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Eigen-solver with displacement-dependent force
Posted Apr 6, 2022, 10:34 p.m. EDT Structural & Acoustics, Studies & Solvers Version 5.5 2 Replies
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I have a 3D mechanical system wherein we examine the stablity, when subjected to an external load, in terms of an eigenvalue problem. The external load is modeled in the following manner:
where 
is an external parameter, 
are coordinates, 
is the displacement along 
axis, and 
is time.
My question is, can we apply this force in the following manner:
in an eigenfrequency solver ?
-------------------I am a student of Mechanics.
IIT Kanpur | Purdue | M3Sim
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The velocity is already available as a built-in variable, so you can use that (solid.u_tZ for example). Since that term is proportional to the velocity, it would be a type of viscous damping (or, dependent on sign, amplification). By including damping, you will get complex valued eigenfrequencies and eigenmodes.
What is more intriguing is the other load term. It is actually not directly displacement dependent, but rather dependent on the displacement gradient. It is a pressure, proportional to the slope. You can use wX, just as you suggest. The only thing to note, is that you when you have 'follower loads', you have to select the Include geometric nonlinearity check box in the eigenfrequency study. That will make the stiffness matrix dependent on the load.
-------------------Henrik Sönnerlind
COMSOL
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Thanks for your reply, Henrick. I indeed expect the eigenvalues to be complex in nature. I will incorporate your suggestions and get back to you.
-------------------The velocity is already available as a built-in variable, so you can use that (solid.u_tZ for example). Since that term is proportional to the velocity, it would be a type of viscous damping (or, dependent on sign, amplification). By including damping, you will get complex valued eigenfrequencies and eigenmodes.
What is more intriguing is the other load term. It is actually not directly displacement dependent, but rather dependent on the displacement gradient. It is a pressure, proportional to the slope. You can use wX, just as you suggest. The only thing to note, is that you when you have 'follower loads', you have to select the Include geometric nonlinearity check box in the eigenfrequency study. That will make the stiffness matrix dependent on the load.
I am a student of Mechanics.
IIT Kanpur | Purdue | M3Sim