## 4 Results and Discussion  
### Proposed Approach vs. ISO 9052-1  
First, electrical input impedance was measured for the mass-loaded actuator when mounted on a rigid floor, \(Z_{ET,0}\) (i.e., w/o resilient material), and when coupled to the slab-material system, \(Z_{ET}\), for different materials. A single measurement was sufficient, provided the location of the actuator was centered as much as possible to minimize the excitation of higher-order modes of vibration in the resulting coupled system. The measured spectrums are plotted in Figure 3 for three of the five specimens under test, M#1, M#3, and M#5, being straightforward to identify the resonance peak frequencies \(f_{1}\) and \(f_{2}\) (blue dots) of the two-degree-of-freedom system resulting from the proposed approach. Secondly, experiments according to the standardized procedure were performed, the measurements being taken three times for each sample to minimize deviations linked to the hammer impact point and the average results being used in the subsequent dynamic stiffness calculations. In Figure 4, the mechanical mobility function was normalized with respect to its maximum value for each tested material is depicted. These curves were obtained both following the standard ISO 9052-1 and predicted using the electrical input impedance data of Figure 3 in the electro-mechanical circuit model (Equation (10)). The results clearly indicate that there is good agreement between the standard measurements and the predictions to identify the resonance frequency\(f_{0}\) (blue dots) necessary to calculate the dynamic stiffness from Equation (1) using the material data in Table 1. Table 3 summarizes the dynamic stiffness results obtained from both procedures and the relative error of the proposed approach with respect to the standard for the analyzed samples.  
Figure 4: Normalized mechanical mobility function frequency response for three of the tested materials: (**a**) M#1; (**b**) M#3; and (**c**) M#5. Continuous lines: experimental data obtained following the standard ISO 9052-1; discontinuous lines: predicted data obtained using the electro-mechanical circuit model (Equation (10)). Blue dots indicate the resonance frequency \(f_{0}\) necessary to calculate the dynamic stiffness of each sample material.  
Figure 3: Measured electrical input impedance: (**a**) mass-loaded actuator when mounted on a rigid floor (\(Z_{ET,0}\)); (**b**) M#1; (**c**) M#3; and (**d**) M#5 (\(Z_{ET}\)). The blue dots indicate the resonance peak frequencies \(f_{1}\) and \(f_{2}\) of the two-degree-of-freedom system resulting from the proposed approach.  
Nevertheless, some points are worth mentioning regarding the proposed approach. On the one hand, the mechanical mobility function derived using the proposed approach shows a secondary spurious peak close to \(f_{0}\) for materials M#1 and M#5 which may mislead the identification of the resonance frequency. This spurious peak (around 25 Hz) corresponds to the resonance of ZET,0 (see Figure 3a) and must therefore be disregarded, not only because of its lower amplitude and narrow bandwidth but also because it has the same value in all measurements. On the other hand, the predicted mechanical mobility function frequency response exhibits differences when compared to that obtained with the standard. In this regard, it should be noted that the proposed approach is focused on successfully identifying the resonance frequency \(f_{0}\) necessary to determine the dynamic stiffness, the extra loss mechanisms linked to the suspension of the actuator and responsible for these differences not being considered.