Base motion for a simple spring mass system

[shah]

Hi all,
I wanted to better understand the modeling set-up for a steady-state dynamics problem with a base motion, so I tried to run a simple spring-mass system analysis. I could not use the mass element for it as it was causing an error during the run, and instead used a beam element B31 to produce a mass. And for the spring, used SPRINGA. The modal damping is via RAYLEIGH method, and I defined the base displacement using AMPLITUDE. The following is the model script, which ran successfully, but I have some doubts about the model response. Specifically, in the model transmissibility vs frequency plot, the curve starts at 1 for low frequency, which is expected, then it peaks at natural frequency, after that, instead of approaching zero, the curve saturates at around 2 for high frequency. Also, the peak transmissibility value does not appear to be correct either. I am wondering if there’s an issue with my setup?
Best,
Shah

**
*NODE,NSET=NALL
1,0.,0.,0.
2,1.,0.,0.
3,2.,0.,0.
*NSET,NSET=NRESPONSE
2
*ELEMENT,TYPE=SPRINGA,ELSET=ESPRING
1,1,2
*ELEMENT,TYPE=B31,ELSET=EMASS
2,2,3
*BOUNDARY
1,1
*BOUNDARY
1,2
*BOUNDARY
1,3
*BOUNDARY
2,2,3
3,2,6
*EQUATION
2
2,1,1.0,3,1,-1.0
*SPRING,ELSET=ESPRING
1.2e7
*MATERIAL,NAME=EL
*ELASTIC
210.e9,0.3
*DENSITY
23.
*BEAM SECTION,ELSET=EMASS,MATERIAL=EL,SECTION=rect
1,1
*AMPLITUDE,NAME=A1
1.,0.01,500.,0.01
*STEP
*FREQUENCY,SOLVER=ARPACK,STORAGE=YES
1
*CLOAD
3,1,0.
*NODE file
U
*NODE PRINT,NSET=NRESPONSE
U
*END STEP
*STEP
*STEADY STATE DYNAMICS
10,400,40
*MODAL DAMPING,RAYLEIGH
,0.,27.e-5
*BASE MOTION,DOF=1,AMPLITUDE=A1,TYPE=DISPLACEMENT
*NODE file
PU,U
*NODE print,NSET=NRESPONSE
U
*END STEP

[Disla]

I also had problems in the past with pure Spring + mass system. It gave a problem related with inexistent density or something like this.
The issue was solved adding a Dummy solid element to the system.

[shah]

Thank you for the feedback Disla. I am using the beam element B31 instead of pure mass for the same reason. In my case, the model is running Ok, but I have questions on the results. I am getting the following transmissibility curve from this analysis (dots are from FE, and the curve is what I expect). The peak level and the curve saturation at 2 for high frequency don’t seem to be correct. That is why I was wondering if anyone can spot an issue with my script posted above.

By the way, this issue is occurring with the base motion input only. If I use the force load, the FE matches the hand calculation perfectly as below:

[JuanP74]

you have a mistake and a typo: the mistake is in equation: you are removing the node at the location where you are requesting output (“The first variable is considered to be the dependent one, and is subsequently eliminated from the equation”). The typo is in modal damping, you have to input 2 blanks before the parameters

**
*NODE,NSET=NALL
1,0.,0.,0.
2,1.,0.,0.
3,2.,0.,0.
*NSET,NSET=NRESPONSE
2
*ELEMENT,TYPE=SPRINGA,ELSET=ESPRING
1,1,2
*ELEMENT,TYPE=B31,ELSET=EMASS
2,2,3
*BOUNDARY
1,1
*BOUNDARY
1,2
*BOUNDARY
1,3
*BOUNDARY
2,2,3
3,2,6
*EQUATION
2
3,1,-1.0,2,1,1.0
*SPRING,ELSET=ESPRING
1.2e7
*MATERIAL,NAME=EL
*ELASTIC
210.e9,0.3
*DENSITY
23.
*BEAM SECTION,ELSET=EMASS,MATERIAL=EL,SECTION=rect
1,1
*AMPLITUDE,NAME=A1
1.,0.01,500.,0.01
*STEP
*FREQUENCY,SOLVER=pardiso,STORAGE=YES
1
*CLOAD
3,1,0.
*NODE file
U
*NODE PRINT,NSET=NRESPONSE
U
*END STEP
*STEP
*STEADY STATE DYNAMICS
10,400,40
*MODAL DAMPING,RAYLEIGH
,,0.,27.e-5
*BASE MOTION,DOF=1,AMPLITUDE=A1,TYPE=DISPLACEMENT
*NODE file
PU,U
*NODE print,NSET=NRESPONSE
U
*END STEP

[JuanP74]

[shah]

Thanks a lot, Juan, that was a big help. I had tried to print the output from node 3 in the past with my original equation since it was an independent node, but that did not print any output for some reason, so had to stick to node 2 instead for output. I hadn’t tried the workaround you pointed out by switching the dependency between nodes 3 and 2 while outputting from node 2, this was the key.