## 3 Ultrasonic Guided Waves (UGWs)  
In this section, active sensing techniques were employed to investigate the response of ultrasonic guided waves (UGWs) in terms of in-plane motion. The focus was on studying the thickness effect on UGWs actuated and recorded by the embedded PZT transducers, with a comparison to previous results obtained from surface-mounted transducers. The aim was to analyze the amplitude and group velocity of the embedded UGWs and understand the influence of thickness on these parameters. This analysis is crucial for developing optimum excitation parameters for damage detection purposes in various plate thicknesses using embedded PZT transducers. The results obtained from active sensing were further utilized for damage detection and localization in structural health monitoring (SHM) applications. To generate the actuation signal, a National Instrument (NI) PXI-5412 arbitrary signal generator was used, while a NI PXI-5105 digitizer was employed to record the measured UGW signals. The actuation signals utilized were five-cycle Hanning-windowed toneburst signals [37] with an input amplitude of 6 V. The sampling frequency was set to 100 MHz, with actuation frequencies of 50 kHz and 250 kHz for different experiments. Path 1-2 of the embedded PZT transducer pair, as shown in Figure 1a, was chosen for all three panels. Figure 5a,b presents the extracted features of the peak amplitude and group velocity, respectively, for the first wave packet of embedded UGWs at 50 kHz and 250 kHz. The corresponding surface-mounted results are also included for comparison in Figure 5c,d. The peak amplitude was determined by selecting the peak of the envelope signals, while the group velocity was calculated by dividing the distance of the embedded PZT transducer pair path 1-2 by the time-of-arrival of the envelope signals. From Figure 5a, it can be observed that the peak amplitudes of both the A\({}_{0}\) and S\({}_{0}\) modes decrease with increasing thickness. In Figure 5b, it is evident that the group velocity of the A\({}_{0}\) mode decreases with increasing thickness at 50 kHz. On the other hand, the group velocity of the S\({}_{0}\) mode for the 9 mm thick panel is faster than that of the 2 mm thick panel but slower than that of the 4 mm thick panel at 250 kHz. Figure 4: Photo of the panel with embedded PZT transducers after trimming. In summary, the thickness of the plate has an impact on the amplitudes of both the A\({}_{0}\) and S\({}_{0}\) modes of embedded UGWs. Additionally, the group velocity of the A\({}_{0}\) mode is influenced by the thickness, whereas the group velocity of the S\({}_{0}\) mode does not exhibit a significant dependence on thickness. These findings provide valuable insights into the behavior of UGWs and the influence of thickness when utilizing embedded PZT transducers. They contribute to the understanding of how to optimize excitation parameters for damage detection and localization in composite structures with different thicknesses, thereby enhancing the effectiveness of SHM applications. Comparing the results obtained from embedded PZT transducers in Figure 5a,b with the surface-mounted PZT transducers in Figure 5c,d [21], some notable differences can be observed. In particular, the amplitude of the S\({}_{0}\) mode for the embedded signals exhibited a dependence on thickness at 250 kHz, whereas the amplitude of the surface-mounted signals did not show a similar trend. Additionally, the group velocity of the A\({}_{0}\) mode showed contrasting behaviors between the embedded and surface-mounted signals at 50 kHz. The group velocity decreased for the embedded signals as the thickness increased, while it increased for the surface-mounted signals. The reason behind these opposite relationships in the group velocity between the embedded and surface-mounted UGWs lies in the different bonding materials used. The embedded PZT transducers were bonded using resin films to comply with composite manufacturing specifications.