Eigenvalues

Hi all,

I am finding out how the compare the stiffness of plate structures. I started with a simply supported column with a unit load of 1 kN. The buckling factor and buckling load from the Karamba output match with the hand calculated buckling load (Euler). 

With plates I was also able to match the Karamba stiffness output with the hand calculated value (simply supported plate on all 4 edges supported). 

I was also looking at the Eigenvalues and I am wondering what they represent and if they can be a measure of optimizing different shapes of plate structures? In a previous discussion on this forum I found the following:

"Another indicator of stiffness is the Eigenvalue of the stiffness matrix. This value is independent of external loads and offers a good basis for comparing structural alternatives in e.g. an optimization. The smaller the value of the eigenvalue, the stiffer the structure." 

But when I change the profile of the simply supported column under compression force to a larger profile, the eigenvalue increases. So my question, what do the eigenvalues represent and can they be a better measure to compare stiffness compared to the buckling factors?

Thanks in advance!