## 2 Experimental Configuration
### Technical Limitations  
After obtaining the velocity signal \(v(t)\) for each applied tensile force, it is possible to realize the dependence of nonlinear modal parameters, i.e., natural frequency \(f_{n}\) and damping \(\eta\) from the vibration amplitude. To this purpose, the free decay of the envelope velocity signal \(v(t)\) from the excitation starting points until the detachment of the shaker tip should be analyzed. However, the signal is still the superposition of all modes of the beam vibration, as shown Figure 6. A filter has therefore been implemented to extract the main modal component without altering the phase of the signal, necessary for subsequent identification of the modal parameters. A Parks-McClellan Finite Impulse Response (FIR) filter with a ripple of 1\(\cdot\)10-40 dB in the passband and a ripple of \(-\)40 dB in the remaining frequency band was adopted (see Figure 7). Figure 4: Laser pointer (1B) and velocity measurement (2B) spots. Figure 5: Strain gauge configuration for strain measurement system. Figure 6: Example of a signal restricted to free decay range. To identify the nonlinear dependence of the natural frequency \(f_{n}\) and the damping \(\eta\) on the amplitude of vibration, the theory of analytical signals and Hilbert transform were utilized following the \"FREEVIB\" method proposed by [PERSON] in [23] for nonlinear systems. It can be only applied to systems that have frequency-independent damping [15; 20]. To obtain a stable solution, particular methods such as that proposed in Ref. [20] should be taken into account due to Kelvin type structural damping in the model. The measurement points, (P1) for the first and (P2) for the second flexural mode is displayed in Figure 8. Concerning the first mode, the dependence of damping on the vibration amplitude for different value of axial loads is shown in Figure 9. For small vibration amplitudes, it observes a constant damping, i.e., independent of amplitude. This suggests the complete adhesion at the contact region, implying the linearity of the system in question. For amplitudes greater than a critical value, the damping shows a steep increase, indicating the beginning of possible sliding in the contact region, and thereby the establishment of the hysteresis loop due to the alternation between adhesion and sliding states during each oscillation cycle. Furthermore, the dissipation peaks at a critical value of vibration amplitude, as can be seen in Figure 9, and eventually decreases as amplitude exceeds that critical value. Moreover, the peak (maximum damping) drops as the traction force \(F\) increases. This is because not all four contact regions are in the state of macro-creep, and some regions are in the state of microslip, i.e., sliding only at edges of the contact regions. Indeed, various combinations of the macroslip and microslip states at the four contact zones could influence the results in different manners. This hypothesis is compatible with the previous supposition on the variation in force normal to the contact region. Figure 8: Measurement points, (P1) for first and (P2) second flexural mode. Figure 7: Adopted Parks-McClellan FIR passband filter. The variation of the frequency against the vibration amplitude is depicted in Figure 10. Based on the figure, rather flat curves for small oscillations suggest linearity of the system, the indication of complete adhesion. As the amplitude grows, the frequency decreases sharply, signaling the occurrence of possible sliding in the contact region. Eventually, the stiffening phenomenon (increase in frequency) is observed for further larger values of vibration amplitude, which can be attributed to the variation of normal force at the contact region caused by the bending of the blade simulacrum. Figure 10: Frequency as a function of vibration amplitude for first flexural mode. Figure 4:0 Damping as a function of vibration amplitude for first flexural mode.