Calculating reaction force from plate recoil

[kodak79]

Does anyone know how to calculate the recoil force from a plate that deflects under a point load?

i.e. if I have a plate that spans a gap and a point load is applied to the centre. When that force is removed and the plate wants to return to its equilibrium position how much will it continue past the equilibrium and how large a holding down force will the plate ends require?

And pointers would be greatly appreciated.

Chris

 

[chicopee]

An interesting problem for which I never had to contemplate. My initial instinct would be a reaction from its inetia less than the force exerted under the point load. On the other hand, if you get a book on vibration, you may get you answer if the plate acts as a beam. You should have more details about the plate anchoring method and possibly other forces beside the point load.

 

[structSU10]

Yes, this is definetly a dynamics problem. You would need to have a forcing function, and could check the plate as a simple span beam with the force applied to it. In your case it would be a pulse load, and you would be able to find the displacement / acceleration at a certain point after the pulse was applied, and derive the end reactions. Most likely the duhamels intergral or other methods such as newmark beta or wilson theta would be appropriate.

 

[MiketheEngineer]

Energy in - energy out. If it takes say 1,000 lbs to move it - then 1,000 approx will come out. That said - you did not specify time period. It may "snap" back un-predictably - but still E in - E out

 

[charliealphabravo]

Is this a purely theoretical discussion or are we talking about a real world application?

If theoretical, then there should be a closed form differential equation that describes the motion.
If real world, then it will probably require an empirical relation to account for all the simplifying assumptions like damping, elastic/plastic zone, friction, tempering, etc.

 

[dhengr]

Oh... Wow.... The questions we ponder? Get your structural dynamics text book out, and study it. If you pulled the plate down with a cable at the center of the plate, and then cut the cable quickly, the plate might well jump off its supports, one problem. If the plate spans a few feet btwn. solid supports and you drive a car wheel over it, you load and unload it slowly enough so it just deflect and then goes back to normal (straight) when the wheel rolls off of it. Here the energy is stored through beam bending, and released as a leaf spring might act. If the plate acts as a tension membrane (a stretched cable or bar, a trampoline surface?) you have a much different problem. In most real world situations I suspect you don’t unload the plate quickly enough to cause much real upward spring action.

 

[kodak79]

Its a real world situation for cars driving over at 40mph - but more likely around 60mph! So it would be a quick load and unload situation, and the question is how much force would the holding down bolts see?

 

[desertfox]

Well if the load is suddenly applied to a bar as in impact by using strain energy one can calculate the deflection.
See this link:-

http://www.roymech.co.uk/Useful_Tables/Fatigue/Mechanics_Impact.html