Eigen Modes vs Natural Vibrations

Grasshopper Karamba3D
1

Hi,
I’m trying to understand the difference between the Eigen Modes (EModes) component and the Natural Vibrations (NVibes) component and whether I can expect similar results between them.

Can you confirm the units of the eigenvalues reported by EVals?
Am I correct in thinking that to convert this to a frequency I need the following conversion?:
frequency = sqrt(eigenvalue) / (2 pi)

I saw on an old post that the Eigen Values component uses the ‘Identity matrix’ while the Natural Vibrations component uses the ‘Mass matrix’.
Is there a simple explanation of the difference between these two?

Thanks
Ewan

2

Hi @Ewan_Macpherson,
the Eigenmodes in Karamba3D are calculated as the Eigenvectors of the stiffness matrix K (elastic and geometric (in case of ThII).

The equation to be solved is Kv= lambdav. Here v is an Eigenvector and lambda an Eigenvalue. Since K contains entries of unit kN/m and kNm/rad the physical unit of lambda needs to be both.

From the Eingenvalues of the stiffness matrix it is not possible to derive the Eigenfrequency. For the latter one needs to include the effect of inertiy via the mass matrix M: Kv = lambdaM*v.

– Clemens