2D coordinate systems
Posted 28 dic 2024, 18:48 GMT-5 Version 6.2 2 Replies
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I'm curious why there are so many 2D coordinate systems in my 2D Component Definitions. I'm trying to simulate a bulk thickness mode of a simplified piezoelectric material. I've reduced the strain-charge form coupling matrix to only have a 33 component, since I'm having a hard time making sense of the eigenmode shapes. There are 6 2D planes in the Component Definition; none have the option to delete. The Geometry and the Rectangle within do not seem to reference any coordinate system. I'm unsure what coordinate system the material properties (and specifically the 33 component) are in reference to. My intention is is for the induced strain and stress to only be in line with the electric field, which should just be vertical between the top terminal and bottom ground. This would give rise to the thickness mode, as I understand it.
The documentation doesn't address my question.
(With my understanding of eigenmode shapes, I should be able to enforce 1D modes that are harmonics of a fundamental, right? I've set up the eigenfrequency search using 
where 
for aluminum nitride and 
is roughly the thickness of the material.
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Your message is clear and professional! Here's a slightly refined version to enhance readability and flow:
Hello,
The default directions of piezoelectric material properties in the built-in COMSOL material library (in 3D space) are as follows: 1 → x-axis 2 → y-axis 3 → z-axis
Typically, the poling direction aligns with the z-axis.
When working on a 2D model, you need to specify the desired plane using one of the six available coordinate systems: XY, YZ, ZX, YX, ZY, or XZ.
I recommend using the default XZ coordinate system, which aligns the x and y axes in the 2D model with the original x and z directions in the 3D coordinate system of the material properties.
Please note that for 2D structural modeling, you must choose between the plane-stress or plane-strain assumptions. Additionally, please be cautious about removing elements of the coupling matrix (d) for reduction purposes, as this may lead to errors in your analysis.
Regards, Milad
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How do I specify the desired plane? What significance is the ordering of the 6 planes systems?
The motivation for removing elements of the coupling matrix is to make the results simpler to understand. My immediate goal is to demonstrate a 1D "piezo spring" by two methods.
- A 2 dimensional simulation with variation in only 1 dimension. I wish to create an artificial material properties such that the piezo coupling is simplest: a single non-zero element in the coupling matrix. I expect the eigenmodes to be simple enough also. The lowest order mode will be half a wavelength across the dimension of variation, and there will be harmonics above that.
- A 1D dimensional simulation using Coefficient Form PDE. COMSOL does not support piezo multiphysics in 1D. I should get the same results as the 2D simulation described already. This model is attached. I have the PDEs setup but I am still working on how to understand the boundary conditions, studies, and results. I don't understand how to constrain the left side of the interval, while the rest of the interval is free to shrink and expand. I want to plot the time domain solution of the some points along the interval.
For both simulations, I want to back out the ideal material electro-mechanical coupling coefficient via measurement, which should be a function of the material properties. If they match, I have confidence in more realistic and complicated resonator design simulation results.
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