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Are you, perhaps, talking about the modes of excitation associated with electromagnetic radiation from rectangular patch antennas? A rectangular patch antenna is essentially a rectangular plate just above a ground plane, with a dielectric in between (but it could be just air) and typically fed at one or more points by a probe or transmission line (or sometimes it is simply coupled capacitively to such a transmission line). If so, see https://www.comsol.com/model/microstrip-patch-antenna-11742 . You can also find a great deal of related information about modes of excitation of rectangular patch antennas on the internet, including nice graphics (some of which may even have been made using Comsol Multiphysics).

Hello,

Interesting question, I assume you are talking about acoustic radiation pattern from an eigenfrequency modal analysis, of let's say a free-free oscillating plate ? If so, it's typically structural physics coupled to pressure acoustics model one should consider.

Now COMSOL Multiphysics proposes only time or frequency domain predefined analysis for its structure and acoustics coupled physics, so one would need to do some manual tuning here.

For me, first we must decide if the coupling structure to acoustic is mono-directional, or bidirectional, the latter is far more complex to implement. But I believe it's reasonable to start with a mono-directional coupling from structure to the acoustic pressure, as the density of air (around 1.2 kg/m^3) is small compared to that of steel or most metals (some 3-4 orders of magnitude) so the pressure of air displacement should not influence too much the eigenmode analysis of the structure alone (perhaps one must consider some damping if you are interested in the higher frequencies, but for a second step). Which means that one may perform first a simple eigenfrequency analysis of the plate structure and then a second separate frequency domain analysis for the acoustics, based on the mode shape displacement and the given eigenfrequency desired. Now do not forget that the eigenfrequencies of a free-free structure is composed of 6 free modes of frequency around 0 Hz and then the "true" (>0 Hz) structural modes starting from mode 6 and thereafter, and that if you add some damping you will get "complex" eigenfrequencies. Finally, the amplitudes from a eigenfrequency study are relative, so they give you only a "shape" information, the absolute value depends on your normalisation. But the radiation pattern should not change, only the amplitude you will get is to be considered as "realtive". Once you have the list of eigenfrequencies and the amplitude shape of your desired mode, you need to perform a second analysis with the acoustic pressure, i.i by mapping with the withsol() operator (check the Blog, the Knowledge Base "operators" and the COMSOL doc) the results (structural displacement) of the desired eigenmode from study 1 (Structure) to the input to study 2 (ACO) and reminding that in frequency domain analysis the velocity of a displacement is the v="amplitude * (2 * pi * freq)" and the acceleration a= "amplitude * (2 * pi * freq)^2" . Furthermore, if you are only interested in the "far field" acoustic pattern (specific node used to calculate this under ACO) I expect that the BEM (boundary element method) is easier to use to calculate as it will use less RAM than a full sphere surrounding your plate. And to keep your computational domain limited, do not forget to add a external spherical shell of a matched layer to simulate and "infinite" extending sphere.

My main suggestion is: start simple, a step at the time, make several simple models, then assemble them once you master each one independently. I still go that way, even after soon 20 years of COMSOLing, particularly when coupling multiple physics, even just 2! :)

I hope this helps on the way, Sincerely, Ivar

Thank you both in for answering me. Ivar you have been very clear and thorough!

Hi again,

You are welcome, the real fun of physics comes with COMSOL Multiphysics, you may really learn how things are linked and how they behave, but be aware one need to connect to reality by comparing the results to measurements (or articles with measurements) to ensure calibration, and the full VV&C (Validation, Verification and Calibration of any model.

What I often do is to sketch up the links, as in the page below from my Remarkable(r) notebook :)

If you want to go a step further, and see the eigenmode changes due to the presence of air (or water if that is your surrounding medium) you should study Nagi's excellent blog, for a first order correction, using Structure without fluid or ACO, see:

https://www.comsol.com/blogs/natural-frequencies-immersed-beams/

Have fun COMSOLing Sincerely Ivar

PS with updated _v2.PNG containing the "i" ...

Perfect, answer very useful for me! Thank you so much!

Hello again,

I noticed I have a slight error in my notes, the displacement, velocity respectively acceleration are dephased by 90°, each, so the correct formula for a boundary displacement is d(x,y,z)[m], the velocity is v(x,y,z)=d(x,y,z) * (2 * pi * i * freq) and the acceleration is respectively a(x,y,z)=d(x,y,z) * (2 * pi * i * freq)^2. As COMSOL is working in true complex notation. You will notice that if you use the ACO boundary "normal displacement", or velocity, respectively acceleration you will find these equations in the "equation view" showing the internal COMSOL equations. the complex "* i" includes then the dephasing, but normally for your case the amplitude shape should not change.

I have updated the PNG above to ..._v2.PNG

Sincerely Ivar