# A Feasibility Study for a Nonlinear Guided Wave Mixing Technique
## 3 Experimental Setup  
### Experimental Setup for Guided Wave Mixing Generation  
A guided wave mixing signal was generated using an aluminum specimen (Al 1050). The specimen thickness is 1 mm. The main purpose of this experiment is to generate an out-of-plane dominant mixing signal from one in-plane dominant signal and one out-of-plane dominant signal. Table 1 shows the primary wave frequencies and modes that are decided based on Equation (18). The primary waves consist of an in-plane-dominant wave (7.83 MHz, S2) and out-of-plane dominant wave (2.06 MHz, S0). In Tables 1 and 2, in order to express the relative magnitude between in-plane and out-of-plane displacement, alphabet letters \(a,b,c,d\) are used. Without this object, \(a,b,c,d\) do not have any other means. \[ \begin{array}{l}u(\omega_{1})+v(0.263\omega_{1})=v(0.737\omega_{1})\\ u(7.83\ \mathrm{MHz})+v(2.06\ \mathrm{MHz})\to v(5.77\ \mathrm{MHz})\end{array}  \tag{18}\]  
Figure 4: Dispersion curve (Al 1050). (**a**) Phase velocity with double symmetric mode; (**b**) Group velocity with double symmetric mode. In the dispersion curve, several modes exist at 5.77 MHz that are mixing waves. However, there are only two out-of-plane dominant modes: S1 and A1 (Table 2). Both mixing signals have the possibility of becoming wave mixing signals. Figure 5a,b show the dispersion curves with the primary waves (Red diamond) and mixing waves (Black square). Figure 6 shows the basic sensor arrangement. To mix the two primary waves, each sensor distance is set differently. The quantity \(b\) indicates the propagation distance of the mixing signal from the mixing point. The experimental setup is configured as shown in Figure 7. The pulser and receiver use RITEC co.'s RAM-5000 and generate a sine wave. Pulser #1 and #2 are used with amplifiers installed, and the received signal can be verified with an oscilloscope. RAM-5000 has two pulsers and two receivers and is actively used in ultrasonic mixing experiments. Each sensor was tested using an Olympus's sensor. \begin{table}
\begin{tabular}{c c c} \hline \hline
**Frequency** & 7.83 MHz & 2.06 MHz \\
**Mode** & S2 & S0 \\ \(|u_{3}/u_{1}|\), Dispersion ratio** & 0.4446 & 9.1419 \\ \(c_{p}\)[mm/\(\mu\)s], Phase velocity & 5.8072 & 4.3877 \\ \(c_{g}\)[mm/\(\mu\)s], Group Velocity & 3.3344 & 2.3600 \\ \(u_{1}\), In-plane displacement & 45.7428 \(a\) & 5.0964 \(b\) \\ \(u_{3}\), Out-plane displacement & 20.3373 \(a\) & 46.5905 \(b\) \\ \hline \hline \end{tabular}
\end{table} 
Table 1: Primary wave information. Figure 5: Dispersion curve showing primary and mixing waves: (**a**) Phase velocity; (**b**) Group velocity. The mixing signal propagation direction was calculated for the two possible modes. Figure 8 shows four experimental setups with different modes and propagation directions. The distances of the sender and receiver sensors are defined as \(a=100\) mm and \(\mid b\mid\,=20\) mm. \[ \begin{array}{l}1:u(6.83\;\mathrm{MHz})+v(2.06\;\mathrm{MHz})\to v(4.77\; \mathrm{MHz})\\ 2:u(7.83\;\mathrm{MHz})+v(2.06\;\mathrm{MHz})\to v(5.77\;\mathrm{MHz})\\ 3:u(8.83\;\mathrm{MHz})+v(2.06\;\mathrm{MHz})\to v(6.77\;\mathrm{MHz})\\ \end{array}  \tag{19}\]  
Figure 6: Basic experimental sensor arrangement. Figure 7: Experimental setup for material evaluation by guided wave mixing. Equation (19) represents the frequency combination for the experiment. The second part of Equation (19) has exactly the same equation as Equation (18), and maximizes the mixing signal amplitude. The first and third frequency combinations have different calculated frequency ratios. These two ratios were implemented to find whether a mixing signal is detected at only the calculated frequency ratio. The second frequency setup is applied to the four experimental setups with different modes and directions. The first and third frequency combinations of Equation (19) are only experimented with when the mixing signal appears in the second frequency combination of Equation (19).