Modal Mass, Effective Mass, etc. 1

[271828]

Hello. Thanks in advance for any help.

I'm trying to apply some of the equations from the 1987 IMAC paper by Rao. It's called "Electrodynamic Interaction Between a Resonating Structure and an Exciter."

In Section 2.1 (in case anybody has this paper), he states that m equals the modal mass, but he gives no indication how it is derived. I've calculated the modal mass for my structure using several different normalization schemes and can't get results that make any sense.

When an author uses the term "modal mass," in a paper like this, what's he talking about? Is there an unstated convention that I haven't picked up on yet?

 

[GregLocock]

Well, 100000e, (sorry had to do that), as you say it comes down to definitions. I haven't got that paper but suspect that he's using the most directly useful form of m, which is the effective mass at the interface between the two systems.

Cheers

Greg Locock

Please see FAQ731-376 for tips on how to make the best use of Eng-Tips.

 

[271828]

Greg, thanks for the reply.

100000e--I've been waiting for somebody to type that!

As for the effective mass at the interface, doesn't it still matter what normalization he used? Normalizing so that PhiTransposed*M*Phi=Identity for example?

I have Ewins and I think he calls this "effective mass," which is a unique number for a given mode and DOF. Is this the one you're typing about?

 

[271828]

Greg, in Ewins' 2nd Ed., the "effective mass at DOF j" is on Page 57, in case you have it.

For Mode r, at DOF j, it has units of mass and is
(mjj)r=1/(phijr)^2

 

[GregLocock]

Yes, the Ewins concept is the one.


Cheers

Greg Locock

Please see FAQ731-376 for tips on how to make the best use of Eng-Tips.

 

[271828]

Thanks again Greg.

 

[hacksaw]

there are two common normalizations, the one with true orthonormal mode shapes common to continous mass distributions, the other with an identity mass matrix, i.e., mass weighted normal modes, common to discrete mass systems.

seems that Rao (don't have his paper), must be using orthonormal modes