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I have a eigenfrequency simulation $ M * \ddot{\vec{x}} + K * \vec{x} = \vec{0} $ and want to add point masses to certain nodes. The only example I have is a 1D matrix where all of the mass at node 1 is added to the x1/x1 element in the matrix.

Since my matrix has 3 main diagonal elements at node 1, x1/x1, y1/y1 and z1/z1, do I add 1/3 at each of these?

I first added the entire mass (which makes sense because if I only move in x direction, I still need to move the whole mass) but then the sum of all masses in the matrix is not consistent with the mass of the system. Which way is correct?

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Full point masses should be on lumped mass matrix diagonal for each direction. Sum of the mass matrix elements does not have to be the full mass, that would make no sense. Full gravity force si pulling you down with the same intensity no matter if you are standing on the ground or accelerating in a horizontal direction.

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  • $\begingroup$ Thanks, yes, that kind of makes sense. I had derived the conclusion that I can sum over the elements of the matrix to get my system mass from a 1D-bar element where it is the case, because there is only one spatial direction I guess. I should still be able to get my system mass that way, by e.g. summing up everything in the x-columns (and rows?)? $\endgroup$
    – Joe
    Commented Feb 3, 2023 at 18:53
  • $\begingroup$ Yes, that is right $\endgroup$
    – Tomáš Létal
    Commented Feb 3, 2023 at 21:32

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