## 4 Discussion of Numerical Results
### High-Mass Floor Sensitivity to Loading Strategy  
A second comparative analysis of parametric numerical results was focused on floor systems F#1 to F#3, in which the structural mass \(M_{s}\) is high compared to the occupant. Still, major variations can be noted in terms of vibration frequency (Table 1).  
Results are collected in Figures 8 and 9 in terms of RMS value, acceleration peak or CREST factor trends for the examined walking frequencies. In addition, the numerical outcomes from the selected SMD models are also compared to the RU modelling approach.  
Figure 7: Numerical results for F#1 to F#4 floor systems, based on equivalent-force calculations (RU model), in terms of RMS acceleration, as a function of walking frequency \(f_{p}\) (ABAQUS).  
Figure 8 shows that the performance indicators of floors F#1 to F#3 show a typically large scatter between the selected SMD models or the RU assumption. This suggests, in terms of vibration serviceability assessment and verification purposes (once experimental methods and records are not available in support of numerical tools), that the RU modelling strategy is generally more conservative than the examined SMD models. Under the lack of more specific comparative data or calculation methods, in this sense, the RU assumption should be preferred for a verification check. Still, it would necessitate, on the other side, an over-design of examined floor systems to satisfy conventional vibration limits.  
In terms of different SMD formulations, for most of the proposed numerical pieces of evidence, it can be noted in Figure 8 that the SMD-4 approach has the minimum scatter towards RU, tending to overestimate the acceleration estimates of SMD-1-to-3 formulations and to underestimate the corresponding CREST. This effect can be noted for all F#1, F#2 and F#3 systems, regardless of the dynamic features of structural systems in terms of vibration frequency, and assuming a relatively \"high\" structural mass for them. Similarly, the SMD-2 model tends to underestimate the numerical predictions of the other formulations in terms of RMS acceleration and peak for all the examined configurations.  
In terms of quantitative analysis of results, the major scatter was indeed noted in terms of RMS and peak accelerations, especially for F#1 and F#3 systems, which are characterized by low-medium vibration frequency \(f_{1}\) and high, similar mass \(M_{s}\), compared to the occupant. The corresponding percentage scatter of SMD averages to RU calculations is proposed in Figure 9 as a function of the imposed walking frequency. Note that for F#1 and F#3, the maximum scatter is estimated in the range of 30%. For the F#2 system only, the calculated percentage scatter is less pronounced in terms of absolute value, especially for faster walks (\(f_{p}>1.8\) Hz). Still, on the other side, it is more sensitive to the walking  
Figure 8: Numerical results for F#1, F#2 (concrete) and F#3 (glass) systems, based on different SMD or RU calculations, in terms of (**a**–**c**) RMS acceleration or (**d**–**f**) CREST factor, as a function of walking frequency \(f_{p}\) (ABAQUS).  
frequency \(f_{p}\), due to additional interaction with motion harmonics, with up to +40% of the variation for \(f_{p}\) < 1.8 Hz.  
Figure 9: Numerical results for (**a,c,e**) RMS acceleration and (**b,d,f**) peak acceleration for F#1, F#2 and F#3 systems, in terms of SMD (average \(\pm\) standard deviation) to RU percentage scatter, as a function of walking frequency \(f_{p}\) (ABAQUS).