Multiple mass-spring-damper system

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The discussion revolves around a complex three-level mass-spring-damper system subjected to a driving force simulating an earthquake. The forces acting on each level include gravitational, spring, damper, and inertial forces, with specific equations provided for each mass. The user is struggling with the dynamics of the system in Simulink, particularly regarding the initial conditions and the driving force's impact on the overall behavior. Clarifications are made about the driving force and initial displacements of the springs, indicating a need for further adjustments to achieve a dynamic response. The conversation highlights the importance of accurately modeling forces to prevent unrealistic outcomes in simulations.
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I posted this in the general forum but it probably belongs here.
This is a tricky one!

I'm unsure about the forces on the ground level.

The problem is a 2-spring-damper system with three levels. A ground level, level 1 and level 2. Then a force is applied to the ground level simulating an Earth quake (eg the force could be sinusoidal). See the attachment for a diagram.

These are the forces I have resolved:

-level 2 mass:
gravitational force, m0*g (down)
Spring Force2, K1*(x1-x0) (up)
Damper Force2, b1*(x1'-x2') (up)
Inertial Force, m*x0'' (down)

-level 1 mass:
gravitational force, m*g (down)
Spring Force1, K1*(x2-x1) (up)
Damper Force1, b1*(x2'-x1')(up)
Inertial Force, m*x1'' (down)
Spring Force2, K1*(x1-x0) (down)
Damper Force2, b1*(x1'-x2') (down)

-level ground mass:
driving force (earthquake) = some function eg sine
g-force, mg (down)
Spring Force1, K1*(x2-x1) (down)
Damper Force1, b1*(x2'-x1')(down)
Inertial Force = m*x2'' (down)

I have tried to solve this using simulink, but for the positions of each level they fall towards negative oblivion. I am thinking I either have forgotten some force added too many.

Have I left anything out? *thinking*
James
 

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Hi, this looks a bit like active suspension control...

i get following equations :

m0x0" = -k1(x0-x1)-b1(x0'-x1') + U
m1x1" = k1(x0-x1) + b1(x0'-x1') - U - k1(x1-x2) - b1(x1'-x2')
m2x2" = k1(x1-x2) + b1(x1'-x2') - U

Ofcourse you need to add the overall gravitational force which you implemented correctly in my opinion.

x : position
x' : velocity
x" : acceleration

just for clarity...

regards
marlon
 
m0 is level two
m1 is level 1
m2 is groundlevel

Just to make sure, ok ?

regards
marlon
 
Thanks Marlon for the reply. What about when I add a driving force on ground level?
This is assuming that the springs are fully relaxed? I have calculted the displacements due to the weight of each level. What should be done to may this system dynamic?

Thanks
James

edit: oops for some reason I thought U=mg. U= driving force! But still does this consider the initial displacement of the springs?
 
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