## 2 Research Methods, Materials and Models
### Selected SMD Models of Literature  
Over the years, several experimental and theoretical studies have been elaborated to efficiently calibrate the input SMD features of a pedestrian on typically slender and flexible structures (Figure 3). The attention of the present investigation, among others, was focused on the effects of SMD proposals described in [5; 6; 7; 8]. \begin{table}
\begin{tabular}{c c c c c c c} \hline \hline
**Floor** & **Material** & **Span** & **Surface** & **Frequency \(f_{1}\)** & **Mass \(M_{\rm s}\)** & **M/\(M_{\rm s}\)** \\  & & **[m]** & **[m\({}^{2}\)]** & **[Hz]** & **[kg]** & **M/\(M_{\rm s}\)** \\ \hline F\#1 & Concrete & 5 & 30 & 11.05 & 10,350 & 1/130 \\ F\#2 & Concrete & 5 & 30 & 5.30 & 3530 & 1/44 \\ F\#3 & Glass & 14.5 & 40.6 & 7.28 \({}^{*}\) & 10,730 & 1/134 \\ F\#4 & Glass & 2.65 & 3.58 & 14.30 \({}^{*}\) & 320 & 1/4 \\ \hline \hline \end{tabular} \({}^{*}\) = experimental data from [16; 18].  
\end{table} 
Table 1: Summary of basic features for the examined floor configurations (with \(M\) = 80 kg). [PERSON] et al. [5], \"SMD-1\" in the following, validated their formulation towards experiments carried out on a low-frequency footbridge prototype (\(f_{1}<5\) Hz). The authors elaborated a regression model for biodynamic SDOF parameters. The equivalent mass \(m\), the damping coefficient \(c\) and the spring stiffness \(k\) can be calculated as a function of walking frequency \(f_{p}\) and pedestrian mass \(M\). The term \(c\) is fitted to \(m\), and the stiffness term \(k\) derives from \(c\), where:  
\[m=m\big{(}f_{p},M\big{)}=97.082+0.275M-37.52f_{p} \tag{1}\]  
\[c=c(m)=107.455+16.208m \tag{2}\]  
\[k=k(c)=5758.441+11.103c \tag{3}\]  
A similar working assumption for SMD elaboration and validation can be found in the proposal by [PERSON] et al. [6] (\"SMD-2\" model, in the following). More precisely, their experimental evidence was processed from 35 instrumented individual pedestrians and further elaborated by Artificial Neural Network (ANN) to correlate the biodynamic parameters to basic walking features. A rigid platform (\(f_{1}=30.1\) Hz) was initially used in the experiments, and then the SMD characterization was extended to a flexible footbridge prototype as in [5], with \(f_{1}<5\) Hz. It was found, for example, that the ANN was able to act  
Figure 3: Biodynamic pedestrian models: (**a**) schematic mechanical model of a pedestrian on rigid or flexible structure (figure reproduced from [6] with permission from Elsevier®, copyright license number agreement 5458710774818, December 2022); (**b**) experimental setup for pedestrian walking on flexible laboratory platform (figure reproduced from [7] with permission from Elsevier®, copyright license number agreement 5458711054568, December 2022); (**c**) experimental analysis by [PERSON] et al. to measure the ground reaction force (figure reproduced from [8] with permission from Elsevier®, copyright license number agreement 5458710094483, December 2022). efficiently with minimum uncertainty, and the final SMD proposal resulted in the following pedestrian parameters:  
\[m=m\big{(}f_{p},M\big{)}=-231.34+3.69M+154.06f_{p}-1.97 Mf_{p}+0.005M^{2}-15.25f_{p} ^{2} \tag{4}\]  
\[c=c(M,m)=-1115.69+92.56M-108.94m+2.91 Mm-1.33M^{2}-1.30m^{2} \tag{5}\]  
\[k=k\big{(}M,f_{p}\big{)}=75601.45-1295.32M-33786.75f_{p}+506.44 Mf_{p}+3.59M^{2} +539.39f_{p}^{2} \tag{6}\]  
The third SMD calibration approach, consisting of the method proposed by [PERSON] et al. [7] and noted as the \"SMD-3\" model in the present study, included several experimental measurements of pedestrians moving on a rigid floor (coinciding with the laboratory foundation slab) and then on a flexible walkway like in Figure 3b, composed of steel-concrete composite deck and characterized on top by two medium-density fiberboard plates, with \(f_{1}=17\) Hz [22]. The monitored experimental configurations included slow, normal, or fast walks.