## 5 Parameterisation Studies
### The Limits of Material Distribution Coefficient \"na\"
The frequency responses are scanned with a sensitivity of \(10^{-8}\) and are presented in the table for different \(na\) values. In Tables 6-8 for different \(na\) values, the maximum force transmissions in the frequency components are indicated with a red base and the minimum force transmissions are marked with a green base. Taking into account the parameters \(na\) and \(c_{A}ratio\), the investigations of Figures 13-20 and Tables 6-8 for the \(T_{R}\) force transmissibility can be grouped as follows:  
1. For the system with the \(Pb\)/\(Cu\), \(Pb\)/\(Br\), \(Pb\)/\(St\) and \(Pb\)/\(Al\) support bars, \(c_{A}ratio>1\) and for the frequency parameters \(SS1\) and \(SS2\), the \(T_{R}\) force transmission values increase with increasing \(na\). The values of the \(T_{R}\) force transmission decrease with increasing \(c_{A}ratio\) if \(c_{A}ratio>1\) (Figure 20 and Table 8). 2. In the frequency parameters \(SS1\) and \(SS2\), the bar material pairs with \(c_{A}ratio>1\)\(Pb\)/\(Cu\), \(Pb\)/\(Br\), \(Pb\)/\(St\) and \(Pb\)/\(Al\) are ranked in insulation quality as the \(na\) value increased towards 100. Excluding \(Pb\)/\(St\), \(T_{R}\) is ranked according to the \(c_{A}ratio\) value (Table 5). It can be seen that the \(Eratio\) for the Pb/\(St\) pair is very low when other material pairs are considered (Table 5). The support bar made of the \(Pb\)/\(Al\) material pair with the highest \(c_{A}ratio\) value provides better insulation (Table 8, Figure 20). 3. When \(c_{A}ratio>1\), the system with \(Pb\)/\(Al\) bars provides the best insulation for all values of \(na\). On the other hand, when \(na=0\), although the bar material behaves like \(Pb\), the insulation is better than the system supported by the pure \(Pb\) bar. The change in force transmissibility of the system using pure \(Pb\) bar supports is shown in Figure 3 and Table 3. Table 6 shows that for the frequency parameter \(SS1\), the \(T_{R}\) value decreases from 243,782 in the \(Pb\) bar-supported system to 123,496 in the \(Pb\)/\(Al\) bar-supported system; for the frequency parameter \(SS2\), the \(T_{R}\) value decreases from 6144 in the \(Pb\) supported system to 3108 in the \(Pb\)/\(Al\) supported system. The lowest \(T_{R}\) value of the frequency parameter \(SS1\), \(na\) = 0, is 4,584,299 for the \(Al\)/\(Pb\) material pair bar-supported system. Whether the Pb material is at the bottom or the top affects the transmissibility (Tables 7 and 8, Figure 20). 4. For the system with the \(Al\)/\(Pb\), \(Ag\)/\(Pb\) and \(Cu\)/\(Pb\) support bars, \(c_{A}ratio<1\), and for the frequency parameters \(SS1\) and \(SS2\), the \(T_{R}\) force transmission values decrease with increasing \(na\). The values of the \(T_{R}\) force transmission increase with increasing \(c_{A}ratio\) if \(c_{A}ratio<1\) (Figure 20 and Table 6). 5. In the frequency parameters \(SS1\) and \(SS2\), the bar material pairs with \(c_{A}ratio<1\)\(Al\)/\(Pb\), \(Ag\)/\(Pb\) and \(Cu\)/\(Pb\) are ranked in terms of insulation quality as the \(na\) value increased towards 100 until the \(na\) = 1 value. Excluding \(Al\)/\(Pb\), the \(T_{R}\) is ranked according to the \(c_{A}ratio\) value (Table 5). The T\({}_{R}\) of the system with the \(Al\)/\(Pb\) bar material pair has a turning point at \(na\) = 2 and then increases. The support bar made of the \(Al\)/\(Pb\) and \(Ag\)/\(Pb\) material pairs with the lowest \(c_{A}ratio\) value provides better insulation for the different \(na\) regions (Table 6, Figure 20). When other material pairs are considered, it is seen that the \(c_{A}ratio\) is very low in the \(Pb\)/\(Al\) pair (Table 6). 6. The \(T_{R}\) force transmission values decrease as the frequency parameters (\(SS1\) compared with \(SS2\), \(SS3\), \(SS4\), \(SS5\)) increase (Figure 20, Tables 6-8). 7. For the frequency parameters \(SS1\), \(SS2\), \(SS3\), \(SS4\) and \(SS5\) and for \(na\) = 0, \(T_{R}\) decreases with increasing \(c_{A}ratio\) if \(c_{A}ratio>1\), while \(T_{R}\) increases with increasing \(c_{A}ratio\) if \(c_{A}ratio<1\) (Tables 6-8). 8.