modal analysis:the frequency is a complex number(a+bi)

[2015James]

hello everyone:
when i do a time history analysis, i used the modal analysis command(eigen <$type> <$solver> $numEigenvalues) to compute the omega^2 in every time step, and update the damping ratio in every step(use this command:rayleigh $alphaM $betaK $betaKinit $betaKcomm), the frequency is needed when compute the $betaK and $alphaM.
but when the PGA is large, the square of the first frequency(omega_1^2 ) will become a negative number， then the first frequency omega is a complex number(a+bi), but the second and third frequency is still a positive real number,convergence can still be reached in the time history analysis, if i want to update the damping ratio in every step. which frequency should i used, should the first frequency(a+bi) be abandoned and the second and third frequency should be used to compute the $betaK and $alphaM?????

annother question is when the first frequency omega is a complex number(a+bi), does it mean the stiffness matrix is a singular matrix or the strucure is dynamic unstable??? but in this case,the convergence can still be reached in the time history analysis.

in this command:eigen <$type> <$solver> $numEigenvalues different $type and $solver are tried ,the problem still exit.


thank you very much.

[wuhaoshrek]

2015James wrote:
> hello everyone:
> when i do a time history analysis, i used the modal analysis command(eigen
> <$type> <$solver> $numEigenvalues) to compute the omega^2 in every time
> step, and update the damping ratio in every step(use this command:rayleigh $alphaM
> $betaK $betaKinit $betaKcomm), the frequency is needed when compute the $betaK and
> $alphaM.
> but when the PGA is large, the square of the first frequency(omega_1^2 ) will become
> a negative number， then the first frequency omega is a complex number(a+bi), but the
> second and third frequency is still a positive real number,convergence can still be
> reached in the time history analysis, if i want to update the damping ratio in
> every step. which frequency should i used, should the first frequency(a+bi) be
> abandoned and the second and third frequency should be used to compute the $betaK and
> $alphaM?????
>
> annother question is when the first frequency omega is a complex number(a+bi), does
> it mean the stiffness matrix is a singular matrix or the strucure is dynamic
> unstable??? but in this case,the convergence can still be reached in the time
> history analysis.
>
> in this command:eigen <$type> <$solver> $numEigenvalues different
> $type and $solver are tried ,the problem still exit.
>
>
> thank you very much.

Same problem, in my case I stop updating the damping coefficients once I tracked the negative eigenvalue which used for Rayleigh damping.
What do you for that issue now? thx.