# Review on Structural Health Evaluation with Acoustic Emission
## 2 Signal Attenuation
### Guided Wave Attenuation on Fiber-Reinforced Composites  
Lamb wave experiments were also conducted at UCLA using fiber reinforced plastics (FRP). Figure 5a,b show two cases for an FRP with woven glass-fiber rovings and epoxy matrix (2.2 mm thickness, density 1.9 g/cm\({}^{3}\), 0.38 fiber fraction). Attenuation data for S\({}_{0}\) mode along the fiber direction at 60 and 100 kHz are plotted against (log) distance. The observed data can be attributed entirely to the 1/\(\surd\)x dependence at 60 kHz, while 100-kHz data matches the 1/\(\surd\)x dependence plus 10.8 dB/m attenuation. These attenuation coefficients are similar to \(a_{\rm p}\) of 4.4 dB/m at 100 kHz for a unidirectional GFRP along the fiber (converted from \(\eta\) of 0.007) [90]. The above findings implies glass-fiber reinforced plastics (GFRP) behave similarly to common structural metallic alloys below 100 kHz. The same attenuation data can also be described conventionally with an attenuation coefficient of 21.2 dB/m (60 kHz) or 33.1 dB/m (100 kHz) including the geometrical spreading as shown in Figure 5c. These conventional attenuation coefficients are lower than \(a_{\rm p}\) of 135 dB/m for another GFRP (with random mat) at 100 kHz, with its \(a_{\rm p}\) increasing to 400 dB/m at 2 MHz [91]. However, this data was in the direction normal to fibers and not directly comparable. When attenuation due to absorption is high, it is convenient to include signal spreading in attenuation parameters in NDE applications. [PERSON] and [PERSON] [48] used complex elastic moduli from [49] and predicted Lamb wave attenuation for unidirectional GFRP, giving S\({}_{0}\)-mode \(a_{\rm L}\) value at 100 kHz of 17 dB/m. For this case, [PERSON] and [PERSON] [49] reported \(\eta_{11}\) = 0.047, \(\eta_{12}\) = 0.043, \(\eta_{133}\) = 0.033, \(\eta_{55}\) = 0.05, \(\eta_{66}\) = 0.038, \(\eta_{12}\) = 0.033, and \(\eta_{13}\) = 0.036 (fiber direction is the 3-direction and fiber volume 0.6). [PERSON] et al. [61]  
Figure 5: Lamb wave attenuation data for S\({}_{0}\) mode along the fiber direction of an FRP. (**a**) Data at 60 kHz match with 1/\(\surd\)x dependence; (**b**) data (blue +) at 100 kHz fit to the 1/\(\surd\)x dependence plus 10.8 dB/m attenuation, shown by red circles; (**c**) the same attenuation data (in dB) plotted against linear distance. Blue points: 60 kHz with the slope of 21.2 dB/m. Red points: 100 kHz with 33.1 dB/m. This FRP was used in an AE study [92]. reported another set of \(\eta_{\rm jj}\) for a GFRP, measured by the Castaings method. This set showed the values of \(\eta_{33}\) and \(\eta_{66}\) to be 70 and 240% higher. These \(\eta\) values by the Castaings method (listed in Table 1) are higher than other published values of \(\eta\), determined from conventional vibration damping methods at lower frequencies. [PERSON] [93] thoroughly reviewed test methods and results. He also gave additional results on damping of composite materials. See also [60], which listed \(\eta\) values from the 1980s as in [93]. For unidirectional GFRP with 0.6-fiber volume fraction, longitudinal damping factor \(\eta\) in the fiber direction was 0.004-0.006, about six-times smaller than the ultrasonic data above [49, 61]. [PERSON] [93] also noted that epoxy matrix has \(\eta\) of 0.022. [PERSON] [94] obtained even lower damping factor values, e.g., \(\eta_{1}\) = 0.002 (or 0.0013 from [60]) and noted \(\eta\) for a single glass fiber to be 0.0015. Data in [60] gave \(\eta_{2}\) of 0.008 and \(\eta_{12}\) of 0.011 for E-glass/DX210 epoxy. These GFRP data are mostly lower than the epoxy data in Table 1[60]. These damping data were all taken under 1 kHz and increasing trends with frequency were reported. If the main contribution to damping comes from the matrix, as existing theories postulated [91], the increase with frequency is likely to be insignificant considering the decreasing trend of damping factor noted on PMMA [42]. In fact, the data of \(a_{\rm P}\) = 400 dB/m at 2 MHz cited earlier [91] correspond to the damping factor of 0.02.