Hi

To scale modes for unity mass (which you seem to be doing) is perfectly alright for any linear structure.

Think about it, if it did not work, it would not be possible to scale modes when using, e.g. lumped masses who have an infinite mass density as they exist only at a single point.

Sincerely

Claes

Thank you for your response, Claes.

Well, it apparently means excluding the lumped mass matrix formulation (I use the consistent mass formulation), am I right?

Hi Petr

We live in a beautiful world. It works for both as you can do it both for continuous structures as well as for purely lumped systems.

There are a several ways to scale modes, e.g.

• Unity max response
• Unity vector length
• Unity modal mass

The advantages is using unity modal mass lies in a diagonal mass matrix (when lumped), which Lanczos solvers like, and that it simplifies substructuring.

Perhaps you want to take a look at these

http://www.spectraldynamics.com/docs/star/modalparam.pdf

http://www.svibs.com/solutions/literature/2005_3.pdf

As far as I am aware, the consistent mass formulation does a better job at capturing rotation inertia and does not produce a diagonal mass matrix and hence, computationally is a little costlier to solve.

/Claes

Hello Petr,

I may suggest to have a look also on the effects on damping matrix: if the proportional damping assumption breaks due to inhomogeneity then you turn to have complex valued modes and you have to do your normalisation with state space matrices (modal A and B).

Regards,

Alessandro

Thank to all for your suggestions!

It is true that the output modes are slightly complex, but right now i am not able to recognize if it is due to errors in input data or it is a problem caused by inhomogenity of densitty field. I will try your suggest to investigate the assumption about the proportional damping.

Hi Petr

From a physics standpoint, complex modes imply a net transportation of energy in the system for which you run modal analysis. Real valued modes exist only for contained systems with evely distrubuted and light damping.

You get complex modes for a variety of reasons

• Fluid-structure systems produce complex modes
• Systems with gross motion driving oscillatory motion (vibration) produce complex modes with positive or negative damping values, e.g. brake squeal and flow excited sound/pulsarion. The latter being a case where the gross motion drives vibration.
• As Alessandro points out, systems with localized and/or unevenly distrubuted damping produce complex modes.
• In experimental modal analysis, you may get complex modes because you measure only on part of the total system. One such situation can be a natural frequency with localized response where you do not have sensors or too few sensors to accurately sample the mode.

Sincerely

Claes