now) and seems to contain just the first mode of vibration.

 I found videos on youtube showing these phenomena : 

explicit  http://www.youtube.com/watch?v=BUzxxG-w9dg

implicit  http://www.youtube.com/watch?v=28vDJhEkGKY

 My fd equation is based on

m*y_tt=-k*y_xxxx

 y being the positon of the beam dependent on space (x) and time (t), translating to

m*(y(t+1,x)-2y(t,x)+y(t-1,x))/dt²=-k*(y(t,x-2)-4y(t,x-1)+6y(t,x)-4y(t,x+1)+y(t,x+2))/dx⁴

 for explicit computation and

m*(y(t+1,x)-2y(t,x)+y(t-1,x))/dt²=-k*(y(t+1,x-2)-4y(t+1,x-1)+6y(t+1,x)-4y(t+1,x+1)+y(t+1,x+2))/dx⁴

Is this wrong ? I don’t understand why the implicit scheme is giving wrong results...

Can anyone shed some light on this for me ?

Thanks,

Martin