## 4 Experimental Results and Comparative Analysis
Considering a mechanical structure with a PZT patch attached by it and \(\Omega_{n}\) as the modal vibration frequency, the maximum vibration damping with an RL shunt method can be obtained for optimal value of the resistor and equal resonant frequency of the electrical circuit, i.e., \(\Omega_{n}=\omega_{e}\). The resonant frequency mistuning effect in the RL shunt vibration damping has been intensive investigated in References [2; 6] and adaptive tuning techniques have been proposed. The VCSI with a linear response for the RL shunt resonant frequency can be considered a big step forward as technological support toward implementing new simplified adaptive methods. By increasing the robustness of the RL shunt against mistuning, future integration of the method in more practical applications is ensured and these investigations are to be a constant research activity in smart materials and the intelligent systems community. To demonstrate the capabilities of the new proposed VCSIs in vibration damping applications based on an RL shunt, Figure 7 shows the simulation results of the mistuning effect due to the resonant frequency nonlinearity of the electrical circuit. In Figure 7a, the simulation results for VCSI based on an analog multiplier is presented in accordance with two reference situations: an open circuit and perfect tuning where \(\Omega_{n}/\omega_{e}=1\). Figure 7: Simulations of the mistuning effect of the voltage controlled synthetic inductors (VCSI) nonlinearity in RL shunt vibration damping: (**a**) VCSI with an AD633 multiplier as a VCR and (**b**) VCSI with an LM13700 OTA as a VCR. Three extreme points of residual analysis, as is shown in Figure 6b, were chosen for vibration damping simulation in this case: \(-\)10 V, \(-\)4 V, and 2 V. The mistuning effect of nonlinear behavior is very low with less than 1.84 dB depreciation of the vibration damping performance of the RL shunt. The simulation results for the VCSI based on an OTA are shown in Figure 7b in accordance with two reference situations: open circuit and perfect tuning where \(\Omega_{n}/\omega_{e}=1\). Based on the residual analysis, as is shown in Figure 6b, three extreme points were chosen for vibration damping simulation in this case: \(-\)2 V, 4 V, and 10 V. Nonlinear behavior regarding voltage control induced a mistuning effect that involved a depreciation of vibration damping performance for the RL shunt of less than 1.15 dB in this case. For both VCSI circuits, the nonlinearity regarding the voltage control induced a mistuning effect in an insignificant range and the circuits can be used with a very good performance for practical applications. In a very large bandwidth for the voltage control from \(-\)10 V to 10 V, the linearity of the VCSI version with an OTA used as a VCR was better in comparison with the VCSI based on an analog multiplier, as shown in Figure 6a. The VCSI based on an analog multiplier was more practical from an experimental point of view and considering only limited voltage control range, it had a better linearity, as shown in Figure 6b. New adaptive and simplified techniques based on open or closed loop strategies can be imagined in the future to improve RL shunt robustness in the presence of uncertainty under cumulated effects induced by environmental temperature, materials aging, or modifications in the geometry of the mechanical structures. The well-known difficulties in tuning the multi-modal RL shunt [6] for more than two modal vibration frequencies of mechanical structures can be avoided using VCSIs with a linear response of the RL shunt resonant frequency regarding voltage control.