# Review on Structural Health Evaluation with Acoustic Emission
## 8 General Summary and Follow-Up Studies  
Signal attenuation considered in Sections 2.1-2.3 led to the confirmation of the guided wave theories through reexamination of data from large structures as well as from laboratory-scale plate experiments. These theories for attenuation in isotropic media can be applied to predict signal loss in real structures of metallic alloys. For the distance of 10 m or so, the inverse square root distance (or \(1/\surd\)x) behavior is enough, while at longer propagation distances material absorption effects need to be added in the form of (\(1/\surd\)x)-exp(-ox). The guided wave attenuation coefficient can be calculated when reliable bulk wave attenuation coefficients are available. However, Section 2.5 revealed the lack of such data for most common alloys. For these cases, one needs to conduct attenuation tests as in [33; 34; 35; 36; 37; 38]. It is hoped that more bulk wave attenuation data will be accumulated in the future, although shear wave attenuation tests are difficult. A new approach for attenuation studies using complex elastic moduli was reviewed in Section 2.4. The damping factors for stiffness coefficients were obtained by the Castaings method. Since no direct verification is feasible, obtained damping factors for PMMA (in Section 2.4) and fiber-reinforced composites (in Section 2.6) were compared with damping factor determination from dynamic mechanical analysis and ultrasonic attenuation studies. The comparison showed Castaings' damping factors to typically be twice higher than those from other methods. Since the Castaings method was developed with sound theoretical foundation, some unaccounted factors appear to contribute to overestimation. A possible source is the common assumption made in most ultrasonic analysis, that is, the wave front to be planar. This was apparently a cause of higher bulk wave attenuation coefficients from immersion or buffer-rod methods as discussed in Section 2.5. In these ultrasonic methods, this point needs to be reevaluated. Clearly, the Castaings method is a valuable addition to viscoelastic analysis and making it verified will be beneficial to the field. Note that mechanical damping and ultrasonic attenuation studies are complementary, but these are usually separated. For example, [PERSON]'s review [17] mentioned no complex elastic moduli works, and [PERSON] and [PERSON] [48; 49] ignored low frequency damping studies. Still, an identical physical mechanism governs vibration energy loss in polymers like PMMA and epoxy [18; 19]. Attenuation studies for fiber-reinforced composites considered in Section 2.6 show significant advances made in the past 15 years. Yet, the fact remains that attenuation in composites is higher than in homogeneous metallic alloys. This is especially true at higher frequencies above a few hundred kHz, where signal analysis must be conducted to characterize microscopic fracture mechanisms, as discussed in detail by [PERSON] [208]. Even from practical engineering approach of using pattern recognition analysis, the availability of high frequency components in AE signals is an important element for success. In composite plate design, ply lay-up sequences are crucial parameters and these also affect attenuation characteristics. This part has not entered into AE or SHM consideration, but will eventually become necessary to incorporate it in attenuation analysis. Initial steps were made in examining the directivity of attenuation behavior [102; 104; 209], but more future works are needed, accompanied by modeling studies to avoid experimentation. Some of the past attenuation studies used a common AE or ultrasonic sensors [104; 209] and this must be avoided in future works. As shown in Figure 6 above, a small aperture sensor of 1-mm diameter gives different attenuation behavior. While sensor aperture effects can be partly corrected by analysis [210], the sensor aperture must be smaller than the wavelength to minimize displacement cancellation effects.