Problems in modelling nonlinear viscous dampers

Dear All,

I am having some problems in modeling nonlinear viscous dampers in Ruaumoko. Indeed, I am working with a single degree of freedom with a nonlinear viscous dampers in order to do a parametric study to see the influence of linear and nonlinear viscous dampers. The model I have created gives exact results (comparing with analytical solution) when I use linear viscous dampers (i.e., alpha = 1). However, when I introduce a nonlinear viscous damper (i.e., alpha < 1) Ruaumoko gives some problems, that are the following:
- when using Ruaumoko3D (all version 2004, 2005 and 2009) the solution does not converge and there are some numerical errors that appear in the output file like these ones:
--RELATIVE DISPLACEMENT SOLUTION.--
* Maximum Iterations: Time 0.3670, Force Norm Ratio 1.079E+00
* Maximum Iterations: Time 1.2350, Force Norm Ratio 1.799E-01
* Maximum Iterations: Time 23.0940, Force Norm Ratio 4.052E-03
I have tried to increase the number of iterations in the integration schemes as well as to reduce the integration time step without any result.

- when using Ruaumoko2D I got convergence of the solution, however using different version of the program gives different results (I have been using 2005 and 2009 version). The 2005 version gives more reasonable results however these are different from the analytical ones (and instead the results should be quite close to the analytical solution).

Anyone has encountered these problems? Any suggestion will be highly appreciated since I am working on this problems since the past two weeks!

Best Regards,

Alberto Lago
Ph.D. Student Rose School (IUSS) Pavia

The dashpot, for ITYPE=2 or 3, non-linear damper, uses the same routines as does the spring with the Hertzian Contact element. The problem with the non-linear dashpot when the power, Alpha, is less than 1.0, is that as the velocity gets small the tangent damping coefficient tends to infinitity. This, multiplied by 2/dt, exacerbates the problem in thee dynamic stiffness matrix, leading to numerical difficulties on computers which use finite precision arithmetic. The program has a test which states if the velocity is small, then a linear damping is used for the tangent damping until a threshold is reached whereupon the system uses the correct tangent damping. The damping forces are always computed from the velocity using the appropriate power Alpha, it is just the tangent damping that is approximated. This may lead to an error in the damping forces compared with that expected by the program from the tangent dynamic stiffness. The error in terms of farce is small but the iteration convergence test is the square of residual forces norm divided by the the square of the applied force norm. The ration may be large, as in your first warning message, but if the applied forces at that step were small this would be insignificant. Your last warning message that you listed showed a norm ratio of the order of 0.1 which probably is also not a problem. Check what happens with a smaller time step, if the error is coming from the damping forces, then this will be something that you may have to live with. You know the times at which this is occurring, check out the magnitude of the damping forces and the velocities at these times to see what is happening. I could try to alter the range where the stiffness is approximated, but this may take a wee while. There is not much point in increasing the number of iterations. In my experience with the time-stepping methods, if the convergence is not available in 5 cycles of iteration, the pointer, for normal time-history problems, the time-step is too large.
Let me know what you find.

Ciao Alberto,
I saw your post about dampers. Let me focus on linear dampers. I am using linear dampers on a pile to account for radiation damping. Anyway, I make the following check:
1) I plot force vs velocity for a damper through HYST in DYNAPLOT. The result is correct, points (vel, force) lie on a line with slope equal to c.
2) But if I calculate (vel@node1 -vel@node2), i.e. relative velocity of the nodes of the damper, then the result is completely different compared with the velocity obtained from 1.

Do you have any idea about this?

Costas, Please see comment in your other question on dashpots. The source code saves the forces, velocities, displacements and member stiffness factors fir the dashpot members and the velocities are those within the element and theses are obtained from the nodal velocities via the transformation matrix. However, rigid end links and non-zero member length will mean that the nodal angular velocities will have a contribution to the dashpot velocities.

Hello all

I'm working with Genetic Algorithms, I generate several models, then the best structures are selected and I generenate new models until I achieve a good performance. The problem is that with two identical models (just diferent file names), I get diferent results. Elastic and inelastic drifts have litle diference in the two models, but the forces in the dashpots are very diferent. Does annybody has an idea of what could be happen? I run the models in batch mode using the program that Domenico posted (killquickwinerr) I don't know if that causes problems to Ruaumoko program. Bye

David

David, Can you email me your data sets, (a.carr@civil.canterbury.ac.nz) there may be that when the damping models are different which is masked by other effects in the structure, i.e. in normal analyses it is assumed that the damping forces are small, for a 5% linear viscous damped system the damping forces are of the order of 10% of the inertia and elastic forces in the system, so maybe small changes of the response may be associated with quite large variations in the damping forces particularly if the damping model is non-linear