# Advanced Hysteretic Model of a Prototype Seismic Isolation System Made of Polymeric Bearings
## 5 Numerical Analysis
### Two-Storey Structure Model
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Numerically obtained acceleration-time history plots for the two-storey structure model, both fixed-base and base-isolated considered as 2-DOF and 3-DOF systems, respectively, are compared with the experimental data (see [28]) in Figures 7 and 8. Computed peak lateral accelerations recorded at the top of the analyzed two-storey structure model, with and without the PBs, are briefly reported in Table 4. Additionally, reduction levels in lateral accelerations are also presented and compared with the results of the previously performed shaking table investigation [28]. Figure 8: _Cont._  
Figure 7: Experimentally determined (**left**) and numerically obtained (**right**) time-acceleration history plots for the fixed-base two-storey model during different ground motions: the 1940 El Centro earthquake (**a**,**b**), the 1971 San Fernando earthquake (**c**,**d**), the 1989 Loma Prieta earthquake (**e**,**f**), the 1994 Northridge earthquake (**g**,**h**), and the 2002 Polkowice mining tremor (**i**,**j**). As indicated by Figures 5-8 and Tables 3 and 4, the results of the numerical analysis explicitly confirm high effectiveness of the developed mathematical model in simulating complex hysteretic behaviour of the prototype base isolation system made of PBs. Close inspection of Tables 3 and 4 demonstrates that the reduction levels in peak lateral accelerations, which were calculated based on both numerical results and previously obtained experimental data (see [28]), are very similar for every ground motion analyzed. In the case of the base-isolated single-storey model, the largest difference between numerical and experimental peak lateral acceleration has been obtained for the 1971 San Fernando earthquake (difference of 7.74%), while the lowest one for the 2002 Polkowice mining tremor (difference of 0.46%). On the other hand, in the case of the base-isolated two-storey model, the largest difference between numerical and experimental peak lateral acceleration has been obtained for the 1971 San Fernando earthquake (difference of 3.86%), while the lowest one for the 1994 Northridge earthquake (difference of 0.78%). Figure 8: Experimentally determined (**left**) and numerically obtained (**right**) time-acceleration history plots for the base-isolated two-storey model during different ground motions: the 1940 El Centro earthquake (**a**,**b**), the 1971 San Fernando earthquake (**c**,**d**), the 1989 Loma Prieta earthquake (**e**,**f**), the 1994 Northridge earthquake (**g**,**h**), and the 2002 Polkowice mining tremor (**i**,**j**). In addition to the peak lateral acceleration values, the whole time-acceleration records (Figures 5-8) were also compared and the difference between numerical and experimental results was assessed using the normalized mean square error. The error calculated for the base-isolated single-storey model for the 1940 El Centro, 1971 San Fernando, 1989 Loma Prieta, 1994 Northridge, and 2002 Polkowice ground motions is as low as 4.56%, 5.21%, 5.59%, 2.41% and 6.21%, respectively. On the other hand, the normalized mean square error calculated for the base-isolated two-storey model for the same suite of dynamic excitations is 7.26%, 5.88%, 7.89%, 6.71%, and 7.53%, respectively. The above results concerning the whole time-acceleration records indicate that the accuracy of the developed mathematical model somewhat drops for the two-storey structure model, which is believed to be triggered by more complex modelling related to the increased number of degrees of freedom. It should also be underlined that the set of function parameters a\({}_{1}\)-a\({}_{5}\) (incorporated in the numerical model) was evaluated to provide the best fit for the frequency range of 1 Hz to 5 Hz, which was taken as the most representative range for all ground motions considered in the present study. That approach has produced satisfactory results as the normalized mean square error has not exceeded 10% for all the earthquakes and the mining tremor analyzed in the research.