Inverse Shape Reconstruction of Inner Cavities Using Guided SH-Waves in a Plate

Table 1

An illustration of validation chart for reflection and transmission coefficients.

Freq.	Number of modes	Ref. or tra. coefficients; inc. wave from left	Ref. or tra. coefficients; inc. wave from right	Relative error of coefficients; for inc. wave from left and right
0.1	1	= 0.011441611	= 0.011441611	0
		= 0.999934543	= 0.999934543	0
		Energy check: = 1.000	Energy check: = 1.000
2.0	2	= 0.174070111	= 0.174910464	0.48%
		= 0.162546674	= 0.161951563	0.37%
		= 0.971008475	= 0.970534705	0.049%
		= 0.02974192	= 0.02468971	16%
		= 0.162862467	= 0.162771155	0.056%
		= 0.038026818	= 0.037097031	2.5%
		= 0.026354694	= 0.027964747	6.1%
		= 0.985423619	= 0.985802799	0.038%
		Energy check: = 1.000463866; = 0.999724501	Energy check: = 0.999369174; = 1.000459824

Definition of coefficients is as follows.
Suppose the mth mode is used as the incident wave; then, we introduce the direction numbers,
1: the left direction of the flaw, 2: the right direction,
and the reflection/transmission coefficients .
Meanings of subindices:
: A-incident direction ( = 1,2); a-incident mode order; -scattered direction ( = 1,2); -scattered mode order ( and the same: reflection coefficient; and different: transmission coefficient).
Wave field:
(+ for incident wave from 2; − from 1);
(− for reflected wave to 2; + to 1);
(+ for transmitted wave to 1; − to 2).
The coefficients are defined as
(reflection coefficient);
(transmission coefficient).