Hello everyone,
Recently, I have read the paper MODELING THE EXCITATION OF LAMB AND SH WAVES BY POINT AND LINE SOURCES (2004, AIP Conference Proceedings).
To fully understand it, I have studied it carefully and tried to validate the results by coding in MATLAB.
The dispersion-related results, including the wave structure, were successfully obtained; however, I met some problems while comparing the harmonic displacement field calculated by Eq. (9) and Eq. (10) with the results from COMSOL (FEM software).
They have mismatched each other in phases, as shown in the attached figure.
I think that can be caused by the phase-ignoring in Eq. (3) but I am not so sure. Here is what I thought.:
Considering the displacement field generated by an infinite line source vibrating in X-direction, as shown in Fig. 1(b) in the paper.
The differences between the phases of different guided wave modes and the harmonic line source should be uniquely determined.
However, using Eq. (3) in the paper, the information about the phase differences was lost.
But as shown in Fig. 4 in the paper, the absolute discrepancy between the results from the two models (Analytical and FEM) is of the order of 2 %.
Then there shouldn't be any phase-related problems with the equations in the paper.
If there is anyone who has ideas about how to fix this problem, please help me.
Thank you so much.
Best wishes,
Hao Qiu
Dear Hao,
in Es. (3) there cannot be an sign information as it is purely the excitability of a mode, i.e., for a mode to be excited the direction does not matter. The mode is excited with the same “strength“ independent of the orientation of the force. Therefore, this should not be a problem.
As seen in the figure you posted the agreement is very good if you would multiply the ur results with -1. The ut results do not show that problem and already coincide. Therefore, one explanation might be that the coordinate systems are not properly aligned. Maybe there is a mismatch between Comsol and your implementation.
The formulae seem fine to me. Maybe the force amplitude should contain the correct sign.
Kind regards
Hao,
As far as I can judge from quickly reading the paper, the convention for complex amplitudes there (and thus probably in your MATLAB code) is :
u(r, t) = U(r) exp(- i w t)
COMSOL always uses the convention exp(+ i w t).
This might explain the difference.
Best regards
Sascha Eisenträger
Dear Sascha,
Thank you so much for answering my question.
Actually, I have tried the approach suggested by you, i.e. changing the phase of Ur by 180 degrees. The problem is that sometimes the needed phase correction is not always 180 degrees. And that may cause trouble in further calculations so I want to figure out the reasons.
What confused me is that:
In Eq. (3), is the surface displacement vk a real number or complex number containing phase information?
Anyway, thanks again for your reply.
Best regards
Olivier Louisnard
Dear Olivier,
Thank you so much for answering my question.
Actually, I have noted that the harmonic item used in COMSOL is exp(+iwt) instead of exp(-iwt). What confused me is another problem which was written in my reply to Sascha Eisenträger.
Anyway, thanks again for your reply.
Best regards
Dear Hao,
you mentioned that the phase difference is not always 180 degrees. What is the actual difference? Both the given analytical solution and the numerical solution (COMSOL) are only approximate in nature and therefore differences are expected. If it is in the order of a couple of percent this is still alright. Keep in mind that both results are based on certain (different) assumptions.
Cheers,
Sascha
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