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Radially Poled Piezoelectric Cylinder
Posted 11.10.2011, 10:32 GMT-4 MEMS & Nanotechnology, Piezoelectric Devices, Acoustics & Vibrations, Mesh, Structural Mechanics 2 Replies
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I am working on a problem with a radially poled hollow piezoelectric cylinder. I have successfully built this model in 2D axi but would like to also have a 3D model that works. Both models (so far) are attached. I am encountering two issues with this transition: meshing the thickness properly and defining the ceramic polarization coordinate system. Help with either issue would be appreciated. Details:
1) Increasing the Mesh density along the thickness. I'd like to get 3-5 elements (preferably quad's to decrease total # elements) meshed in the thickness direction since that is the direction of polarization. However, I don't need tons of elements along the height (maybe 10 or so), so a user-defined mesh makes sense in this case because I can't solve for even medium size models on my machine. I tried to do a mapped mesh but the problem is there is no "edge" to define a distribution on in the thickness direction. I also tried to made a line (bezier polygon) along the length just for meshing purposes but that failed because I got an "isolated entites found." message. I reverted to the "full auto" mesh just to have it solve something.
2) The piezoelectric materials (in the material browser or in general for piezo materials) are defined in a cartesian (x1,x2,x3) manner, with x3 being the direction of polarization. I need the ceramic to be poled in the radial direction as it is in the 2D zxisymmetric model. I can define and apply a cylindrical material coordinate system but that still doesn't fully solve the issue because (x3) is still the Z direction so it thinks it's poled along the height even though the electrodes are applied at the inner and outer surfaces. How can I define the radial direction in 3D as the polarization direction?
Thanks!
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Hello Marc
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define a mapped system with frame type(material) and coordinate names(phi, z, r);
notice the direction 'r' must be the third axis because 'z' in defult coordinate(x, y, z) is the defult pole direction.
in the coordinate expression column type these respectively:
phi: atan2(y,x)[rad] (or 'atan2(y,x)*(y>=0)+(2*pi+atan2(y,x))*(y<0)' for range adjust)
z: z
r: sqrt(x^2+y^2)
select the 'assume orthonormal' check box
now you have a material cylinder coordinate and you can apply it in
model builder> piezoeletric devices>piezoelectric material model 1>coordinate system selection
by the way, times memory is required with this method, and still i am not sure will this method work out the correct result. if someone find a better way, please share it.
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Since v. 4.3, using a Mapped co-ord sys with piezoelectrics does not seem to work. Hopefully this will be fixed soon. Of course, Comsol support was excellent about this issue and recommended using the following solution, which I personally like better than the mapped coordinate approach.
apply a Base Vector System with:
x y z
x1 = 0 0 1
x2 = -sin(atan2(y,x)) cos(atan2(y,x)) 0
x3 = cos(atan2(y,x)) sin(atan2(y,x)) 0
Make sure these settigns work for your case by plotting a Coordinate System Volume with the material coordinates. BLUE (= 3 direction) arrows should be in the direction of polarization. You can apply an axis offset (x0,y0) easily by subsituting "y" for "y-y0" and "x" for "x-x0" in the equations above, or a rotation by adding the offset in each trig function.