## 4 Results and Discussion
### Remarks on the Applicability of the Proposed Approach  
The above preliminary results showed the proposed approach to be a valid methodology for obtaining the dynamic stiffness of resilient materials using cost-effective laboratory equipment. The use of a stationary source exhibited more stable results than the transient impulser, which required three measurements for each sample to reduce uncertainties linked to point force excitation (as recommended in the standard [3]). Moreover, the proposed arrangement is easier to implement than those using a supported shaker and an impedance head with acceleration and force sensors [5]. Also, the above approach may serve to provide additional data such as the mechanical mobility function of the mechanical system to which the actuator is coupled, thus serving as an alternative to ISO 7626-2 [20]. In this regard, as mentioned above, further research is necessary to account for the loss mechanisms linked to the actuator for a proper determination thereof. Even though other approaches can be also found in the literature, such as the equations derived by [PERSON] et al. [21], a modified dynamic stiffness calculation method for rubber isolators [22], or empirical formulas for lightweight laminate floors [23], the proposed approach was shown to be a simple and straightforward procedure for the determination of the dynamic stiffness of resilient materials.  
Notwithstanding these advantages, it should be noted that the proposed approach does not use an 8 kg load plate made of steel (as specified in the standard) because it would influence the electromagnetic field of the mechanical actuator [19]. Alternatively, heavier electrodynamic actuators or other transduction types such as piezoelectric ones could be used following a very similar measurement procedure [15]. Nevertheless, given that the standard is mainly intended to be used for comparing production samples of similar materials for loadings between 0.4 kPa and 4 kPa and that our study uses samples 0.2 \(\times\) 0.2 m\({}^{2}\) and a total loading mass of 3.45 kg, the resulting prostatic load (above 0.845 kPa) still lies in a valid range of analysis. In fact, the standard states that the differences between dynamic stiffness values measured with a static load of 2 kPa in accordance with this part of ISO 9052 and those measured with a very low preload are of the order of 10% to 20%.  
Regarding the applications of the proposed approach, some examples can be the evaluation of the long-term sound reduction performance of resilient materials used in floating floor systems by monitoring their dynamic stiffness [24] or the experimental  
\begin{table}
\begin{tabular}{c c c c} \hline \hline
**Sample** & \(\boldsymbol{S_{\text{ISO 9052-1}}}\) & \(\boldsymbol{S_{\text{approach}}}\) & **Relative Error** \\
**ID** & **(MN/m\({}^{\text{3}}\))** & **(MN/m\({}^{\text{3}}\))** & **(\%)** \\ \hline M\#1 & 3.33 & 3.43 & 3.00 \\ M\#2 & 3.20 & 3.25 & 1.56 \\ M\#3 & 14.10 & 14.70 & 4.26 \\ M\#4 & 29.93 & 29.28 & 2.17 \\ M\#5 & 1.63 & 1.60 & 1.84 \\ \hline \hline \end{tabular}
\end{table}
Table 3: Dynamic stiffness results obtained from both methods and relative error of the proposed approach with respect to the standard for the resilient materials under study.  
analysis of the dynamic stiffness in industrial robots [25]. Even though further research would be necessary to make the proposed approach extensible to these applications, the preliminary results are encouraging and set a good starting point for its future development.