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Eigenfrequency Analysis: Rigid Body Motion

Posted 1 feb 2018, 20:02 GMT-5 Structural & Acoustics, Acoustics & Vibrations, Structural Mechanics 3 Replies

Ganesh Patil
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I did an eigen frequency analysis of a solid cube with homogeneous Isotropic material. When I extracted 10 modes, I see first 6 modes with no real values but pure imaginary number.

Since Rigid body motion has zero frequency, having zero real number makes sense, but why do I get Imaginary number even if I dont have damping in my system. Is it FEM numerical approximation? I also get imaginary number for higher frequncy modes.

For my free-free analysis, I was expecting 3 translation and 3 rotational modes, but my 6 modes are giving me all rotational mode.

3 Replies Last Post 5 feb 2018, 07:27 GMT-5
Henrik Sönnerlind COMSOL Employee

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Posted: 7 years ago 2 feb 2018, 02:49 GMT-5

Hi Ganesh,

Here is a quote from the User's guide:

In practice, the natural frequencies of the rigid body modes are not computed as exactly zero, but can appear as small numbers which can even be negative or complex. If rigid body modes are present in the model, then it is important to use a nonzero value in the Search for eigenfrequencies around text field in the settings for the Eigenfrequency study step. The value should reflect the order of magnitude of the first important nonzero eigenfrequency

Your six rigid body modes are all linear combinations of the three translations and three rotations.

Regards,

Henrik

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Henrik Sönnerlind
COMSOL
Hi Ganesh, Here is a quote from the User's guide: > In practice, the natural frequencies of the rigid body modes are not computed as exactly zero, but can appear as small numbers which can even be negative or complex. If rigid body modes are present in the model, then it is important to use a nonzero value in the **Search for eigenfrequencies around** text field in the settings for the Eigenfrequency study step. The value should reflect the order of magnitude of the first important nonzero eigenfrequency Your six rigid body modes are all linear combinations of the three translations and three rotations. Regards, Henrik
Ganesh Patil
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Posted: 7 years ago 2 feb 2018, 11:54 GMT-5

Hi, Thank you very much, that does resolve lot of queries. I still have one. I am getting a modal frequency with same real and imaginary values but it is shown with different sign. PFA image (Last two frequencies)

The mode shape for both of them is same. Why is that?

Hi, Thank you very much, that does resolve lot of queries. I still have one. I am getting a modal frequency with same real and imaginary values but it is shown with different sign. PFA image (Last two frequencies) The mode shape for both of them is same. Why is that?

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Henrik Sönnerlind COMSOL Employee

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Posted: 7 years ago 5 feb 2018, 07:27 GMT-5

Hi Ganesh,

The complex conjugate pair is probably numerical noise. Note that the imaginary part is small relative to the real part. If you have a good value for Search for eigenfrequencies around (like 2e5), and still get this behavior, I would suggest tightening the Relative tolerance in the Eigenvalue Solver node.

Regards,

Henrik

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Henrik Sönnerlind
COMSOL
Hi Ganesh, The complex conjugate pair is probably numerical noise. Note that the imaginary part is small relative to the real part. If you have a good value for **Search for eigenfrequencies around** (like 2e5), and still get this behavior, I would suggest tightening the **Relative tolerance** in the **Eigenvalue Solver** node. Regards, Henrik

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