To begin with, you will need to create a model of the phononic crystal in COMSOL. You can do this by following these steps:

1. Start a new model in COMSOL and select "Acoustics" as the physics interface.

2. Use the "Geometry" tab to draw the geometry of the phononic crystal. You can use the drawing tools in COMSOL to create a 2D or 3D model of the crystal.

3. Use the "Materials" tab to specify the material properties of the phononic crystal. You will need to specify the density and sound speed for each material.

4. Use the "Meshing" tab to generate a mesh for the model. Make sure to use a fine enough mesh to accurately capture the behavior of the phononic crystal.

5. Use the "Physics" tab to set up the simulation. You will need to specify the frequency range of interest and the type of boundary conditions to use.

Once you have set up the model, you can use the "Frequency Domain Acoustics" interface to perform a frequency-domain simulation. This will allow you to compute the transmission spectra of the phononic crystal as a function of frequency.

If you need more guidance on how to set up and run this simulation, you may find it helpful to consult the COMSOL documentation or to watch some of the tutorials available on the COMSOL website. There may also be other tutorials or online resources available that cover the specific topic of phononic crystals and transmission spectra.

dear Salman

thanks a lot for your attention and detailed answer. according to some documents, boundary probe must be defined to get the transmission curve. would you mind explaining me how boundary probe must be defined? what I found in COMSOL documentation and COMSOL website were related to sonic crystal where background pressure was used as a source.

Dear Mohammad,

In order to calculate the transmission spectra of a phononic crystal using COMSOL, you will need to define boundary probes at the boundaries of the model. These probes allow you to measure the acoustic pressure and particle velocity at the boundaries, which you can use to compute the transmission spectra. I provided a list of steps outlining how to define boundary probes in COMSOL in my response. Try to follow these steps:

1. In the "Model Builder" window, navigate to the "Boundary Properties" node for the physics interface you are using (e.g., "Frequency Domain Acoustics").

2. Click on the "Add Probe" button. This will open a new window where you can specify the probe type, location, and other properties.

3. In the "Type" dropdown menu, select "Pressure" or "Velocity" to measure the corresponding quantity at the boundary.

4. Use the "Location" dropdown menu to specify the boundary at which you want to place the probe. You can choose from the list of boundaries defined in the model, or you can use the "Add Surface" button to add a new boundary.

5. You can use the other options in the window to customize the probe further if needed. For example, you can specify a frequency range or select a specific component (e.g., x-velocity) to measure.

6. Once you have defined the probe, you can run the simulation and use the "Results" tab to plot the transmission spectra. To do this, select the "Probes" result type and choose the boundary probe you defined from the list of available probes. This will display the measured pressure or velocity at the boundary as a function of frequency, which you can use to compute the transmission spectra.

dear Salman. thanks a lot for useful answers.

Dear Salman

thank a lot for your good answers.To calculate transmission spectra of the crystal, I know that one should follow the procedure like this:

"To calculate transmission spectra of the crystal,a sample with five(for example) unit cells in x direction and one unit cell in y direction was oriented along ГX direction and surrounded by two homogenous regions. The perfectly matched layer(PML) was adopted as the absorbing boundary condition for the left and right boundaries of the computational domain. For the top and bottom boundaries the periodic boundary condition was used.

Gaussian wave packet was launched along the x direction at the left homogenous region. The x component (y component) of displacement was recorded at middle of right homogenous region and averaged over a lattice constant. By taking fast Fourier trans- form of this average,transmission spectra through the crystal for longitudinal (transverse)polarization of incident waves was obtained"

actually, I dont know how to define Gaussian wave packet( source and how to taking fast Fourier transform in Comsol.