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Bent bow modes
Posted Jan 30, 2011, 9:16 a.m. EST 3 Replies
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I am writing a text book and want to use COMSOL to illustrate the coupled modes of a bent bow tensioned by a string across its ends. I am using a 3d model for the bow and a 1-D model euqtion-based for the transverse waves on the string - How can I couple the two systems. Any advice would be gratefully received _ I guess its simple.
3 Replies Last Post Jan 30, 2011, 11:49 a.m. EST
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Posted:
1 decade ago
Hi
first of all which version ?
you should be able to make a 3D geometrical model with the cord defined as a "line" connecting the two sides of the bow then you need to define the physics interacting. On a point, in 3D, it's "Force" by default in structural (pressure over an area would be better, as a point force interaction is a "singularity" w.r.t FEM approach and the stress values around this point will be very wrong, but I suppose that is not your main issue).
One thing is that you need to "preload" the bow first to start at the stationary case with cord and bow stressed.
Not sure how to propose that.
If you can start with a bow that has a U shape, then you could do a parametric continuation sweep to increase the tension of the cord to get the bow correctly armed, and then switch physics and use your 1D theory on the cord, connected to the prestressed bow. You should also be able to do a pre-stressed eigenfrequency analysis with that. Also this is probably a good candidate for the option "large deformation" "on"
Nice project, pls keep us informed ;)
by the way a 1D truss elemetn shoudl do the job too, you must just correctly connect all dependent variables between the two physics, truss have rotations that are not in 3D solid.
However, I believe you should use pinned I/F and leave the rotations free for the truss
--
Good luck
Ivar
first of all which version ?
you should be able to make a 3D geometrical model with the cord defined as a "line" connecting the two sides of the bow then you need to define the physics interacting. On a point, in 3D, it's "Force" by default in structural (pressure over an area would be better, as a point force interaction is a "singularity" w.r.t FEM approach and the stress values around this point will be very wrong, but I suppose that is not your main issue).
One thing is that you need to "preload" the bow first to start at the stationary case with cord and bow stressed.
Not sure how to propose that.
If you can start with a bow that has a U shape, then you could do a parametric continuation sweep to increase the tension of the cord to get the bow correctly armed, and then switch physics and use your 1D theory on the cord, connected to the prestressed bow. You should also be able to do a pre-stressed eigenfrequency analysis with that. Also this is probably a good candidate for the option "large deformation" "on"
Nice project, pls keep us informed ;)
by the way a 1D truss elemetn shoudl do the job too, you must just correctly connect all dependent variables between the two physics, truss have rotations that are not in 3D solid.
However, I believe you should use pinned I/F and leave the rotations free for the truss
--
Good luck
Ivar
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Posted:
1 decade ago
Thank for the very helpful reply
I am retired and am using my old 3.2 version of COMSOL.
My bow is a tapered violin bow with attached head and frog - I have successfully used large deformation analysis to obtain bending profiles with the bow subject to a number of forces and couples across ends of the bow - and have derived the associated eigen modes of the freely supported bow. I now want to investigate the influence of hair tension on the coupled tensioned hair and bow modes.
Your point about singularities using a line to connect points on hte 3D model is very helpful - I could equally well use an edge-connected, tensioned 2-dimensional ribbon, which would eliminate the sigularity problem. Perhaps I could tension the hair using thermal contraction?
I am retired and am using my old 3.2 version of COMSOL.
My bow is a tapered violin bow with attached head and frog - I have successfully used large deformation analysis to obtain bending profiles with the bow subject to a number of forces and couples across ends of the bow - and have derived the associated eigen modes of the freely supported bow. I now want to investigate the influence of hair tension on the coupled tensioned hair and bow modes.
Your point about singularities using a line to connect points on hte 3D model is very helpful - I could equally well use an edge-connected, tensioned 2-dimensional ribbon, which would eliminate the sigularity problem. Perhaps I could tension the hair using thermal contraction?
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Posted:
1 decade ago
Hi
Well, I have still almost deceny to run ;) and before I can take time to write books ...
v3.2 is really old for me, I started with v3.3; but it's probably OK for your purpouse. If I remeber right, stressed eigenfrequency runs required matlab (in v3) to store the stationary case and restart the eigenfrequency case loaded, such to get the stress stiffening. I beleive you have trusses also in 3.3, no ?
Then the point load singularity is not necesarily a true issue for you, so long you ignore the stress in the bow just (2-3 elements) around the load point. But if you can use an edge, it should be better.
Your violin bow has anyhow a shape that easily allows it to be prestressed, and I agree large deformations would be required.
One thing with large deformations, if it's as per v4, the large deformation formula is not compatble with "antisymmetric" boundary conditions, so such anti-symmetries BC should be avoided, but I believe it's OK with a symmetric condition, as the extended stress formula adds a cross product term that is symmetric.
--
Good luck
Ivar
Well, I have still almost deceny to run ;) and before I can take time to write books ...
v3.2 is really old for me, I started with v3.3; but it's probably OK for your purpouse. If I remeber right, stressed eigenfrequency runs required matlab (in v3) to store the stationary case and restart the eigenfrequency case loaded, such to get the stress stiffening. I beleive you have trusses also in 3.3, no ?
Then the point load singularity is not necesarily a true issue for you, so long you ignore the stress in the bow just (2-3 elements) around the load point. But if you can use an edge, it should be better.
Your violin bow has anyhow a shape that easily allows it to be prestressed, and I agree large deformations would be required.
One thing with large deformations, if it's as per v4, the large deformation formula is not compatble with "antisymmetric" boundary conditions, so such anti-symmetries BC should be avoided, but I believe it's OK with a symmetric condition, as the extended stress formula adds a cross product term that is symmetric.
--
Good luck
Ivar