# Review on Structural Health Evaluation with Acoustic Emission
## 2 Signal Attenuation
### Laboratory Attenuation Measurements  
As a part of guided-wave sensor studies at UCLA [40; 41], Lamb wave attenuation was measured for large aluminum (Al) plates (6.4-mm thick 1100 Al and 12.7-mm thick 6061 Al), steel (3.2-mm thick 410 stainless), soda-line glass (4.7-mm thickness), PMMA (6.4-mm thickness), and polyvinyl chloride (PVC, 4.6-mm thickness). For the three metal and glass plates, the inverse-square root distance behavior prevailed with a few exceptions (when combined modes started to split at larger travel distances at some frequencies). The maximum travel distance was 500 mm and the frequency range was from 100 to 1500 kHz. The result of the \(1/\surd\)x behavior for 410 stainless steel (SS) was surprising because this steel (along with pure Fe and pure Ni) was expected to show high bulk wave attenuation  
Figure 2: Attenuation data (amplitude in dB vs. distance in m) on steel structures. (**a**) Signal attenuation on a pipeline at 30 kHz by [PERSON] [34]; (**b**) Signal attenuation on a gas cylinder at 150 kHz by [PERSON] [35]; (**c**) Signal attenuation on a pipeline at 30 kHz by [PERSON] et al. [36]. Lines drawn represent \(1/\surd\)x dependence. Measured data points are shown by + (blue) and modeled points are in filled circles (red) in (**a**,**c**).  
due to its magnetic properties [42]. However, [PERSON] [43] reported only moderate attenuation for a comparable 416 stainless steel (\(a_{\mathrm{P}}=20\) dB/m at 4 MHz). [PERSON] [43] did find Ni to have a high \(a_{\mathrm{P}}\) of 120 dB/m at 2 MHz. [PERSON] [44] calculated Lamb wave attenuation curves for glass, showing less than 0.1 dB/m attenuation below 0.5 MHz for a plate (3.9-mm thickness). Thus, the \(1/\surd\)x behavior found here for glass confirms the calculation. In highly attenuating polymeric plates, signal levels were strongly reduced as shown in Figure 3. At 75 kHz on 6.4-mm thick PMMA (Figure 3a), S\({}_{0}\)-mode waves propagated with symmetric excitation and showed the \(1/\surd\)x behavior plus \(a_{\mathrm{L}}\) of 25 dB/m. At 380 kHz on PMMA (Figure 3b), seven Lamb modes are expected with the group velocity of 0.8 to 1.1 mm/us according to dispersion curve calculation. Since the duration of excited signals was about 50 us, mode separation was not observed and the entire wave packets were analyzed. Attenuation \(a_{\mathrm{L}}\) beyond the geometrical spreading was higher at 121 dB/m. A 4.6-mm thick PVC plate exhibited even higher attenuation, reflecting its higher bulk wave attenuation [45]. As shown in Figure 3c, 130-dB/m attenuation was observed beyond the geometrical spreading at 75 kHz. For PMMA, the values of \(a_{\mathrm{P}}\) and \(a_{\mathrm{t}}\) below 100 kHz were available from resonant ultrasonic spectroscopy [46; 47]. Assuming that the damping factor (\(\eta\)) values of 0.035 and 0.025 reported for 50 and 60 kHz, respectively, hold at 75 kHz, \(a_{\mathrm{P}}\) and \(a_{\mathrm{t}}\) are found as 27.3 and 52.0 dB/m for PMMA at 75 kHz. Using the Zhukov theory for \(a_{\mathrm{L}}\) and calculated coefficients given, the attenuation of S\({}_{0}\)-mode waves was obtained as 33.7 dB/m for the frequency-thickness product of 0.48 MHz-mm for PMMA thickness of 6.4 mm. The observed \(a_{\mathrm{L}}\) value for S\({}_{0}\)-mode is 25 dB/m, so \(a_{\mathrm{L}}\) matching is good between theory and experiment. [PERSON] and [PERSON] [48; 49] obtained complex elastic moduli for PMMA and predicted Lamb wave attenuation for five lowest modes. At 75 kHz, \(a_{\mathrm{L}}\) for S\({}_{0}\) was 21.5 dB/m, while \(a_{\mathrm{L}}\) values ranged from 145 to 300 dB/m at 380 kHz. Thus, theory and experiment agree reasonably well also. When the observed \(a_{\mathrm{P}}\) and \(a_{\mathrm{t}}\) values are inserted to the Viktorov equation [20] for Rayleigh wave attenuation, \(a_{\mathrm{R}}=\mathrm{A}\ a_{\mathrm{P}}+(1-\mathrm{A})\)\(a_{\mathrm{t}}=51.0\) dB/m as A = 0.05 with [PERSON]'s ratio of 0.37 for PMMA. This is in good agreement with 47 dB/m at 75 kHz, obtained by [PERSON] and [PERSON] [23].  
Figure 3: _Cont._