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# Coupling of Translational Mass Components, What This Mean?

## Coupling of Translational Mass Components, What This Mean?

(OP)
Dears,

While reading the MSC/NASTRAN, "Linear Static Analysis" User' Guide, came across the following sentence,
"The principal mass axes are axes that have no coupling between the translational mass components."

What is the concept/meaning of "Coupling between Translational Mass Components."

Thanks for your time to explain or referring to a Technical Literature/Article/Book dealing the subject.
Replies continue below

### RE: Coupling of Translational Mass Components, What This Mean?

It’s out of context but it seems to apply to concentrated mass elements. There should be some chapters in the documentation describing their implementation in more detail.

### RE: Coupling of Translational Mass Components, What This Mean?

I this is out of context though conceptually isn't this just saying that the three axes are orthogonal?

A translation along one of these axes doesn't not cause translation along the either of the other two.

### RE: Coupling of Translational Mass Components, What This Mean?

As the documentation puts it “In real structures, the mass of structure is generally the same in all directions”, but simulation is about accounting for the effects of physical phenomena such that the response you get is useful and meaningful, and if possible realistic.

In MSC Nastran you are not restricted to the same mass in each coordinate direction, and you may have wondered why the mass (or actually weight) output by MSC Nastran in the Grid Point Weight Generator (GPWG) output (i.e. when you request PARAM,GRDPNT,n) has 3 values described in the MASS column, and 3 associated centres of gravity. The documentation you cited explains that directional mass can occur if you define scalar mass entries like CMASSi, or the jewel in the crown CONM1, but it can also occur if DMIG mass is entered either deliberately or mistakenly with directional mass. The documentation goes on to describe in some great detail what is going on in the GPWG, but doesn’t really go into the physical situation in which directional mass may occur.

Aside from special modelling situations that come up from time to time (a good example escapes me for the moment), there is a good example of when directional mass occurs when you use virtual mass to account for a fluid being present. Virtual mass is defined by a an MFLUID entry in the input file, which defines a couple of parameters like how deep the fluid is relative to a coordinate systems origin and the density of the fluid; it also references ELIST entries which specify which elements may be “wet” by the fluid. The fluid is not meshed explicitly, but is represented by its effect on the structure it touches – it is a boundary element method.

To the first time user, a curious characteristic of virtual mass is that it is, in the general case, directional. Physically this may be explained by imagining your morning mug of coffee filled to some nominal level commensurate with your need for a caffeine boost. If you were now to accelerate the mug of coffee vertically upwards, you would feel the mass of the mug and the entire mass of the coffee (the fluid). If you were to accelerate the mug in a transverse direction, you would feel the mass of the mug and only part of the fluid mass as some of the fluid tries to pile up the side of the mug opposite to the direction of acceleration. This added mass effect on the structure is dependent on the dimensions of the container, your mug in this case. If you had a rectangular shaped mug, you would see more virtual mass in the transverse direction normal to the longer edges of the mug than the direction normal to the shorter edges, but unless the mug had a top, the transverse direction mass will always be lower than the vertical direction. Note that in this method, it is assumed that elements that are wet to begin with stay wet and elements that are dry to begin with remain dry – it is a small displacement method, which also ignores the fact that if you accelerated the mug downwards, the coffee would be left behind and make a mess. This is a good example of a method that is not realistic, but useful and meaningful in the results you obtain.

Now if your mug were conical in shape, with the base of the mug larger than the aperture so the side walls of the mug tapered in towards the top of the mug, when you move the mug in the transverse direction, as the coffee piles up the side, it is able to push on the sloped side of the conical mug which it could not before when the side walls of the mug were vertical. This effect introduces mass coupling in the translational directions – a movement in one of the coordinate axes will see mass effects in the two other orthogonal directions.

DG

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