## 3 Experimental Analyses
The laser vibrometer is the ideal sensor to capture the propagation of mechanical waves because, in addition to high spatial and temporal resolution, it does not interact with the wave and does not interfere with its propagation [40]. Through this experimental setup, the propagation in the specimen was analyzed. The upper face of the specimen at one end is the ideal place to apply the surface force using the PZT transducer with transverse polarization, that is, polarization in Axis 3 as it is depicted in Figure 9c. Hence, it is possible to generate the modes of torsion and bending around Axis 2. Using the same logic, with the PZT transducer with longitudinal polarization, that is, polarization in Axis 1 generates an axial displacement (longitudinal) and a bending around the Axis 3. Consequently, the four fundamental modes of propagation in a rectangular waveguide are achieved: longitudinal, torsional, and both bending modes, as presented in Figure 7.  
Figure 8: Frequency response of the piezoelectric transducers used during the tests. Considering the degrees of freedom of the platform where the vibrometers are fixed (Figure 9d), it is possible to measure the displacement at the centerline of the waveguide surface which is called, up to this point, \"scan line\", black line indicated in Figure 9a,e at 1.2 m from the PZT. At every interval of time, the displacement in 150 points (the point separation being of 1.0 mm) over the scan line are acquired during such intervals of time using an adequate frequency of acquisition. The data stored  
Figure 9: Details of the experimental setup: (**a**) laser vibrometer position to obtain displacements \(\mathbf{u}_{1}\) and \(\mathbf{u}_{2}\). Using piezoelectric ceramics (PZT) with longitudinal polarization to induce longitudinal and flexural around Axis 3 wave modes. (**b**) Laser vibrometer position to obtain displacements \(\mathbf{u}_{2}\) and \(\mathbf{u}_{3}\). Using PZT with transversal polarization to induce the flexural around Axis 2 and torsional wave modes. The black line indicates the scanning region, and the green arrow shows the polarization of the PZT transducer. (**c**) Detail of the PZT transducer glued to the beam tip. (**d**) The platform where the vibrometers are fixed (the red arrows indicate the degrees of freedom of the platform). (**e**) Diagram of the experimental setup where the main dimensions were indicated. was organized in an array, where one of the dimensions represents space [m], and the other time [s]. With the data arranged in a matrix form, it is possible to apply a double Fourier transform to represent the results in the dispersion curve domain (frequency [1/s] \(\times\) wave number [1/m]). The acquisition frequency and the distance between the points considered in the scan line must be adequate to avoid the aliasing effect in the data acquisition. The Nyquist theorem [41] indicates a frequency of acquisition as at least twice the frequency of the signal, in this case, the excitation frequency, and considering the space domain. The sample size must contain a complete period plus a half period before and after it. The distance between points in the scan line must also follow this premise, that is, the scan line needs to contain enough points to precisely describe two periods of the shortest wavelength expected in the space domain.