Discussion Forum

Hi Joseph,

There are some things that need to be corrected first in the model before evaluating any results.

• There is no Study step in Study 1. If solving for the steady-state, time harmonic fields add a Frequency Domain Step
• There is no material assignment to the PML, which also needs a material assignment.
• The lateral boundaries of the PML should not be fixed.
• It is recommended to use Form Union as the final geometry step for this case, not Form Assembly. You can find more details here: https://www.comsol.com/support/learning-center/article/The-Usage-of-Form-Union-and-Form-Assembly-74571
• The Young's Modulus for Structural Steel 1 (mat2) is not properly defined. The function YM needs to be called correctly with its proper argument (ex: YM(x)).
• The boundary load is 0 in all directions, hence there is no applied load. Consider applying a nonzero load in the lateral direction of the beam to excite a flexural wave.

As a suggestion, first try to get the model to run for some simple loading condition and then check the results (displacements, vibration mode) to see if this is physically what is expected based on the inputs provided to the model.

-Mark

Hi Mark thanks for the reply. I've added my updated version to this post. I still keep getting that pml error and I have no idea how to fix it. I did everything you said apart from the form union part because the model didnt work when I did it. It also still says my YM is unkown in the structural steel 1(mat2) for some reason. Any help would be appriciated. Thanks

The PML error is due to use of Form Assembly. Form Union is the recommended approach here. Also both the boundary load and fixed constraint should not be applied to the same boundary.

I tested the following and the model did run: 1) Change to Form Union and Build All 2) Apply the boundary load to boundary 6 3) Run the study at 100 Hz.

How would the reflection coefficient then be found? And how would a plot of reflction coefficient against frequency be created?

Sweep over a range of frequency in the frequency domain study by adding a frequency range in the study settings. This sets the model up to solve at every given frequency, so any result can be computed and plotted vs. frequency.

To find reflection coefficient, use beam theory to separate the wave into the incident and reflected amplitudes. This has been done in the literature, for example here: https://pubs.aip.org/asa/jasa/article-abstract/145/6/3488/940291/A-parametric-study-of-an-acoustic-black-hole-on-a . The computation uses the displacment fields at two points along the beam.

In COMSOL, this can be implemented by: setting up two point probes for displacement and then creating variables to compute the reflection coefficient which is a function of the displacements, flexural wave number, and distance between the points.

As a suggestion, first check that the calculation is working as expected for a simple benchmark case. For a beam with a free end at the origin and the incident wave traveling from x=L toward x=0, the reflection coefficient should be R=-1i which can be shown analytically (ex: https://www.sciencedirect.com/science/article/abs/pii/0022460X84903201).

It is actually quite similar to the two microphone method in acoustics for measuring reflection/absorption coefficient in an impedance tube.

Hi Mark, how would you find the dispalcement when the point probes are set up? I know how to set up the probes up but i just dont understand how the displacement is calculated. Thanks

The dispalcement is calculated when solving the study. The point probe stores displacement value at a particular point. For example in the screenshot, point probe 1 is setup to store the z component of displacement at point 16. It is stored to a variable named p1.

I understand. And with these displacements how would the total reflection coefficient be plotted?