How to calculate the energy reflection coefficients in LAMB wave edge reflection problem?

09 December 2020 3 1K Report

Hello everyone,

Has anyone ever succeeded in calculating the energy reflection coefficients in LAMB wave edge reflection problem? Or any available code resources?

I am a third-year master student majored in solid mechanics. I have been stuck with the energy conservation problem for so long now.

Dispersion curves, mode structures, and power flux of individual mode are consistent with the results from the software DISPERSE. However, the sum of energy reflection coefficients did not equal 100%, even in the normal incident edge reflection case with a single layer isotropic plate.

By comparing with results from different resources (details can be seen in CodeValidation.png), the correctness of my SCM method should have been validated, as shown in figs. 1-3.

However, the energy reflection coefficients just didn't sum to 100%. As shown in fig.4, the A0-A0 energy reflection coefficients matches with Gunawan's results, but A0-A1 energy reflection coefficients failed to match. That's wierd but I can't find the causes.

I am wondering if I have treated the wavenumber k in a wrong way:

For LAMB waves propagating in +x direction, the displacement field was assumed as u = U*exp(i(kx-wt)). The numerically obtained k may have the form a + bi, a - bi, -a + bi, -a - bi (a and b are positive real numbers). In the GetkInOrder.m, I have kept only those k with positve real part (+x propagating) and positive imaginary part (physically decaying with propagation).

For LAMB waves propagating in -x direction, the displacement field was assumed as u = U*exp(i(-kx-wt)), so the k will be still kept k = a+bi (a>0 and b=0; or a=0 and b>0 ).

Am I wrong about the selection of calculated wavenumber k? Maybe it is the error in this step that makes the energy conservation cannot be met?

The same problem is met while calculating the excitability, which is defined as the parameter that relates the amplitude of the excitation force and the modal response of a particular mode at a specific frequency.

I have emailed many authors who have published papers about this topic with their articles, my codes, and detailed ideas of my codes and method; however, most of them did not reply while others can not help me.

I understand that every program is hard-won and they have no duty to help me. But this problem is really important to me. I have been stuck for months and I am still trying.

If there is anyone who has ideas about how to fix this problem, please help me. Thank you so much.

Best wishes,

Hao Qiu

Kosuke Kanda

I think when you calculate scattering coefficients, you should classify modes according to sign of group velocity.

Even if phase velocity is positive, group velocity is not always positive.

For example, group velocity of S1-mode near the cut-off frequency is negative.

Thank you for your reply.

I have found that last week and my program works now.

It sounds good.

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