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Mass matrix construction, natural frequency calculation

Mass matrix construction, natural frequency calculation

Mass matrix construction, natural frequency calculation

(OP)
Mass matrix construction, natural frequency calculation:
I have a 3D element with a 12x12 consistent mass matrix.
However, the element also has a lumped mass on one side.
How do I incorporate this lump in the 12x12 matrix?
Just add the mass to the 6 diagonal elements of the joint it is attached to?
And what if the mass is attached excentrically?

RE: Mass matrix construction, natural frequency calculation

How many nodes does the element have? Does your element have rotational degrees of freedom? How did you come to 6 diagonal elements in the mass matrix when the mass is attached to one side?

RE: Mass matrix construction, natural frequency calculation

(OP)
Ah, yes. Sorry: its a beam element: 2 nodes, each 6 DOF.
the 6 diag. nodes in the MM refer to one node, don't they?
I thought, maybe you just have to add the consistent MM and the lumped (mass at extremity) MM.
and a lumped MM is diagonal-elements-only.

RE: Mass matrix construction, natural frequency calculation

Well, you would typically add that Mass as a mass to all the translational degrees of freedom. You could convert it into a mass moment of inertia and put it in the rotational degrees of freedom as well. But, that is less common and it requires that you know more about the spacial distribution of the "lumped" mass.

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