## 4 Results and Discussion
### Attenuation Behavior of Fiber-Reinforced Materials  
Eleven fiber-reinforced composite materials were tested. E-glass fibers, carbon fibers (grades AS-4, G50, and T700) and Kevlar fibers were used for reinforcement and epoxy resin was the matrix using most cases (exceptions are noted). All reinforcement used continuous fibers. These were named glass-fiber-reinforced composite (GFRC), carbon-fiber-reinforced composite (CFRC), and Kevlar-fiber-reinforced composite (KFRC). For GFRC, both unidirectional (UD) and woven roving cross-ply (XP) composites were available. For CFRC, UD and quasi-isotropic (QI) composites were used. Only woven roving XP composites were available for KFRC. While fiber orientation is usually noted in degrees off the main direction, the wave directions will be referred to as before, with L, T, and S. Here, L coincides with 0\({}^{\circ}\) fiber orientation, T matches 90\({}^{\circ}\) orientation regardless of plate or rod shape, and S refers to the surface normal for a composite plate. The attenuation parameters from these tests (R1 to R34) are given in Table 7. This table shows that anisotropic wave velocity and attenuation are common to all composites reinforced with continuous fibers. This anisotropy appears in the wave velocities in the three directions (L, T, and S). While v\({}_{\rm L}\) values in the T and S directions were similar for a given UD composite, v\({}_{\rm L}\) in the L direction was larger by a factor of 1.5 to 5. This tendency extended to XP and QI composites as well. UD composites always have low attenuation values below 155 dB/m at 1 MHz in the L direction, but attenuation increases in the T or S direction. This difference depends on fiber-resin combinations. The attenuation ratio (= C\({}_{\rm d}\)(T or S)/C\({}_{\rm d}\) (L)) was the largest in T700 CFRC at 25 between the L and S directions. In the QI-CFRC with T700 fibers, the orientation difference was much smaller, as expected from its layup design (having 0\({}^{\circ}\), \(\pm\)45\({}^{\circ}\), and 90\({}^{\circ}\) fiber orientations in plane). The XP composites of GFRC and KFRC also showed similarly smaller differences between the L and S directions in terms of the attenuation ratio. The first four tests were performed on a UD-GFRC rod measuring 63 mm in diameter, cut into two lengths. This was done by pultrusion at Glasform, Inc. (Birmingham, AL, USA), and is typical for high-voltage insulators containing 0.565 volume fraction of E-glass fibers in epoxy matrix. Figure 18 shows observed spectral data in the L direction, with purple and green curves for attenuation from TDM-1 and TDM-2 methods (tests R1 and R2), respectively. Purple and green dotted lines represent linear regression fits, giving C\({}_{\text{d}}\) = 74.6 and 72.6 dB/m/MHz, with R\({}^{2}\) values of 0.951 and 0.927, respectively. These two C\({}_{\text{d}}\) values agree well. The green dashed curve is for the attenuation spectrum when the diffraction correction (shown by the red dotted curve) was applied. The results were reduced to negative attenuation below 1.7 MHz, making the linear fit unacceptable. Thus, for composite tests in this section, no diffraction correction was applied. Some studies attempted to obtain this correction for anisotropic solids [99,100], but these were inapplicable for the cases in this section. When the T\({}_{\text{c}}\) term was omitted (test R3), the C\({}_{\text{d}}\) value increased to 84.2 dB/m/MHz. However, the linear fit was better with R\({}^{2}\) = 0.966. Since the TDM-1 result was between the results of TDM-2 tests with or without the transmission coefficient, the latter two can be used in estimating the TDM-1 value. Test R4 was in the S direction, which is the normal direction relative to glass fibers. The attenuation was 2.3 times higher. The attenuation spectrum for test R4 follows the Biwa relation (Equation (8)); that is, \(\alpha\) consists of the damping and Biwa scattering term of cubic frequency dependence [53,54]. The C\({}_{3}\) coefficient is listed in Table 7 under the C\({}_{\text{n}}\) heading.