# Calculation of Guided Wave Dispersion Characteristics Using a Three-Transducer Measurement System
## 6 Experimental Demonstration  
### Test Setup  
The specimen is a 4 m by 2 m aluminium plate of 3 mm thickness. Two piezoelectric transducers were used, one transmitter and one receiver. The transmitter was fixed at the centre of the plate using a tool that provides force over the transducer; and the receiver was manually attached at various distances from the transmitter. For the evaluation of the S\({}_{0}\) mode, the receiver was placed at 45, 50 and 55 cm from the transmitter. For the case of the A\({}_{0}\) and SH\({}_{0}\) modes, the receiver was set at 25, 30 and 35 cm from the transmitter. Those distances were selected to minimize the wavepacket distortion due to overlaps.  
A pulser-receiver (Teletest(r) unit) was used to excite the transducer and acquire the signals. Two independent channels were used for the excitation and acquisition. A PC with the Teletest(r) software was used to control the pulser-receiver and configure the experimental parameters. Input signals of five-cycle Hanning-windowed bursts with centre frequencies from 40 kHz to 140 kHz in steps of 5 kHz were used to excite the transmitter. This frequency range was chosen since it is the operating frequency range of the transducers used in the experiment. Signals were recorded with a 1 MHz sampling frequency; 32 averages were taken, and the record length of the signals was 1 ms. The experimental setup is presented in Figure 12.  
Two types of piezoelectric transducers (PI Ceramic GmbH) were used in the experiment, a shear piezoelectric element (d\({}_{15}\) type) and a compressional piezoelectric element (d\({}_{33}\) type), both with an active contact area of 13 mm by 3 mm. Figure 13 shows the direction of poling and corresponding shear deformation for the shear transducer. The shear transducer was used to evaluate the S\({}_{0}\) and SH\({}_{0}\) wave modes, and the A\({}_{0}\) wave mode was analyzed using the compressional transducer, which mainly produces an out-of-plane vibration. Using the shear transducer, S\({}_{0}\) waves are generated in the direction of the poling axis, and SH\({}_{0}\) in the perpendicular axis. A small amount of A\({}_{0}\) is also generated on the poling axis. In the case of the compressional transducer, S\({}_{0}\) and A\({}_{0}\) are created omnidirectionally. The averaged amplitudes of the S\({}_{0}\) and SH\({}_{0}\) modes using the shear transducer at the propagation distances specified above are 13 mV and 33 mV, respectively; and the amplitude of the A\({}_{0}\) mode is 63 mV using the compressional transducer.  
Figure 12: Experiment setup: **Left–**diagram of the experiment, **Right–**photo of the real experiment environment.  
Experimental signals were acquired at a sampling frequency of 1 MHz providing a poor time resolution for the wave velocities of interest. Therefore, the sampling rate of the signals was increased by a factor of 10 using cubic spline interpolation to give a time accuracy of 0.1 \(\upmu\)m (10 MHz). The interpolation is a necessary step when the propagation distance is a few cm, as the propagation time of the faster modes, such as S\({}_{0}\), is of the same order of magnitude as the original sampling period. By reducing the sampling period by means of interpolation, the accuracy of the group velocity is increased. However, a small error is introduced in the signal due to the interpolation. Overall, the improvements gained for the velocity calculation are more significant than the errors introduced in the signals. The signal-to-noise ratios of the S\({}_{0}\), A\({}_{0}\) and SH\({}_{0}\) signals were around 30 dB, 37 dB and 35 dB, respectively.