How to apply stiffness and mass proportional Rayleigh damping separately?

[zhangbaozai]

Dear All:


I had a question about applying mass proportional and stiffness proportional Rayleigh damping. The traditional way of applying Rayleigh Damping is using the command like below:
rayleigh $alphaM $betaKcurr 0 0;


For example, if I have a model with the element numbers as follow:
Ele # 1-1000
Ele # 2000-4000
Ele # 10000-12000

If I only want to apply stiffness proportional damping to elements 1-1000 and 2000-4000 and apply mass proportional damping to all the nodes, I used the following commands:

region 4 -eleRange 1 4000-rayleigh 0.0 $betaKcurr 0.0 0.0;
region 5 -nodeRange 1 50000 -rayleigh $alphaM 0.0 0.0 0.0;

But it seems like the 2nd command replace the command of applying stiffness proportional damping, meaning that the analysis I ran only has mass proportional damping considered.

May I ask if you have any comments on this?

Thank you very much for your help.

[selimgunay]

You can try

region 4 -eleRange 1 4000-rayleigh $alphaM $betaKcurr 0.0 0.0;
region 5 -nodeRange 4001 50000 -rayleigh $alphaM 0.0 0.0 0.0;

[zhangbaozai]

Hi, Selimgunay:

Thank you for your reply. It seems works. May I ask if I understand the Rayleigh Damping command correctly in the following?
1. we can use multiple Rayleigh Damping commands to assign different Rayleigh Damping at different parts of the model;
2. If we assign multiple Rayleigh damping to the same region, then only the last Rayleigh Damping command will be in effect.

For example, if I have a Ele #1000 with nodes 1000, 1001. I did not assign mass density to Ele #1000 and only assign nodal mass to nodes 1000, 1001.

If I first assign stiffness damping to Ele 1000 and then use a second command assigning mass damping to Nodes 1000, 1001. In OpenSees, only the mass damping will be in effect because nodes 1000, 1001 are affiliated to Ele 1000, so the 1st stiffness damping command is ignored by OpenSees. If I assign stiffness damping and mass damping to Ele 1000 in one command, the mass damping will be assigned to the nodes (1000, 1001) that are affiliated to the element (Ele 1000) that I mentioned in the command.

May I ask if I interpret the Rayleigh Damping command correctly?



As a second follow up question, Dr. Anil mentioned of using Modal damping for time history analysis. I tried to use 20 modes-modal damping and 40 modes-modal damping for a 20-story building. I thought the more modes I considered, the better the response will be. But actually, the 40 modes-modal damping produces super small structural displacement responses (close to 0). May I ask what is your comment on this?

Thank you very much.


Sincerely,
Zhi