Impact loading on a mass / mass-less beam

[tjbr]

Hey guys, I've got a problem that I have been puzzling over for a long time now. I think that the mass of a beam should not affect the amount that the beam deflects when another mass is dropped on it, however my mechanics lecturer thinks otherwise, i don't understand his logic.

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. This means that some of the potential energy of the mass being dropped gets turned into kinetic energy, but ultimately it all gets turned into strain energy.

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, but i don't see how it can't be the case, all the energy must end up as strain eventually!

 

[nvn]

tjbr: If you, for simplicity, neglect energy losses, and if the beam mass is modeled as a lumped mass M, shouldn't the conservation of energy equation also include a term for the initial potential energy of the beam, M*g*delta? How would this affect your solution for delta?