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Multiple mass-spring-damper system |
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| Oct30-04, 09:57 AM | #1 |
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Multiple mass-spring-damper system
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 |
| Oct30-04, 11:42 AM | #2 |
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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 |
| Oct30-04, 11:45 AM | #3 |
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m0 is level two
m1 is level 1 m2 is groundlevel Just to make sure, ok ??? regards marlon |
| Oct30-04, 06:21 PM | #4 |
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Multiple mass-spring-damper system
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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