Learning Forum

[Tonmoy]

Hello!

I generated a model which is a cylinder resting on a foundation, and I extracted the natural frequencies from it to check its accuracy. The cylinder and the foundation pad have the `*CONTACT_AUTOMATIC_SURFACE_TO_SURFACE` defined between them. In the keyword, I just selected the master and slave surfaces and changed the FS and FD parameters.

However, after checking the eigout file, I found that the first couple of rigid body modes are showing negative eigenvalues. I checked with different meshing of the foundation pad and the cylinder, and sometimes I can see the negative eigenvalues, and sometimes not.

I want to understand why this is happening and if it indicates that I am doing something wrong in my model. Also, apart from doing a convergence study, how to understand if the extracted frequencies are nearly accurate?

Thank you in advance for your time and response.

Regards,Tonmoy.

[Reno Genest]

Hello Tonmoy,

Is your model fully constrained? Or do you have parts that can move as a rigid body in space (not fully constrained)? The negative and zero frequency modes are probably due to rigid body modes. You can animate the modes and see what deformation they produce. You should be able to see the rigid body modes if you have any.

To get rid of the rigid body modes, you need to use *BOUNDAY_SPC or *BOUNDARY_PRESCRIBED_MOTION or other constrains (joints, tied contacts, etc.) so that no parts can fly away. This should eliminate the zero or negative frequencies.

If you don't want to fully constrain your model, you can ignore the negative or zero frequency modes and look at the first positive non zero frequency. Animate the mode to make sure it is the real first mode of vibration (lowest stiffness of your system).

Let me know how it goes.

 

Reno.

[Tonmoy]

Hi Reno!

Thank you for your response. I applied fixed boundary conditions (BCs) at the bottom of the foundation pad, but I didn't apply any BCs for the cylinder as we want to understand the response of the it during earthquake excitation.

The model should clearly exhibit some rigid body modes, and it's expected to find responses such as the cylinder moving left to right or up and down in the x-y plane during the first few modes. However, sometimes I encounter modes that seem unusual or unexpected. For instance, in one case, instead of the expected left-right rigid body mode, the cylinder showed a tilted response (as if the contact surface was holding a corner of the cylinder while allowing the rest of the body to move freely). In another case, the cylinder was moving in an inclined direction in the x-y plane, which is not something we expect in the first couple of modes.

In these situations where the rigid body modes appear to be incorrect or unrealistic, I've noticed that LS-DYNA reports negative eigenvalues. So, I wanted to understand why the negative eigenvalues generally appear and if there are any documents reflecting the theory of computing eigenvalue that ls-dyna employs in this kind of cases.

Thanks a lot again for your time and response.

 

Regards, Tonmoy.

[Reno Genest]

Hello Tonmoy,

The negative eigenvalues are the rigid body modes. You can ignore those. Even if the parts are moving in the XY plane or around a node, they are still moving as a rigid body (rigid body translations and rotations). 

Here is more information from our knowledge database:

"

First of all, always use a double precision executable when doing an eigenvalue analysis.

Eigenvalues near zero (negative or positive) are associated with rigid body modes.    For confirmation, animate the modes using the d3eigv database.    If you see no motion, then plot velocity vectors, which is a trick we use to identify nodal rotation.  

To eliminate rigid body modes, one would normally define (additional) constraints in the model.   If you're unconcerned about the rigid body modes, then do nothing.
-----------------------------
Computation of the eigenvalues occur in floating point arithmetic.
You should ignore the sign associated with near zero eigenvalues and
just treat them as zero.  An eigenvalue of value -1.0e-6 should just be recognized as an eigenvalue of 0.0.
The difficulty we have is deciding what is "near zero" as the we do not have the units of the model.  Changing
the units in which the model is described will change the tolerance for what is near zero.  Also whether the
analysis is performed in single or double precision.  I strongly recommend that all eigenvalue computation
be performed in double precision to accurate computation of the zero eigenvalue modes. "

Let me know how it goes.

 

Reno.

[Tonmoy]

Thanks Reno for the details. That answers my questions perfectly.

 

I really appreciate your time and help. Have a good rest of your week!

 

- Tonmoy

[Reno Genest]

Hello Tonmoy,

You're welcome!

Have a great day!

 

Reno.