sigularity of the mass matrix

When analyzing trusses, one can compute the natural frequencies of the truss, using matrix methods, i.c. solve the eigenvalue problem associated with the construction. One needs to assemble the **mass matrix** for that. This mass matrix is singular and can therefor not be inverted. What does it physically mean, that the mass matrix is singular ?

(The corresponding stiffness matrix is also singular, meaning the truss cannot deform, without being supported in some manner.).

Would the singularuity of the mass matrix mean, that the truss cannot

**vibrate** without being supported ?
Reply to
Osiris
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My linear algebra is a bit rusty, but I don't believe a singular matrix necessarily has any bearing on the stability of the truss. A singular matrix just means the equations describing the motion/forces on the individual bodies are not independent. This is believable considering truss systems often have redundant members. For example, if the forces on member A can be fully realized if one knows the forces on members B, C and D, then the equations for member A can be omitted. Leaving them in your calculations will lead to a system matrix that is singular. The rank of your matrix (number of linearly independent columns) will be less than the actual dimension of the matrix. If you want the a nonsingular version of your matrix, you'll need to do some row reduction techniques. Hope this helps.

Reply to
takedown

That is an answer to another question, I think. again: what does it **mean** that a mass matrix is singular ?

Reply to
Osiris

"A singular matrix just means the equations describing the motion/ forces on the individual bodies are not independent."

So if you have a 10x10 mass matrix that is singular (det=0), then this matrix can likely be reduced to a 9x9 or less.

Reply to
takedown

that is the mathematical meaning. now for the physical meaning.

Reply to
Osiris

I've answered your question twice already now, but I'll try to paraphrase for your benefit.

"A singular matrix just means the equations describing the motion/ forces on the individual bodies are not independent." This means the forces on one or more of your truss members depends completely on the forces of neighboring members. Therefore, the portion of the mass matrix describing the ODE for that member can be omitted.

Reply to
takedown

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