Multiple springs and masses system

[blckwtr]

I have this mass spring system consisting of 4 masses and 4 springs. It is preloaded, and I want to know the velocity on the "free" side of the system at a certain point. Also would be interesting to know the remaining forces when that mass hit the end stop...

 

[BrianE22]

Well, for starters, with no damping you'll have infinite displacement and velocity at the resonant frequencies.

 

[GregLocock]

@OP Can you solve it for a single spring mass system? If not then you'd better figure out how to do that.

@Brian, I think it is under a static precompression so in all probability we are just talking about the initial acceleration of the system once the trigger is released. The dynamic deflection from the zero point cannot exceed the static deflection, I think.

Cheers

Greg Locock


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[blckwtr]

It is under static precompression both in initial state and after it is released, so the "free mass" hits a boundary after a couple of mm. So the equations is easily set up, I just don't know how to solve them to get velocity, accelleration etc...

 

[JBlack68]

solving in time or frequency domain?
if you have the response (displacement) of a mass i d_mi(t) then v_mi(t) =d_mi(t) dt, etc

 

[blckwtr]

For my application, the forces are released before a full endstop, so time?!

 

[blckwtr]

OK, I have the M and the K matrices already defined, I just need a little help refreshing my memory from university... BC's: x_i for al masses, v_i and a_i = 0. Also final position of one of the masses...

 

[FeX32]

Are you looking for analytical solution or numerical? I suggest numerical - the solution is pretty easy and the setup depends mostly on how you want to numerically solve it.