Eigenvalue analysis

[Drej]

Could someone please explain to me in child-like terms exactly what "Mass Normalised Eigenvectors" actually means. I appreciate that that N eigenvalues are the N natural frequencies of a structure/system, and that the corresponding eigenvectors are essentially the displaced or mode shapes for each eigenvalue. I also understand that in a modal analysis the eigenvectors are normalised - since no load is applied - to the mass matrix, amongst other matrices. So, my burning questions are: why do this? why not normalise to something else? what exactly do the resulting "displacements" actually represent (apart from relative displacement of course)?

Thanks in advance.

 

[pjhype]

Mass Normalization means that each eigenvector is scaled to a unit value of generalized mass, that is,

(PHI-transpose)* M * (PHI) = 1.0

Where PHI is the eigenvector and M is the modal mass matrix. This is done in order to simplify computational and storage requirements in the finite element code. The "displacements" are still arbitrary, but they are just scaled in this manner to simplify the mass matrix.

There are other ways to normalize the eigenvectors based on your finite element code. NASTRAN allows you to normalize the eigenvectors to MASS, MAXimum displacement, or to a specific POINT displacement component.

pj

 

[labosonic]

I ll try to answer in child like terms ...
This is only a convention to get infos about your analysis but it s also a way to calculate the Modal Mass Participations (automatically computed since Nastran 2001 - but sometimes bugged) which can be a very simple way to determine which modal analysis is efficient to do modal approximation on a response analysis. Many people are according to say that 90 % of the total modal mass participation is only needed to make a correct forced response. If you want more details say it, i ll check out my old nastran courses ...

 

[Drej]

My understanding is that mass normalisation is just an operation which modifies the mass matrix (orthogonality of modes and all that), but doesn't aid massively in post-processing. The resultant plotted "displacements" here are then based on scaled values of the mass matrix.(?) When the eigenvectors are UNIT normalised (one option in ANSYS), the largest component is normalised to unity (which is useful for post-processing).

-- drej --

 

[Spirit]

Drej,

your assertion is correct, what I would like to point out is that what you refer to as 'mass matrix' is more precisely the 'modal mass matrix', that is [Mode matrix](Transposed)x[Mass Matrix]x[Mode matrix]. This is due to that an eigenvalues problem is, in its nature, the result of a linear problem degeneracy, thus giving a set of equation which do not have one but infinite solutions. Mass-normalizing is just one way to choose one of these solutions.


'Ability is 10% inspiration and 90% perspiration.'

 

[richard98]

Drej,

An PDF document in the following website may be helpful to you:

http://twist.lib.uiowa.edu/vibrations/Soln3-14.pdf

I am also trying to understanding the real meaning of displacement in ANSYS modal analysis, in which the switch "Nrmkey" in the command MODMOP is set to OFF.

Richard