Impact loading on a massed beam

tjbr

Hey guys, I've got a problem that I have been puzzling over for a long time now.

If I have a beam, which has no mass, and a weight is dropped onto the centre of the beam, then the deflection is easy to work out, we let the strain energy of the beam equal the potential energy of the mass:

1/2 P*delta = mg(h + delta)

and delta = PL^3/(48 EI)

However, if we say that the beam did have a mass, how would this effect the deflection? I was reasoning that the potential energy would be turned into kinetic energy when it hits the mass, however, when the beam is at its greatest deflection, the kinetic energy = 0.

So does this mean that the weight of a beam plays no part in the deflection caused by dropping a mass onto it? It seems backwards to think so, so i'm a bit puzzled here.