Damping in Nonlinear Transient Analysis
Hi everybody,
I am currently trying to better undestand the introduction of damping in nonlinear transient simulations.
I set up a simple model composed by a cantilever beam which is released from a bent condition and let free to vibrate.
Since I would like to gain some confidence with the Rayleigh damping (and the correct use of the coefficients alpha and beta) I tried to find the critical damping condition for my structure, but actually I found out that every effort to introduce damping into the model turned out to be ineffective: the model remains undamped.
I tried to impose damping in the following ways (not simultaneously, obviously):
- PARAM ALPHA1 and ALPHA2. The corresponding values where identified by imposing one of the two equal to zero and finding the value for the other in order to have a critical damping condition and for a frequency of interest equal to the first natural frequency of the beam, identified through a modal analysis. No effect on the nonlinear transient response.
- Use of structural damping PARAM G and conversion into equivalent viscous damping through the use of PARAM W3, which, according to the manual, should be supported for nonlinear transient analysis. W3 was found converting the first natural frequency in radians per second. No effect on the nonlinear transient response.
- Use of Structural Element Damping Coefficient GE and conversion into equivalent viscous damping through the use of PARAM W4. No effect on the nonlinear transient response.
- The only way left would be to impose directly ALPHA and BETA into the TSTEP card, which doesn't seem to work. The following error is reported in this case: "Incorrect data in field # 3." According to the manual, if I'm not wrong, the field #3 of the TSTEP card is the one devoted to the "Number of time steps of value DT#", which are yet specified in the TSTEP card.
I am running short of ideas, since every effort seems to be ineffective. Even unreasonably high values of damping have no effect on my model.
I would really appreciate any kind of suggestion and/or comment, which might help me figuring out what's the problem.
I attach the described models and the related solutions.
I am currently running the 2021 student edition of HyperWorks.
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Altair Employeeare you able to share a simple model as an example for this application, as a reference for others?
@Adriano A. Koga
Sure!
I attach four models corresponding to the four described procedures.
I also noted a further problem, which I couldn't solve yet.
Plotting the oscillation graph of the top of the oscillating cantilever beam, I found out that the response of the models in which damping was imposed thorugh the use of the Rayleigh damping ("PARAM ALPHA1 and ALPHA2" and "TSTEP ALPHA and BETA") was correct: it corresponded to the critical damping I was trying to impose.
Instead, in the case of the models in which damping was imposed through the use of structural damping "PARAM G" and "Structural Element Damping Coefficient GE", the response was overdamped.
I doublechecked all the parameters I gave in but I couldn't find my mistake.
(I chose as frequency of interest for parameters PARAM W3 and PARAM W4 the first natural frequency: is it right?)
I would be really glad if you gave me a hint about that.
I attach the plot of the responses.
Your in-depth review and results for non-linear transient damping is well done. The one question that I am curious on with your analysis for Alpha1 and Aplha2 is how you determined the values for Alpha1 and Alpha2? There are many articles that highlight the solving of simultaneous equations IF you have two natural frequencies from modal. However, if there is only one natural frequency for the system what method steps are done?
Can you provide any insight into part of your solution using Alpha1 and Alpha2? I also only have a single damping ratio due to a single natural frequency. I have tried to use Alpha1 =2*damp ratio/fn^2 and also Alpha2=2*damping ratio.
Each time I get a lot of noise in my response with regards to displacement and acceleration. If this is done with a linear analysis using G and W3 things look very nice with smooth sine wave results and evident damping.
Any insight into Alpha1 and Alpha2 is appreciated.
Attached graphic has the blue curve the acceleration output and the red curve is the acceleration input.
Thank you,
Luke
Update:
For what regards case 4 (ALPHA and BETA in TSTEP card). It turned out that the field #3 is the one devoted to the time integration method for nonlinear transient subcases (TMTD).
This entry has a default value of 1 (Generalized alpha method). For some reason (which I can't figure out), in case ALPHA and BETA are specified within TSTEP, this entry has to be specified explicitly.
This way, ALPHA and BETA are correctly exported as coefficients for the Rayleigh damping, which does work correctly in this case.
For what regards the other three cases: The mistake turned out to be quite silly.
Checking the .fem files, I found out that no PARAM setup was exported. I eventually discovered to have accidentally unflagged the "Status" option in the PARAM card.