Eigenvalue analysis generalized mass
Eigenvalue analysis generalized mass
(OP)
My understanding of the meaning of generalized mass from an eigenvalue analysis is that it represents inverse damping, ie, the higher the generalized mass, the lower the damping at the calculated modal frequency. A supplier provided eigenvalue calculations for a 100+ node pump and motor giving generalized masses for 100+ "resonant" frequencies ranging from less than 1 to over 4000. Are there any general guidelines for lumping the GM numbers into a few categories between say "overdamped" and "zero damping"?
vanstoja
vanstoja





RE: Eigenvalue analysis generalized mass
"Generalised mass" is a term which usually means a representation of the "physical" mass matrix which has been transformed from "physical" (also called "nodal" in FE) coordinates to generalised (also called "modal") coordinates.
The eigenvalue analysis produces eigenvalues, which are related to the system natural frequencies (actually 2*pi*f^2), and eigenvectors, which are the mode shapes associated with each of those frequencies. If all these eigenvectors put together into one matrix, with each column of the matrix being one eigenvector, then we have the "modal matrix" of the system. Each column may be scaled in any way you wish. Often the columns are scaled so that each has a maximum value of 1.
The physical mass, stiffness and (if needed) damping matrices can be converted to generalised coordinates by post-multiplying by the modal matrix and pre-multiplying by the transpose of the modal matrix.
These new generalised mass and stiffness matrices will always be diagonal. The same is true of the damping matrix provided a Rayleigh damping model has been assumed. There is now a generalised mass, stiffness and damping value associated with each mode. However, these generalised values are not unique. They depend entirely on the scaling of the eigenvectors in the modal matrix. A generalised mass matrix is pretty useless unless you know the modal matrix which was used to calculate it.
One form of modal scaling which is often used is "unity modal mass". The modal matrix is scaled such that the generalised mass matrix is the identity matrix.
I hope this sheds some light on your problem, but I must stress again that generalised mass values have nothing to do with damping.
Michael
RE: Eigenvalue analysis generalized mass
(2*pi*f)^2
not
2*pi*f^2
M
RE: Eigenvalue analysis generalized mass
Philippe
RE: Eigenvalue analysis generalized mass
RE: Eigenvalue analysis generalized mass
"How, with generalized stiffness and damping given, do I determine the relative hierarchy of the
100 or so calculated frequencies with respect to imminent disaster level if I happen to have a
potent vibration source fundamental or harmonic at that frequency?"
That's a much better question. The answer is that you need to need to do a forced response analysis, ie drive your linear model with a representatitive forcing function and if you are a great believer in software you can even do a fatigue analysis. Concentrate on the red bits. In general you can't really do a fatigue analysis on an unknown (ie poorly understood) structure in the frequency domain - time history is the way to go, but if you have a strong tonal source you may get away with it.
However linear FE, as such, does not understand damping in any useful fashion, you will need to assign a different damping value to each mode if you wish to estimate stresses and get good correlation. A more realistic alternative is to dump your linear model into a program that does understand discrete damping in assemblies. The ones we use are called FDYNAM, FLAP and VSIGN, but I'm sure there are many alternatives, I assume Nastran, and and I know ABAQUS, has extensions to allow this.
Cheers
Greg Locock