Is "nodeEigenvector" using initial or current stiffness?

[IsmBaha]

Hello Frank,
I wonder if "nodeEigenvector" and "eigen" commands are using the current stiffness or the initial stiffness at the time it is being called? Thanks.

[selimgunay]

"eigen" command uses the current stiffness.

[IsmBaha]

Thank you for your reply.

[IsmBaha]

I have one more followup for the "eigen" or "nodeEigenvector" commands.

How do those commands calculate eigen values and vectors when the stiffness negative or, e.g. in the unloading branch?

Isn't there a complication of negative lambda values? I remember seeing in some posts that there may be negative eigen values obtained. Is there such a case when using "eigen" or "nodeEigenvector" commands? Frank was suggesting to use the last successful (non-negative) eigen values.

[selimgunay]

For an SDOF system, when the tangent stiffness becomes negative, eigenvalue becomes negative. For an MDOF system, it is more complicated, but it is possible to achieve negative eigenvalues when the stiffness contributions of a significant portion of elements become negative. At that stage, the response is severely degraded, so I don't know if it is any useful to use those eigenvalues

[IsmBaha]

Notwithstanding it is complicated, those eigen values should still be meaningful in terms of the frequency that the building experiences, right?

The eigen values I get with the "eigen" are not negative during an analysis I ran. I wonder if this is just by luck all positive or not?

Similarly I am getting eigen vectors using "nodeEigenvector" as normal values, wondering if this is similarly just by luck?

[selimgunay]

The eigenvalues are useful to observe the period elongation due to damage, but I am not aware of a period-based damage indicator, while there are other such as ductility, dissipated energy, plastic rotation, etc.

[IsmBaha]

Thank you for your reply.

I am actually thinking it as earthquake forces experienced by the building right at that step while building is going through different periods, rather than its damage implication.

It makes me think about the meaning of periods that "eigen" command give in each time step because the period is a phenomena for a cycle. But calculating many periods during an inelastic cycle, which continuously change every time step since stiffness keeps changing, makes things complicated b/c period keeps changing and reaching to very large values (3-4 times the initial T1). When I look at the response on the other hand, I see the corresponding cycle doesn't really have a period of 3-4 times of initial, but much smaller. Maybe the max period value obtained with the "eigen" in each time step doesn't make sense at all. Or average of those periods obtained with "eigen" should be corresponding to the period of that cycle?

[selimgunay]

You can compute the fourier amplitude (or response spectrum) of accelerations any where on the structure and that will indicate an average elongated period. You are right, instantaneous periods do not provide such indication

[IsmBaha]

Yeah, though FFT peaks are cumulative measurements of time history. But I have been thinking if there is a way to see the mode shapes (therefore force distributions) instantaneously as the system goes through transitioning modal coordinates since every little change in the stiffness due to inelasticity will alter them. Still thinking if I can make sense of mode shapes obtained with tangent stiffness at each time step though.