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Acoustic Band Structure in 2d

Posted Sep 28, 2009, 2:51 p.m. EDT Modeling Tools & Definitions, Parameters, Variables, & Functions, Structural Mechanics Version 5.1 38 Replies

Sean Langelier
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Hi Folks - Ive posted a couple of questions to some related discussion but it looks like they haven't been visited in a while so I thought I would make a new discussion group.

I am interested in finding out whether or not it is possible to calculate acoustic band structures using a reciprocal lattice simulation and periodic boundary conditions. I understand this is typically done by solving for eigan solutions to the helmholtz equation as you vary the direction of the plane wave vector. My question is... while performing an eigan value analysis and say, computing 100 eigan values in the vicinity of the stop band, how does one back out the wave vector direction related to the given eigan values

Thanks

Sean
38 Replies Last Post Jun 23, 2017, 10:48 a.m. EDT
Rubén Picó
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Posted: 2 decades ago Oct 5, 2009, 4:23 a.m. EDT
Hi Sean and all,

I'm also interested in getting the a simple code for the band structure for a phononic crystal. I've being trying two moths ago to "adapt" the band structure calculation from a photonic crystal (there is a model example in the COMSOL Gallery, Band Gap Analysis Photonic Crystal, I send it attached) but I left after some problems with the eigenfrequency resolution. I didn't have good values for the eigenfrequencies.

I hope this could help.


Rubén
Hi Sean and all, I'm also interested in getting the a simple code for the band structure for a phononic crystal. I've being trying two moths ago to "adapt" the band structure calculation from a photonic crystal (there is a model example in the COMSOL Gallery, Band Gap Analysis Photonic Crystal, I send it attached) but I left after some problems with the eigenfrequency resolution. I didn't have good values for the eigenfrequencies. I hope this could help. Rubén
Sonali Dasgupta
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Posted: 2 decades ago Oct 15, 2009, 11:21 a.m. EDT
Hi Sean, Ruben,

I am also interested in getting a solution to the same problem, but seems like not many people in this forum are working on it! Would be great to get some responses !

Thanks

Hi Sean, Ruben, I am also interested in getting a solution to the same problem, but seems like not many people in this forum are working on it! Would be great to get some responses ! Thanks
Yun Jing
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Posted: 2 decades ago Oct 20, 2009, 4:33 p.m. EDT
Hi, guys

I have been doing some research for acoustic band structures too, but only for 1D cases. I'd love to discuss this with you

Yun
Hi, guys I have been doing some research for acoustic band structures too, but only for 1D cases. I'd love to discuss this with you Yun
Sean Langelier
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Posted: 2 decades ago Oct 20, 2009, 5:47 p.m. EDT
I have actually finally got this to work out. The basic idea is to create your 2d unit cell (1st irreducible brill zone), apply scalar expressions for the periodic boundary conditions i.e., expressions of the form gx=g*exp(i*kx*x), and then vary the components of the k wave vector using a matlab script.

Sean
I have actually finally got this to work out. The basic idea is to create your 2d unit cell (1st irreducible brill zone), apply scalar expressions for the periodic boundary conditions i.e., expressions of the form gx=g*exp(i*kx*x), and then vary the components of the k wave vector using a matlab script. Sean
Rubén Picó
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Posted: 2 decades ago Oct 22, 2009, 4:10 a.m. EDT
Hi Sean and all,

Thanks for your mail. I have now a script to get the dispersion relation in a particular direction. There must be a problem with the eigenfrequency solver. I still don't know how to select the right values from the solutions provided by the simulation.

When the problem is solved with periodic boundary conditions, an eigenfrequency value is chosen in order to search around. If I understand well, this value allows us to "choose" the band. If the value of k is increased (for a particular direction) I'll expect to have a mostly linear curve from the origin for the fist band. Instead, I have sudden changes for the values of the eigenfrequencies when the value of k is increased...(?).

Matlab script is attached.

Thanks in advance.

Rubén
Hi Sean and all, Thanks for your mail. I have now a script to get the dispersion relation in a particular direction. There must be a problem with the eigenfrequency solver. I still don't know how to select the right values from the solutions provided by the simulation. When the problem is solved with periodic boundary conditions, an eigenfrequency value is chosen in order to search around. If I understand well, this value allows us to "choose" the band. If the value of k is increased (for a particular direction) I'll expect to have a mostly linear curve from the origin for the fist band. Instead, I have sudden changes for the values of the eigenfrequencies when the value of k is increased...(?). Matlab script is attached. Thanks in advance. Rubén

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Rubén Picó
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Posted: 2 decades ago Oct 22, 2009, 4:10 a.m. EDT
Hi Sean and all,

Thanks for your mail. I have now a script to get the dispersion relation in a particular direction. There must be a problem with the eigenfrequency solver. I still don't know how to select the right values from the solutions provided by the simulation.

When the problem is solved with periodic boundary conditions, an eigenfrequency value is chosen in order to search around. If I understand well, this value allows us to "choose" the band. If the value of k is increased (for a particular direction) I'll expect to have a mostly linear curve from the origin for the fist band. Instead, I have sudden changes for the values of the eigenfrequencies when the value of k is increased...(?).

Matlab script is attached.

Thanks in advance.

Rubén
Hi Sean and all, Thanks for your mail. I have now a script to get the dispersion relation in a particular direction. There must be a problem with the eigenfrequency solver. I still don't know how to select the right values from the solutions provided by the simulation. When the problem is solved with periodic boundary conditions, an eigenfrequency value is chosen in order to search around. If I understand well, this value allows us to "choose" the band. If the value of k is increased (for a particular direction) I'll expect to have a mostly linear curve from the origin for the fist band. Instead, I have sudden changes for the values of the eigenfrequencies when the value of k is increased...(?). Matlab script is attached. Thanks in advance. Rubén
Sean Langelier
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Posted: 2 decades ago Oct 22, 2009, 10:59 a.m. EDT
Good. The sudden increase in eigan frequencies is correct. The reason is that for any given wave vector, from 0 to k* (k* being the limit in the first brill zone), there is a set of eigan frequencies that satisfy the wave equation. Sweeping from k=0 to k=k* and plotting the entire set will give you the complete band structure (well only as complete as the number of eigan values you choose to solve for. Hope that helps.

Sean
Good. The sudden increase in eigan frequencies is correct. The reason is that for any given wave vector, from 0 to k* (k* being the limit in the first brill zone), there is a set of eigan frequencies that satisfy the wave equation. Sweeping from k=0 to k=k* and plotting the entire set will give you the complete band structure (well only as complete as the number of eigan values you choose to solve for. Hope that helps. Sean
Rubén Picó
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Posted: 2 decades ago Oct 23, 2009, 5:01 a.m. EDT
Hi Sean,

Thanks again for your mail.

For a rectangular crystal of length, the k* in the x direction would be pi/d. Thus, varying k from 0 to pi/d no sudden changes should be observed, but the bands. Am I right?
Instead I observed them. (bloch4.m)

After several trials without results with my models, I've decided to take your .mph file (eigan_periodic_test.mph, the one you sent in you first message), change the periodic boundary conditions (with the constrictions of the Bloch theorem: p=p·exp(kx*x) and idem for the y) and loop for kx while ky=0.
The file is attached (sean4.m). The result is very strange: the values of the eigenfrequencies are always the same for different 'kx' but with changes of sign. Do you know why?

Thanks a lot!

Rubén


Hi Sean, Thanks again for your mail. For a rectangular crystal of length, the k* in the x direction would be pi/d. Thus, varying k from 0 to pi/d no sudden changes should be observed, but the bands. Am I right? Instead I observed them. (bloch4.m) After several trials without results with my models, I've decided to take your .mph file (eigan_periodic_test.mph, the one you sent in you first message), change the periodic boundary conditions (with the constrictions of the Bloch theorem: p=p·exp(kx*x) and idem for the y) and loop for kx while ky=0. The file is attached (sean4.m). The result is very strange: the values of the eigenfrequencies are always the same for different 'kx' but with changes of sign. Do you know why? Thanks a lot! Rubén

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Sean Langelier
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Posted: 2 decades ago Oct 23, 2009, 11:32 a.m. EDT
I looked at your code and there are some problems. Firstly, the normalized wave vector for a square lattice will go from 0 to 2pi/a not pi/d. Second, you need to make sure you are establishing periodic boundaries for x_velocity,y_velocity, and p in your geometry. My advice is to make sure, make absolutely sure (as this is what held me up when I was trying to figure this out) that all of your dimensions are correct and that you are varying k* over the proper scale.

boundary conditions should look something like this

% Scalar expressions
fem.expr = {'u1','u*exp(i*kx*x)', ...
'v1','v*exp(i*kx*x)', ...
'p1','p*exp(i*kx*x)', ...
'u2','u*exp(i*ky*y)', ...
'v2','v*exp(i*ky*y)', ...
'p2','p*exp(i*ky*y)'};

where kx and ky are constants that you vary in a loop

make sure also that if you change the geometry that you rescale k*

hope that helps

Sean
I looked at your code and there are some problems. Firstly, the normalized wave vector for a square lattice will go from 0 to 2pi/a not pi/d. Second, you need to make sure you are establishing periodic boundaries for x_velocity,y_velocity, and p in your geometry. My advice is to make sure, make absolutely sure (as this is what held me up when I was trying to figure this out) that all of your dimensions are correct and that you are varying k* over the proper scale. boundary conditions should look something like this % Scalar expressions fem.expr = {'u1','u*exp(i*kx*x)', ... 'v1','v*exp(i*kx*x)', ... 'p1','p*exp(i*kx*x)', ... 'u2','u*exp(i*ky*y)', ... 'v2','v*exp(i*ky*y)', ... 'p2','p*exp(i*ky*y)'}; where kx and ky are constants that you vary in a loop make sure also that if you change the geometry that you rescale k* hope that helps Sean
Dominic Bosomtwi
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Posted: 2 decades ago Nov 4, 2009, 5:17 p.m. EST
Hi...
Hi...
Rubén Picó
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Posted: 2 decades ago Nov 5, 2009, 4:48 a.m. EST
Hi Sean,

thank you for your mail. It was a great help.

Bests,
Rubén
Hi Sean, thank you for your mail. It was a great help. Bests, Rubén
kodanda
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Posted: 1 decade ago Jan 18, 2011, 11:22 a.m. EST
Hi,


I have actually finally got this to work out. The basic idea is to create your 2d unit cell (1st irreducible brill zone), apply scalar expressions for the periodic boundary conditions i.e., expressions of the form gx=g*exp(i*kx*x), and then vary the components of the k wave vector using a matlab script.

Sean


are you using COMSOL 4.1 now? If so how do you prescribe the above periodic boundary conditions?

In 4.1 the periodic BCs are now re-formatted and they now purely periodic BCs i.e. equating displacement on the boundaries.

Best,
Kodanda
Hi, [QUOTE] I have actually finally got this to work out. The basic idea is to create your 2d unit cell (1st irreducible brill zone), apply scalar expressions for the periodic boundary conditions i.e., expressions of the form gx=g*exp(i*kx*x), and then vary the components of the k wave vector using a matlab script. Sean [/QUOTE] are you using COMSOL 4.1 now? If so how do you prescribe the above periodic boundary conditions? In 4.1 the periodic BCs are now re-formatted and they now purely periodic BCs i.e. equating displacement on the boundaries. Best, Kodanda
Alireza Bayat
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Posted: 1 decade ago Oct 15, 2012, 7:18 p.m. EDT
does anyone work on this subject by any chance?

I have the same trouble finding the band structure of a phononic crystal, seems in 4.3 one can not define the floquet boundary conditions. any idea?
does anyone work on this subject by any chance? I have the same trouble finding the band structure of a phononic crystal, seems in 4.3 one can not define the floquet boundary conditions. any idea?
Rubén Picó
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Posted: 1 decade ago Oct 16, 2012, 4:27 a.m. EDT

does anyone work on this subject by any chance?

I have the same trouble finding the band structure of a phononic crystal, seems in 4.3 one can not define the floquet boundary conditions. any idea?


Hi Alireza,

I'm interested in the topic. I've not yet implemented the calculation of Band structures in the 4th version. I've seen in 4.2 that there is a periodic condition. In the help it is explained:

To add a periodic boundary condition, in the Model Builder, right-click a physics interface node and select Periodic Condition. The periodic boundary condition typically implements standard periodicity (that is, the value of the solution is the same on the periodic boundaries), but in most cases you can also choose antiperiodicity so that the solutions have opposing signs. For fluid flow interfaces, the Periodic Flow Condition provides a similar periodic boundary condition but without a selection of periodicity.

I hope it help you.



[QUOTE] does anyone work on this subject by any chance? I have the same trouble finding the band structure of a phononic crystal, seems in 4.3 one can not define the floquet boundary conditions. any idea? [/QUOTE] Hi Alireza, I'm interested in the topic. I've not yet implemented the calculation of Band structures in the 4th version. I've seen in 4.2 that there is a periodic condition. In the help it is explained: To add a periodic boundary condition, in the Model Builder, right-click a physics interface node and select Periodic Condition. The periodic boundary condition typically implements standard periodicity (that is, the value of the solution is the same on the periodic boundaries), but in most cases you can also choose antiperiodicity so that the solutions have opposing signs. For fluid flow interfaces, the Periodic Flow Condition provides a similar periodic boundary condition but without a selection of periodicity. I hope it help you.
Nagi Elabbasi Facebook Reality Labs
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Posted: 1 decade ago Oct 16, 2012, 1:57 p.m. EDT
I used COMSOL a while back for a similar problem involving the band gap of a phononic crystal (see attachment). At that time I had to implement the Floquet/Bloch boundary condition manually. Now it is available as a boundary condition for structures but I have not yet tried it. You define it by creating a Periodic Condition and in Type of Periodicity select Floquet periodicity.

Nagi Elabbasi
Veryst Engineering
I used COMSOL a while back for a similar problem involving the band gap of a phononic crystal (see attachment). At that time I had to implement the Floquet/Bloch boundary condition manually. Now it is available as a boundary condition for structures but I have not yet tried it. You define it by creating a Periodic Condition and in Type of Periodicity select Floquet periodicity. Nagi Elabbasi Veryst Engineering

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Alireza Bayat
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Posted: 1 decade ago Oct 16, 2012, 6:50 p.m. EDT

I used COMSOL a while back for a similar problem involving the band gap of a phononic crystal (see attachment). At that time I had to implement the Floquet/Bloch boundary condition manually. Now it is available as a boundary condition for structures but I have not yet tried it. You define it by creating a Periodic Condition and in Type of Periodicity select Floquet periodicity.

Nagi Elabbasi
Veryst Engineering


Thank you guys both.

Yeap, that was my bad, I should have written 4.2 instead of 4.3. It seems that it is fixed in 4.3 but you cannot apply Floquet boundary in 4.2.


Nagi: did you draw the eigenfunctions in your band diagram with Acoustic module?

Ruben; Good that you are still working on this. Seems that you have been working on this subject for a while. Anyways, I don't have the 3.5 to check the .mph and .m files you and Sean have uploaded in 2009 but it seems you already solved this with MATLAB livelink.


I just have started to work on this and wonder if it is possible to draw the band structure with Acoustic or PDE interface or it needs MATLAB livelink.

I would welcome any comments.

Alireza
[QUOTE] I used COMSOL a while back for a similar problem involving the band gap of a phononic crystal (see attachment). At that time I had to implement the Floquet/Bloch boundary condition manually. Now it is available as a boundary condition for structures but I have not yet tried it. You define it by creating a Periodic Condition and in Type of Periodicity select Floquet periodicity. Nagi Elabbasi Veryst Engineering [/QUOTE] Thank you guys both. Yeap, that was my bad, I should have written 4.2 instead of 4.3. It seems that it is fixed in 4.3 but you cannot apply Floquet boundary in 4.2. Nagi: did you draw the eigenfunctions in your band diagram with Acoustic module? Ruben; Good that you are still working on this. Seems that you have been working on this subject for a while. Anyways, I don't have the 3.5 to check the .mph and .m files you and Sean have uploaded in 2009 but it seems you already solved this with MATLAB livelink. I just have started to work on this and wonder if it is possible to draw the band structure with Acoustic or PDE interface or it needs MATLAB livelink. I would welcome any comments. Alireza
Nagi Elabbasi Facebook Reality Labs
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Posted: 1 decade ago Oct 17, 2012, 12:07 a.m. EDT
Thanks Alireza,
Actually that is an Excel generated plot. I had a very similar one generated within COMSOL (no modules were required I believe).
Thanks Alireza, Actually that is an Excel generated plot. I had a very similar one generated within COMSOL (no modules were required I believe).
Alireza Bayat
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Posted: 1 decade ago Oct 17, 2012, 12:49 p.m. EDT

Thanks Alireza,
Actually that is an Excel generated plot. I had a very similar one generated within COMSOL (no modules were required I believe).


Nagi,

Which solver did you use? Stationary or eigenfrequency? How did you plot the eigenfunctions?
[QUOTE] Thanks Alireza, Actually that is an Excel generated plot. I had a very similar one generated within COMSOL (no modules were required I believe). [/QUOTE] Nagi, Which solver did you use? Stationary or eigenfrequency? How did you plot the eigenfunctions?
Nagi Elabbasi Facebook Reality Labs
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Posted: 1 decade ago Oct 17, 2012, 3:17 p.m. EDT
Alireza,

I used an eigenfrequency solver with a parametric sweep over the wave number, and modified its settings to handle complex numbers and the complex Hermetian matrices. For plotting in COMSOL I generated a 1D Plot of that solution Data Set.

Nagi Elabbasi
Veryst Engineering
Alireza, I used an eigenfrequency solver with a parametric sweep over the wave number, and modified its settings to handle complex numbers and the complex Hermetian matrices. For plotting in COMSOL I generated a 1D Plot of that solution Data Set. Nagi Elabbasi Veryst Engineering
Felix Guldner
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Posted: 1 decade ago Oct 18, 2012, 6:25 a.m. EDT
Hello,

I am also trying to compute the mechanical band structure of a phononic crystal. The only tutorial I found about how to compute band structures in Comsol was the "Bandgap Analysis of a Photonic Crystal" attached in this topic.

Unfortunately, I do not have the RF module, so I cannot reproduce it. I am using the Structural Mechanics Module. Does anyone know any other tutorial that describes, how to calculate band structures? That would be very helpful!

I tried to adapt the steps described for the photonic crystal to my simulation, but I am facing the same problem concerning the periodicity: I don't know, how to select "Floquet periodicity" (Comsol 4.1).

Thanks and best regards
Felix
Hello, I am also trying to compute the mechanical band structure of a phononic crystal. The only tutorial I found about how to compute band structures in Comsol was the "Bandgap Analysis of a Photonic Crystal" attached in this topic. Unfortunately, I do not have the RF module, so I cannot reproduce it. I am using the Structural Mechanics Module. Does anyone know any other tutorial that describes, how to calculate band structures? That would be very helpful! I tried to adapt the steps described for the photonic crystal to my simulation, but I am facing the same problem concerning the periodicity: I don't know, how to select "Floquet periodicity" (Comsol 4.1). Thanks and best regards Felix
Nagi Elabbasi Facebook Reality Labs
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Posted: 1 decade ago Oct 18, 2012, 1:36 p.m. EDT
Hi Felix,

The Floquet periodicity was only added to the Structural Mechanics Module in version 4.3. You can either switch to the newer version or implement the periodicity condition manually.

Nagi Elabbasi
Veryst Engineering
Hi Felix, The Floquet periodicity was only added to the Structural Mechanics Module in version 4.3. You can either switch to the newer version or implement the periodicity condition manually. Nagi Elabbasi Veryst Engineering
Felix Guldner
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Posted: 1 decade ago Oct 19, 2012, 2:39 a.m. EDT
Hi Nagi,

unfortunately switching to 4.3 is currently not an option for me, so I will have to specify the periodicity manually. But I don't really know where to do that (I'm quite new to Comsol). Any help on that problem would be very welcome.

I assume somewhere I would have to specify that u(x+a)=exp(ika)*u(x) where u is the displacement and a is the lattice constant.

Thanks again!
Felix
Hi Nagi, unfortunately switching to 4.3 is currently not an option for me, so I will have to specify the periodicity manually. But I don't really know where to do that (I'm quite new to Comsol). Any help on that problem would be very welcome. I assume somewhere I would have to specify that u(x+a)=exp(ika)*u(x) where u is the displacement and a is the lattice constant. Thanks again! Felix
Alireza Bayat
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Posted: 1 decade ago May 21, 2013, 3:02 p.m. EDT


I used an eigenfrequency solver with a parametric sweep over the wave number, and modified its settings to handle complex numbers and the complex Hermetian matrices. For plotting in COMSOL I generated a 1D Plot of that solution Data Set.
I used an eigenfrequency solver with a parametric sweep over the wave number, and modified its settings to handle complex numbers and the complex Hermetian matrices. For plotting in COMSOL I generated a 1D Plot of that solution Data Set.
Zularifin Sejo
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Posted: 1 decade ago Jun 10, 2013, 6:26 p.m. EDT
Hi Alireza,

May I know how actually do you manage to plot a bandgap. I have been trying to do using the bandgap_photonic_crystal_sbs example but to no avail. Basically I am trying to model a 2D structure as shown in the attached photo.

What I've done so far is making sure that the mesh at the boundaries are the same by copying one edge of the rectangle to the rest of the boundaries. I then set the kx and ky in the floquet boundary condition using the example in the bandgap_photonic_crystal_sbs.

I then used the parametric sweep in the study computation. When i plot k against the eigenfrequency, I always get the same plot no matter what I did to the dimension of the rod. Should I use 1 or 2 boundary conditions?

I would appreciate if you or anybody else can help. Thanks.
Hi Alireza, May I know how actually do you manage to plot a bandgap. I have been trying to do using the bandgap_photonic_crystal_sbs example but to no avail. Basically I am trying to model a 2D structure as shown in the attached photo. What I've done so far is making sure that the mesh at the boundaries are the same by copying one edge of the rectangle to the rest of the boundaries. I then set the kx and ky in the floquet boundary condition using the example in the bandgap_photonic_crystal_sbs. I then used the parametric sweep in the study computation. When i plot k against the eigenfrequency, I always get the same plot no matter what I did to the dimension of the rod. Should I use 1 or 2 boundary conditions? I would appreciate if you or anybody else can help. Thanks.

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Alireza Bayat
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Posted: 1 decade ago Jun 10, 2013, 11:16 p.m. EDT
Hi Zularifin

I followed the same approach as in "photonic bandgap" example and defined two boundary conditions for parallel boundaries of the square.
Hi Zularifin I followed the same approach as in "photonic bandgap" example and defined two boundary conditions for parallel boundaries of the square.
Zularifin Sejo
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Posted: 1 decade ago Jun 11, 2013, 12:41 p.m. EDT
Hi Alireza,

I will try that. Thanks
Hi Alireza, I will try that. Thanks
Zularifin Sejo
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Posted: 1 decade ago Jun 11, 2013, 1:23 p.m. EDT
Hi Alireza,

If you don't mind, I very much like to see your .mph file to study and understand it. I would appreciate it if you can help.

Thanks.
Hi Alireza, If you don't mind, I very much like to see your .mph file to study and understand it. I would appreciate it if you can help. Thanks.
Jay Yang
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Posted: 1 decade ago May 7, 2014, 7:54 a.m. EDT
Hi Nagi
I really want to know how to set floquet boundary condition manually in weak form PDE? Could you help me?
Yang
Hi Nagi I really want to know how to set floquet boundary condition manually in weak form PDE? Could you help me? Yang
Nagi Elabbasi Facebook Reality Labs
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Posted: 1 decade ago May 13, 2014, 2:40 p.m. EDT
Hi Yang,

I did not implement the Floquet boundary condition in weak form so I have no specific tips to share. When I implemented it as a boundary condition before the feature was added to COMSOL I had to prescribe the displacement on one boundary (say the right boundary) to be something like u=bndsim1(u)*exp(i*kx*L1) where L1 is the cell size, kx is the x-component of the wave number and bndsim1 is a boundary similarity operator with the left boundary as its Source and right boundary as its Destination. I hope that helps.

Nagi Elabbasi
Veryst Engineering
Hi Yang, I did not implement the Floquet boundary condition in weak form so I have no specific tips to share. When I implemented it as a boundary condition before the feature was added to COMSOL I had to prescribe the displacement on one boundary (say the right boundary) to be something like u=bndsim1(u)*exp(i*kx*L1) where L1 is the cell size, kx is the x-component of the wave number and bndsim1 is a boundary similarity operator with the left boundary as its Source and right boundary as its Destination. I hope that helps. Nagi Elabbasi Veryst Engineering
Ukesh Koju
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Posted: 9 years ago Jun 10, 2015, 5:54 p.m. EDT
Hi Nagi,

I am trying to get a band structure for a simple 2d sq lattice (solid circle in a solid matrix); but I did not get the z-mode (longitudinal mode), just the transverse mode only , what i did was: (I am using comsol 4.4)

1. used acoustic-structure interaction, elastic wave (elw) module
2. chose both domain linear elastic material.
3. Floquet periodicity (1,4) and (2,3) boundaries.
4. took the parametric sweep for kx = 0 to pi/a
5. finally got kx vs freq (derived values > global evaluation),

but this kx vs freq gave me just transverse modes only, longitudinal mode missing. I am lost. Please suggest me how to get longitudinal modes. Any help would be greatly appreciated.

Also I am having problem with liquid matrix with solid scatterer.

Thank You very much,

Ukesh
Hi Nagi, I am trying to get a band structure for a simple 2d sq lattice (solid circle in a solid matrix); but I did not get the z-mode (longitudinal mode), just the transverse mode only , what i did was: (I am using comsol 4.4) 1. used acoustic-structure interaction, elastic wave (elw) module 2. chose both domain linear elastic material. 3. Floquet periodicity (1,4) and (2,3) boundaries. 4. took the parametric sweep for kx = 0 to pi/a 5. finally got kx vs freq (derived values > global evaluation), but this kx vs freq gave me just transverse modes only, longitudinal mode missing. I am lost. Please suggest me how to get longitudinal modes. Any help would be greatly appreciated. Also I am having problem with liquid matrix with solid scatterer. Thank You very much, Ukesh
Ahmed Nagaty
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Posted: 9 years ago Nov 26, 2015, 2:01 p.m. EST
Hi
I want to calculate the band gap of a 1D phononic crystal...
Hi I want to calculate the band gap of a 1D phononic crystal...
Ahmed Nagaty
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Posted: 9 years ago Dec 15, 2015, 3:26 p.m. EST
i did the band structure for 1D periodic structure of phononic crystal but the curve is not good as show in the attached image .....any one has any help ??
i did the band structure for 1D periodic structure of phononic crystal but the curve is not good as show in the attached image .....any one has any help ??

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Nagi Elabbasi Facebook Reality Labs
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Posted: 9 years ago Jan 25, 2016, 12:49 p.m. EST
I uploaded a COMSOL file to the Model Exchange that shows how to set up a phononic band gap eigenfrequency analysis. Here is the link: www.comsol.com/community/exchange/432/.

Nagi Elabbasi
Veryst Engineering
I uploaded a COMSOL file to the Model Exchange that shows how to set up a phononic band gap eigenfrequency analysis. Here is the link: http://www.comsol.com/community/exchange/432/. Nagi Elabbasi Veryst Engineering
Minoo Kabir
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Posted: 9 years ago Mar 1, 2016, 12:49 p.m. EST
Hi Nagi,
The model looks very interesting.
I was wondering if you modeled the vibration isolation with COMSOL as well?
Would you please describe a bit about the vibration isolation modeling?

Thanks a lot,
Minoo
Hi Nagi, The model looks very interesting. I was wondering if you modeled the vibration isolation with COMSOL as well? Would you please describe a bit about the vibration isolation modeling? Thanks a lot, Minoo
Hongyangyang Shi
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Posted: 9 years ago Mar 17, 2016, 2:14 a.m. EDT
Hi Sean and all,

I am currently doing band structure analysis on periodic structures, but I am pretty new in this area, and I do not have very solid background on solid physics. Could you guys please recommend me some textbook or material to read on the procedure of constructing the band diagram?

Personally I have no idea how the eigenvalue problem of field equation is solved and how do we relate the wave vector k to the Irreducible Brillouin Zone ( which will be stretched as the x axis in band diagram, if I am understanding correctly).

Thank you!!

Hongyangyang Shi
Hi Sean and all, I am currently doing band structure analysis on periodic structures, but I am pretty new in this area, and I do not have very solid background on solid physics. Could you guys please recommend me some textbook or material to read on the procedure of constructing the band diagram? Personally I have no idea how the eigenvalue problem of field equation is solved and how do we relate the wave vector k to the Irreducible Brillouin Zone ( which will be stretched as the x axis in band diagram, if I am understanding correctly). Thank you!! Hongyangyang Shi
Ahmed Nagaty
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Posted: 9 years ago Mar 22, 2016, 4:10 p.m. EDT
www.google.com.eg/url?sa=t&rct=j&q=&esrc=s&source=web&cd=1&cad=rja&uact=8&ved=0ahUKEwipleaujNXLAhUHVhoKHT6KA9YQFggnMAA&url=http%3A%2F%2Fwww.springer.com%2Fus%2Fbook%2F9781461493921&usg=AFQjCNHG16FLaEs4gfGA5Ugx4lXmz7Upvg&bvm=bv.117218890,d.d24....
.
this is a good data for phononic crystal ..
https://www.google.com.eg/url?sa=t&rct=j&q=&esrc=s&source=web&cd=1&cad=rja&uact=8&ved=0ahUKEwipleaujNXLAhUHVhoKHT6KA9YQFggnMAA&url=http%3A%2F%2Fwww.springer.com%2Fus%2Fbook%2F9781461493921&usg=AFQjCNHG16FLaEs4gfGA5Ugx4lXmz7Upvg&bvm=bv.117218890,d.d24.... . this is a good data for phononic crystal ..
Zhuhua Tan
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Posted: 9 years ago May 16, 2016, 2:10 a.m. EDT

I uploaded a COMSOL file to the Model Exchange that shows how to set up a phononic band gap eigenfrequency analysis. Here is the link: www.comsol.com/community/exchange/432/.

Nagi Elabbasi
Veryst Engineering


Hi Nagi,

Thank you for your model. It is very useful for me.

And I have a question about the wave vector in the model:

Why did you define the wave vector kx and ky as following:
kx= if(k<1,pi/L1*k, if(k<2,pi/L1,(3-k)*pi/L1))
ky=if(k<1,0,if(k<2,(k-1)*pi/L1,(3-k)*pi/L1))

Maybe it is just a sample. if in a real calculation, how to define kx and ky?

Thank you very much!

Best Regards,
Zhuhua Tan
[QUOTE] I uploaded a COMSOL file to the Model Exchange that shows how to set up a phononic band gap eigenfrequency analysis. Here is the link: http://www.comsol.com/community/exchange/432/. Nagi Elabbasi Veryst Engineering [/QUOTE] Hi Nagi, Thank you for your model. It is very useful for me. And I have a question about the wave vector in the model: Why did you define the wave vector kx and ky as following: kx= if(k
Anisuzzaman Boni
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Posted: 7 years ago Jun 23, 2017, 10:48 a.m. EDT
the pi value of the brullian zone is 180 or 3.1416. If i am not wrong, k= 0 to 2*pi covers the whole brullian zone.

Thanks in advance.
the pi value of the brullian zone is 180 or 3.1416. If i am not wrong, k= 0 to 2*pi covers the whole brullian zone. Thanks in advance.

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