# Bar-Wave Calibration of Acoustic Emission Sensors
## 3 Results and Discussion  
### Displacement  
The normal displacements at L = 300 mm are shown in Figure 2a at the center and in Figure 2b at 5 mm off-center. The peak values were around 1 nm. Waveforms were similar to each other (and to that previously reported: see p. 260 of reference [8]), but the peak amplitude was about 2 dB lower at 5 mm off-center. No reflected signals were detected within the 300 us segment. These waveforms clearly show less low frequency oscillations that were visible previously [8]. The fast Fourier transform (FFT) magnitude spectra of the displacements are given in Figure 3a,b. Figure 3a is for the center position at L = 300 mm, given in dB scale in reference to 0 dB at 1 nm (with the frequency step of \(\Delta\)f = 1.90735 kHz). This spectrum peaked at 94.7 dB at 336 kHz and decreased sharply below 120 kHz. The spectral intensity above 1 MHz was also low. In the previous testing, the low frequency region below 120 kHz showed an increase of more than 30 dB (p. 261 in reference [8]). The new transmitter produced less effects of radial resonance that contributed to the low-frequency rise observed previously. Figure 3b shows five displacement spectra at 300 mm obtained at the center, 1, 2, 3 and 5 mm off-center). While the data scatter was \(\pm\)5 dB or more (less scattering below 500 kHz), the average spectrum, shown by the red curve, represented the general trend well. \begin{table}
\begin{tabular}{c c c c} \hline
**Transducer Model** & **Manufacturer** & **Frequency MHz** & **Element Size (mm)** \\ \hline FC500 & AET Corp & 2.25 & 19 \\ B1080-LD & Digital Wave & 0.2–1.5 & 3.2 \\ SH-225 & Dunegan Engineering & 0.225 & 6.3 \(\times\) 12.6 \({}^{*}\) \\ KRNBB-PCP or -PC & KRN Services & 0.1–1 & 1 \\ V101 & Olympus & 0.5 & 25.4 \\ V103 & Olympus & 1 & 12.7 \\ R6-alpha & Physical Acoustics & 0.06 & 12.7 \\ R15 & Physical Acoustics & 0.15 & 12.7 \\ R15-alpha & Physical Acoustics & 0.15 & 12.7 \\ F30-alpha & Physical Acoustics & 0.2–0.7 & 12.7 \({}^{**}\) \\ Pico & Physical Acoustics & 0.5 & 3.2 \\ S9220 & Physical Acoustics & 0.9 & 8 \\ HD-50 & Physical Acoustics & 0.5 & 3 \\ WD & Physical Acoustics & 0.3–0.5 & 12.7 \({}^{**}\) \\ u30D & Physical Acoustics & 0.3 & 8 \\ Pinducer VP-1093 & Valpey-Fisher & 0.1–2 & 1.35 \\ \hline \end{tabular} \({}^{*}\) Rectangular shear element; \({}^{**}\) Multiple elements.  
\end{table} 
Table 1: Transducers used. Figure 1: Bar-wave test set-up. An Al6061 bar of 25.4 mm \(\times\) 6.4 mm \(\times\) 3660 mm was shaped as shown with an initial straight segment of 700 mm length. FC500 transmitter was glued to its end. The Choi-Williams transform (CWT) was applied to the displacement waveform (Figure 2a) using AGU-Vallen Wavelet Transform software (Vallen Systeme, Icking, Germany). Figure 4 shows an expanded waveform (of the 40-200 \(\upmu\)s segment or 7.5-1.5 mm/\(\upmu\)s in terms of wave velocity) and time-frequency spectrogram below 1 MHz. The highest peak intensity was found at 160 \(\upmu\)s and 350-400 kHz and marked cw1. At L = 300 mm, this peak corresponds to 1.9 mm/\(\upmu\)s propagation velocity. A faint trace is visible from the initial weak peak at 70 \(\upmu\)s (corresponding to 4.3 mm/\(\upmu\)s, marked cw2) and 150-200 kHz to the main peak (cw1), passing through peaks marked cw3, cw4 and cw5. A few other traces may exist, but these traces are quite faint, except a vertical line at 130 \(\upmu\)s (2.4 mm/\(\upmu\)s), stretching from 400 to 800 kHz (marked cw6). The spectral intensity below 100 kHz was weak in this plot. The dispersion curves for bar waves using the parameters for the present experiment are shown in Figure 5. This calculation utilized the theory and semi-analytical finite-element (SAFE) algorithm developed by [PERSON] et al. [9]. The present SAFE calculation utilized 16 \(\times\) 4 elements as shown in the insert of Figure 5a that indicated the directions where z refers to the bar length, y the bar thickness and x the bar width, respectively. Frequency step was 5 kHz and calculations were for 5-1000 kHz.