While teaching piezoelectrical materials in my course at the Politecnico di BARI, I have explored the Matlab example "deflection-of-a-piezoelectric-actuator" which can be found in the official matlab web site https://it.mathworks.com/help/pde/ug/deflection-of-a-piezoelectric-actuator.html
The result of the example itself may be correct because it is checked against some reference solution.
However this is when the voltage across the bilayer actuator is simply linear across the y-direction because uniform voltage is imposed on the top surface and on the bottom one. However, when I asked the students to reproduce other conditions, like for example voltage only across part of the top surface and on the bottom one, or across the lateral surfaces, the resulting electrical field is very weird and very unlikely to be correct.
After all, although the problem is strictly speaking coupled between the electrical field and the mechanical one, I would not expect the electrical field to be very different from the classical electrical or thermal problem in the same domain, with imposed voltage (or temperature). And this problem, solved with Matlab or with other means, shows much smoother results.
The treatment of matrices is so involute that it is hard to check if the formulation is correct.
But when we checked the solution using ANSYS, even the coupled piezoelectrical problem shows smooth results, which differ from this example. So be aware that there must be some error in the formulation!
We can provide more info if you are interested.
It would be nice to get in touch with anyone using Matlab for PZT problems.
Prof. Michele Ciavarella Politecnico di BARI
Dear Michel,
As I know, no one has used MATLAB for Pieoelectrical materials. If you get some information regarding this, please let me know. I too interested to know about it.
Dear Michele,
I have used Matlab for one of my experiment and results were accurate. The only thing is you need to spend time for parameters identification. Small change in for example damping ratio can change the result dramatically. Please see this paper:
Article Optimizing orientation of piezoelectric cantilever beam for ...
thanks everybody. the matlab people did explain that b.c. need to be defined with care, and (at least this example I am considering) seems to work ok.
Dear Michele
I had tested the piezoelectric transducer by using Mat-lab Simulink in my paper
" Influence of a silver epoxy dopant on the performance of broken piezoelectric
ceramic transducer based on an analytical model"
I hope to benefit you
please find the attached file
Very interesting question!! I looked at the link you provided and realized the way that constitutive equation (PDE) is formed for this problem is very specific in such that you need to provide a non zero value (Voltage) for the top edge (referring to E5), therefore, if you apply zero values, then you will create a discontinuity (that may result in partial singularity in the stiffness matrix) which result in significant error in the numerical results. Another thing is that, the instruction for this element explicitly says that left lateral edges (E6 and E7) are accepting structural boundary conditions only and not the electrical ones.
Basically, what you are dealing with is a very specific bimorph element that accepts a very specific BCs (as mentioned above) and if you do not follow the instruction, then you will not get meaningful results.
You also mentioned that you setup the analysis that you was interested in ANSYS and you got the correct result. The reason is that, ANSYS provides a general environment where you can apply structural and electrical BCs wherever you want in the model and setup the contact between bimorph materials (Elements 226 and 227).
Hope this answer helps!!
I've used MATLAB for piezoelectric simulations, but I don't really care for MATLAB, it's too much like programming in Basic. My preferred program is Mathcad and I have accumulated more than 2000 Mathcad simulations involving piezoelectrics and ultrasound.
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