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Finding part of the function that describes displacement-at-a-point
Posted Mar 2, 2011, 3:52 p.m. EST Modeling Tools & Definitions, Parameters, Variables, & Functions Version 4.1 3 Replies
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Hi,
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! :-)
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! :-)
3 Replies Last Post Mar 6, 2011, 2:09 p.m. EST