# Review on Structural Health Evaluation with Acoustic Emission
## 2 Signal Attenuation
### Guided Wave Attenuation on Fiber-Reinforced Composites
When the same data is plotted in a log-log graph, only geometrical spreading effect or 1/\(\surd\)x behavior is found without additional attenuation. No signal loss was observed for S\({}_{0}\)-mode at 300 or 500 kHz, as shown in Figure 6b. This behavior appears to come from a sharp directivity for the UD plate observed previously [106]. In contrast, attenuation for A\({}_{0}\)-mode at 300 or 500 kHz was substantial. Values of \(a_{\rm L}\) were 78 and 178 dB/m beyond geometrical spreading for A\({}_{0}\)-mode propagation along the fiber direction, as shown in Figure 7a,b. Thus, the \(a_{\rm L}\) values for A\({}_{0}\) are within a factor of two with the Calomfirescu calculation [63]. However, \(a_{\rm L}\) for S\({}_{0}\) at 0\({}^{\circ}\) vanished in our tests beyond geometrical spreading. [PERSON] et al. [65] used another approach in characterizing CFRP properties. They measured Lamb wave propagation utilizing air-coupled ultrasonic techniques and deduced the dispersion curves and attenuation behavior. The data was then used to construct an analytic model. Their modeling relied on higher order plate theory and the attenuation utilized hysteretic model where the damping coefficients (\(\eta_{\mathrm{ij}}\)) are independent of frequency. The values of \(\eta_{\mathrm{ij}}\) were given in [PERSON] et al. [66] and listed in Table 1. It appears that an UD plate is marked 45\({}^{\circ}\) considering C\({}_{\mathrm{ij}}\) values. Assuming  
Figure 6: **(a)** UD-CFRP attenuation for S\({}_{0}\) (blue) and A\({}_{0}\) (red) modes at 100 kHz, amplitude in dB scale; **(b)** UD-CFRP attenuation for S\({}_{0}\) mode at 300 kHz (blue) and at 500 kHz (red), amplitude was calculated using the square root of the wave packet energy. Information on the UD-CFRP plate was given in [106]. Figure 7: UD-CFRP attenuation for A\({}_{0}\) modes vs. (log) distance. Observed data (blue +), modeled attenuation of geometrical spread plus attenuation (red circle), geometrical spread (gray circle). Amplitude in dB scale. **(a)** Attenuation of 78 dB/m for 300 kHz; **(b)** attenuation of 178 dB/m for 500 kHz. Amplitude was calculated as in Figure 6.  
this to be the case and noting that their \(\eta_{\mathrm{ij}}\) stand for C\"\({}_{\mathrm{ij}}\), some of these are two-to-five times smaller than the corresponding values from the Castaings method [49]. However, off-fiber parameters of \(\eta_{\mathrm{22}}\), \(\eta_{\mathrm{133}}\), and \(\eta_{\mathrm{23}}\) are grossly overestimated with \(\eta_{\mathrm{23}}=0.26\) being five-times higher than \(\eta_{\mathrm{12}}\) of PMMA. In dealing with different composite layups used, lamination theory was incorporated. An example given shows calculated attenuation coefficients for \(S_{0}\) and \(A_{0}\) modes on a quasi-isotropic CFRP plate. At 122 kHz, they obtained attenuation coefficients for \(S_{0}\) and \(A_{0}\) modes to be 4.3 and 50.2 dB/m beyond geometrical spreading. Another set of attenuation coefficients for \(S_{0}\) and \(A_{0}\) modes were reported graphically (CFRP layup was not given, but it seems to be UD). At 300 kHz, these were 31 and 140 dB/m, respectively. These \(a_{\mathrm{L}}\) matched with their experimental values. These were higher than our data that included geometrical spreading effects [106], and our new test data discussed above showing no attenuation at 100 kHz. Only the \(A_{0}\) data at 300 kHz matched within a factor of two. [PERSON] et al. [65] included geometrical spreading in their modeling. This needs to be probed, however, since properly modeled calculations should predict \(1/\surd x\) behavior from the viscoelastic parameters for quasi-isotropic CFRP, and a directional behavior for unidirectional CFRP. More comparative studies are obviously needed to obtain representative CFRP wave propagation characteristics.