## 5 Parameterisation Studies
### The Limits of Material Distribution Coefficient \"na\"
\begin{table}
\begin{tabular}{c c c c c c c c c c c c c c c c} \hline \hline
**Pb/Cu** & & & & & & & & & & & & & & & & & \\ \(SN1\) & \(SS2\) & \(1.Region\) & & & & & & & & & & & & & \\ \(nn\) & \(\lambda\) & \(T_{R}\) & \(\lambda\) & \(T_{R}\) & \(\lambda\) & \(T_{R}\) & \(\lambda\) & \(T_{R}\) & \(\lambda\) & \(T_{R}\) & \(\lambda\) & \(T_{R}\) & \(\lambda\) & \(T_{R}\) & \(\lambda\) & \(T_{R}\) \\ \hline
0 & 3.14285 & 243,782 & 9.401217 & 6144 & 11.33643 & 61 & 15.711125 & 4056 & 19.627 & 18 & 22.02075 & 1412 & 25.3654 & 10 & 28.27558 & 619 & \\
0.5 & 3.14285 & 243,782 & 9.401217 & 6144 & 11.33643 & 61 & 15.711125 & 4056 & 19.6277 & 18 & 22.02075 & 1412 & 25.3654 & 10 & 28.27551 & 489 & \\
1.3 & 3.1428  
\begin{table}
\begin{tabular}{c c c c c c c c c c c c c c c c c c c} \hline \hline \multicolumn{1}{c}{_Data_} & \multicolumn{1}{c}{_S51_} & \multicolumn{1}{c}{_S52_} & \multicolumn{1}{c}{_1.Region_} & \multicolumn{1}{c}{_S53_} & \multicolumn{1}{c}{_2.Region_} & \multicolumn{1}{c}{_S54_} & \multicolumn{1}{c}{_3.Region_} & \multicolumn{1}{c}{_S55_} & \multicolumn{1}{c}{_4.Region_} \\ \cline{2-13} \multicolumn{13}{c}{m} & \(\lambda\) & \(T_{R}\) & \(\lambda\) & \(T_{R}\) & \(\lambda\) & \(T_{R}\) & \(\lambda\) & \(T_{R}\) & \(\lambda\) & \(T_{R}\) & \(\lambda\) & \(T_{R}\) & \(\lambda\) & \(T_{R}\) & \(\lambda\) & \(T_{R}\) \\ \hline
0 & 3.141255 & 136.651 & 9.41014 & 3273 & 11.33569 & 36 & 15.71126 & 2238 & 19.62808 & 10 & 22.00273 & 320 & 25.36269 & 6 & 28.27557 & 359 & \\
0 & 2.34149 & 1.218263 & 9.41881 & 15.124 & 13.18868 & 58 & 15.72276 & 9941 & & 21.9897 & 933 & 22.9042 & 42 & 28.26020 & 760 & 29.55703 & 18 \\
0 & 0.314593 & 3.26817 & 9.42113 & 35.7666 & 14.56947 & 15.18 & 15.74291 & 4001 & & 21.99007 & 5018 & 25.03086 & 28 & 22.29897 & 2848 & \\
1 & 3.141558 & 7.7503,313 & 9.42219 & 67.918 & 15.54333 & 148 & 15.94383 & 1029 & 21.99647 & 11.693 & 27.3117 & 86 & 28.32286 & 1903 & \\
2 & 3.14156 & 14.12936 & 9.42281 & 141.4927 & 15.6737 & 9356 & 16.85631 & 30 & 22.00043 & 19.956 & & 28.24004 & 2343 & 29.20481 & 122 \\
5 & 3.141575 & 25.25782 & 9.4221 & 181.572 & 15.69094 & 20.2017 & 17.80223 & 247 & 20.00124 & 27.9593 & & 28.27194 & 9453 & \\
10 & 3.14157 & 29.201,923 & 9.42353 & 220.150 & & 15.69408 & 29.4922 & 18.21691 & 254 & 22.00599 & 30.154 & & 28.27438 & 11,992 & \\
100 & 3.141579 & 36.374675 & 9.42348 & 26.4857 & & 15.69642 & 38.9179 & 18.65109 & 275 & 22.00829 & 31.984 & & 28.27741 & 16.476 & \\ \hline \multicolumn{1}{c}{_Data_} & \multicolumn{1}{c}{_S51_} & \multicolumn{1}{c}{_S52_} & \multicolumn{1}{c}{_1.Region_} & \multicolumn{1}{c}{_S53_} & \multicolumn{1}{c}{_2.Region_} & \multicolumn{1}{c}{_S54_} & \multicolumn{1}{c}{_3.Region_} & \multicolumn{1}{c}{_S55_} & \multicolumn{1}{c}{_4.Region_} & \multicolumn{1}{c}{_S55_} & \multicolumn{1}{c}{_4.Region_} \\ \multicolumn{1}{c}{na} & \(\lambda\) & \(T_{R}\) & \(\lambda\) & \(T_{R}\) & \(\lambda\) & \(T_{R}\) & \(\lambda\) & \(T_{R}\) & \(\lambda\) & \(T_{R}\) & \(\lambda\) & \(T_{R}\) & \(\lambda\) & \(T_{R}\) & \(\lambda\) & \(T_{R}\) \\ \hline
0 & 3.141286 & 136.604 & 9.41015 & 3388 & 11.3356 & 34 & 15.71126 & 2268 & 19.62814 & 20.20273 & 21.536191 & 6 & 28.2756 & 34.01 & \\
0 & 2.34150 & 1.2182,530 & 9.42169 & 41.670 & 14.97299 &When \(na\) goes from 0 to 100, the material changes from \(Al\) to \(Pb\). Looking at Figure 13, at \(na\) = 100 the \(Pb\) material dominates in the bar, its response close to the pure \(Pb\) characteristic shown in Figure 11. At \(na\) = 100 the \(Pb\) material characteristically dominates the bar, i.e., the number of side frequency bands increases to three. This is the same for other material pairs as shown in Figures 14-19. Due to the symmetry of the boundary conditions and the applied force, only symmetry-symmetry frequencies arise. For ease of examination of the frequency response, the beam-dominated frequency parameters are divided into SS components, and the bar-dominated components are divided into regions 1, 2, 3 and 4.