## 2 Materials and Methods
### Parameters of the Linear and Non-Linear Model  
The simulation calculations were carried out for the 'quarter-car' model data corresponding to rear suspension systems of medium-class passenger cars Opel Astra Van (segment C of the market) and Opel Agila (segment VAN micro of the market). The data for the linear and non-linear models of both vehicles have been summarised in Tables 1-4. The data also include specifications of the diagnostic tester used in the experiments; the data will be described hereafter. The values of parameters of the non-linear model correspond to the results of laboratory measurements carried out on real objects. There is adequate conformity between geometric and mass parameters, as well as spring and damping characteristics of the suspension system (inclusive of the sliding friction forces) and of the tyre. The suspension damping coefficient c1 in the linear model stems from the assumption made that the value of energy dissipated during a single cycle in the linear symmetric shock absorber being simulated (Figure 2a,b) is equal to that in the real non-linear shock absorber. The c\({}_{1}\) value thus determined is taken as a basis for determining the relative suspension damping \(\vartheta_{1}\) (see (19)). The sliding friction force Fts\({}_{1}\) is not taken into account in the linear model. This means that \(\vartheta_{1}\) represents the damping of the shock absorber alone instead of the total damping of the complete car's suspension system. \begin{table}
\begin{tabular}{c c c} \hline \hline
**Symbol** & **Unit of Measure** & **Value** \\ \hline m\({}_{1}\) & kg & 160 \\ m\({}_{2}\) & kg & 35 \\ k\({}_{1}\) & N/m & 24,882 \\ k\({}_{2}\) & N/m & 206,526 \\ c\({}_{2}\) & N-s/m & 150 \\ f\({}_{01}\) (\(\omega_{01}\)) & Hz (rad/s) & 1.87 (11.77) \\ f\({}_{02}\) (\(\omega_{02}\)) & Hz (rad/s) & 12.96 (81.42) \\ c\({}_{\mathrm{kr1}}\) & N-s/m & 3770 \\ \hline \hline \end{tabular}
\end{table} 
Table 1: Parameters of the linear model of the rear ‘quarter’ of the Opel Astra car. \begin{table}
\begin{tabular}{c c c} \hline \hline
**Symbol** & **Unit of Measure** & **Value** \\ \hline A1s\({}_{1}\) & N/m & 450,000 \\ A2s\({}_{1}\) & N/m\({}^{3}\) & 0 \\ B2s\({}_{1}\) & N/m\({}^{2}\) & 0 \\ C2s\({}_{1}\) & N/m & 24,887 \\ D2s\({}_{1}\) & N & 425 \\ u1 gr & m & 0.001 \\ cm0\({}_{0}\) & m & 0.001 \\ Ats\({}_{1}\) & N & 0.005 \\ Ats\({}_{1}\) & N/m\({}^{3}\) & 0.005 \\ c\({}_{\rm u}\) & N-s\({}^{\rm Wu}\)/m\({}^{\rm Wu}\) & 14,000 * \\ c\({}_{\rm o}\) & N-s\({}^{\rm Wu}\)/m\({}^{\rm Wu}\) & 6700 * \\ Wu & - & 1.9 * \\ Wo & - & 1.6 * \\ i & - & 0.7068 \\ As\({}_{2}\) & N/m\({}^{3}\) & -3.021 \(\times\) 10\({}^{7}\) \\ Bs\({}_{2}\) & N/m\({}^{2}\) & 3.592 \(\times\) 10\({}^{6}\) \\ Cs\({}_{2}\) & N/m & 1.553 \(\times\) 10\({}^{5}\) \\ R & m & 0.311 \\ m\({}_{3}\) & kg & 14.5 \\ \(\zeta_{\rm min}\) & m & 0.000 \\ \(\zeta_{\rm max}\) & m & 0.006 \\ \hline \hline \end{tabular}  
* Values for the experimental (adjustable) viscous damper set to '19' (\(\bar{\theta}_{1}\) = 0.496); lower damping levels were obtained by multiplying the damping force (described by a power function) in succession by 0.26; 0.30; 0.34; 0.49; 0.62; and 0.78 so as to represent the damping curves of the experimental viscous damper for its settings being changed in succession from ‘12’ to ‘18’ (\(\bar{\theta}_{1}\) = 0.131; \(\bar{\theta}_{1}\) = 0.155; \(\bar{\theta}_{1}\) = 0.173; \(\bar{\theta}_{1}\) = 0.207; \(\bar{\theta}_{1}\) = 0.242; \(\bar{\theta}_{1}\) = 0.300; \(\bar{\theta}_{1}\) = 0.366).  
\end{table} 
Table 2: Additional parameters of the non-linear model of the rear ‘quarter’ of the Opel Astra car and of the diagnostic tester.