## 3 Experimental Methodology
The signals emitted by the transducers varying in frequency are called mirroring parameters or S11 and S22, in the case of the simple structural sandwich with only two UTs. If they have more UTs, more mirroring parameters are available; for each UT combination, there will be two mirroring parameters. The VNA has the function of sending a pulse for multiple PZTs, which receive the same excitation. However, in the propagation environment, the wave propagates at different speeds. This fact occurs due to variations in the resonance frequency that can be generated due to external factors, such as poor adhesion of the system, the appearance of bubbles, or some variation in the geometry or property of the material. For this reason, analyzing parameters S11 and S22 individually for power transmission systems and communication between UTs is insufficient because it is necessary to understand this mirroring parameter transducer-receiver, so the parameter of interest to be analyzed in this article is S21 because it relates to the sender (1) with the receiver (2). Figure 4: Schematic of the Test Model 1—the temperature variation test. (**a**) Photograph of the temperature variation test bench. (**b**) Test Model 1 diagram. (1) The test controller computer; (2) the climatic chamber in which the specimen is allocated; and (3) the vector network analyzer which sends and receives signals S21. Figure 3: The two models of specimens used in the 4 test models carried out were made in stainless-steel. (**a**) SP.1 dimensions: this specimen is used in the Test Models 1 and 2, in Conf.1 and Conf.2. (**b**) SP.2 dimensions: this specimen is used in the Test Models 3 and 4 and only in Conf.1. (**c**) Photograph of SP.1 with the ultrasonic transducer coupled; one can also observe the electrical wires already soldered and side holes where the sealing box will be attached for Conf.2. (**d**) Photograph of SP.2 with the ultrasonic transducer coupled; one can also observe the electrical wires already soldered. Another consideration about this S21 mirroring parameter is the valley of the curves, where the highest energy transmission occurs. This value also maximizes the transition impedance; temperature variation, mechanical deformation, and the horizontal non-alignment of the transducers influence its variations and alternations. The VNA receives and sends signals S11, S22, and S21, and the equipment is connected by electrical cables previously welded in the PZT. To carry out the communication and data acquisition, a computer with MATLAB(r) is used to pre-process the data together with the VNA. Experimental validation was carried out in four experiments. Test Model 1 is a temperature variation test only. The temperatures of this test model were applied in a cycle between temperatures from 40 \({}^{\circ}\)C to 140 \({}^{\circ}\)C with steps at intervals of 20 \({}^{\circ}\)C, at which the temperature was kept fixed for two hours. The temperature interval was chosen according to the polarization of the PZT; according to literature data, above 80 \({}^{\circ}\)C, the PZT begins to depolarize [54,55]. However, preliminary tests indicated that the amplitude of the S21 signal was optimized up to 100 \({}^{\circ}\)C. After this temperature, the parameter deteriorated in its response. For this reason, the tests were carried out with temperatures up to 140 \({}^{\circ}\)C. Figure 4a shows the experimental bench for this test, and the schematic for the experiment and its properties are shown in Figure 4b. Test Model 2 is a test immersed in the thermal bath with the fluid barrier, where the transducers have horizontal linearity variations of 100%--fully aligned--to 0% misaligned. The horizontal linearity test of the plates (Model 2 test) was set to maintain a fluid barrier distance of 100 mm between them. The bath temperature was fixed at 30 \({}^{\circ}\)C ambient temperature. Figure 5a shows the thermal bath used, and it is possible to observe the two SP.1 plates in parallel inside the thermal bath.