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Finding part of the function that describes displacement-at-a-point
Posted 02.03.2011, 15:52 GMT-5 Modeling Tools & Definitions, Parameters, Variables, & Functions Version 4.1 3 Replies
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Imagine a thin disk that is supported in the center and free on the edges. Now look at a volume element somewhere in the disk. Imagine that this disk is vibrating in some way, so that the volume element is displaced by some small amount (u,v,w) in the r, phi, z direction.
OK now that we are all set up, here's the question. I can write down the form of u, v, and w, (and this is in many mechanics books) as
u = U(r) cos(n phi) exp(-i k z) exp(i w t)
v = V(r) sin(n phi) exp(-i k z) exp(i w t)
w = W(r) cos(n phi) exp(-i k z) exp(i w t)
or alternately I can write it as
u = U(r,z) [ C(t) cos(n phi) + S(t) sin(n phi) ]
v = V(r,z) [ C(t) sin(n phi) + S(t) cos(n phi) ]
w = W(r,z) [ C(t) cos(n phi) + S(t) sin(n phi) ]
OK so the question is, for a particular set of integrals I need to find only the U, V, W (capitals) in either of the two cases above. I can draw the structure in COMSOL and find the eigenmodes or see the frequency response or do any number of other things, but I'm stuck as to computationally finding U, V, W using comsol. (Once I have those I simply put them inside a big integral with a bunch of other terms and I'm done.)
Any ideas?
Thanks! :-)
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for me it looks like an optimisation problem you are looking for
if you define U(r) as an global equation with the condition
(u-U(r) cos(n phi) exp(-i k z) exp(i w t))^2 = 0
you need to define the variables r, phi, n, k, w and t if not already there or simplify the equation depending on how you extract u (eigenfrequency or frequency scan ...)
for a few variables you can do it directly in standard COMSOL, but the optimisation toolbox would make your life easier I believe
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Good luck
Ivar
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isnt it close to this (I have still not managed to update it to V4 ;):
www.comsol.eu/community/forums/general/thread/236/
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Good luck
Ivar
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Here is another example, a plate is deformed under gravity and pressure load (2D axi example) and I fit a 2nd order analytical function to the deformation shape. It's done without the optimisation module (would be even simpler with, particularyl if one want a higher order or more complex fitting).
It's a 4.1.0.154 model
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Good luck
Ivar
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