## 2 Composite Plate and Material Characterization  
The CFRC composite plate sample consists of 20 plain weave pattern laminas of 0.3 mm thickness each oriented in [45/0/0/45/0/45/0/45/0/45]\({}_{\mathrm{S}}\) directions. The average thickness of the 50 \(\times\) 50 cm\({}^{2}\) composite plate is approximately 6.2 mm. The homogenized elastic moduli are optimized by matching them with the experimental group velocities of A\({}_{0}\) and S\({}_{0}\) Lamb modes for a given set of frequencies and the through thickness ultrasonic bulk wave velocities. The schematic of the composite plate as well as the measurement directions of the excited Lamb waves are shown in Figure 1. The homogenized composite plate is transversely isotropic (quasi-isotropic) with \(Y\)-axis as axis of symmetry. The A\({}_{0}\) and S\({}_{0}\) Lamb wave velocities are measured around the emitter (shown in red dot) along different angular positions and in a straight line from the emitter (shown in green and blue dots respectively) in \(XZ\)-plane. Velocities were found to be unchanged for all directions in the considered frequency range, namely 10 kHz-150 kHz. Under the transversely isotropic condition, the inversion method was performed by fitting the analytic group velocity dispersion curve with the experimental group velocities corresponding to A\({}_{0}\), S\({}_{0}\) and SH\({}_{0}\) modes as well as bulk ultrasonic waves generated around the abovementioned frequency domain. The density \(\rho\) of the plate is first measured as 1.55 \(\pm\) 0.05 g/cm\({}^{3}\). The elastic constant \(C_{22}\) (along \(Y\)-axis) is obtained by measuring the longitudinal wave velocity along \(Y\)-axis where \(V_{L}\) = 2860 \(\pm\) 10 m/s, which gives \(C_{22}\) = \(V_{L}^{2}\) * \(\rho\) = 12.6 GPa. The measured shear wave velocity propagating along \(Y\)-axis and vibrating in \(Z\)-axis is found to be equal to \(V_{T}\) = 1550 \(\pm\) 10 m/s giving the elastic constant \(C_{44}\) = \(V_{T}^{2}\) * \(\rho\) = 3.72 GPa. The group velocity related to SH\({}_{0}\) wave is found to be equal to 3300 \(\pm\) 100 m/s. The value of the constant \(C_{13}\) is then adjusted in the dispersion curve to achieve the same velocity, where \(C_{13}\) is found to be equal to 17.8 GPa. On the other hand, the group velocity of \(S_{0}\) Lamb mode at 100 kHz is 5700 \(\pm\) 100 m/s and the one corresponding to A\({}_{0}\) mode at 40 kHz is 1500 \(\pm\) 100 m/s. The speed of A\({}_{0}\) mode primary depends on the constant \(C_{44}\), which is obtained using the abovementioned shear wave velocity \(V_{T}\). The speed of S\({}_{0}\) mode (at 100 kHz) depends on the constants \(C_{11}\) and \(C_{12}\), whose optimization is essential to the constant \(C_{55}\), where \(C_{55}\) = 1/2 * (\(C_{11}\)-\(C_{13}\)) in the case of a transversely isotropic symmetry. The constants \(C_{11}\), \(C_{12}\) (or \(C_{23}\)) are optimized using the S\({}_{0}\) wave velocity. It is observed that a linear increase of \(C_{11}\) (keeping other constants fixed) will result in a linear increase in the group velocity of S\({}_{0}\) mode while a linear increase of \(C_{12}\) (or \(C_{23}\)) will result in a linear decrease in the group velocity of S\({}_{0}\) mode (keeping other constants fixed). The change in \(C_{12}\) from 2 GPa to 10 GPa results in a linear decrease from 5800 to 5000 m/s in the group velocity of S\({}_{0}\). The values of \(C_{11}\) and \(C_{12}\) are adjusted to fit the measured velocity of 5700 m/s. The optimized values of the stiffness tensor are given in Table 1.  
Frequency dispersion curves corresponding to phase velocities are computed using the semi-analytic finite element (SAFE) method for the composite plate using the optimized elastic constants given in Table 1 and shown in Figure 2. Finally, we note that the attenuation is determined by measuring the amplitude variation for a given propagation distance in the far field.