## 4 Parameter Study  
Influence of the Isolator Parameters \(k_{d},l_{d}\), \(\varphi_{d0}\) on Vibration Isolation Performance  
To further reveal the influence of the design parameters on the vibration isolation performance, the effects of the structural parameters \(k_{d},l_{d},\varphi_{d0}\) on the vibration transmissibility \(T\) of the BI-DSVI are investigated in this section. In the following analysis, the value of \(a\) is set to 0.25 m, and \(b\) is 0.2 m. The other parameter values are taken from Table 1 and the initial phase of the base excitation is \(\phi_{01}=\phi_{02}=\phi_{03}=\phi_{04}=0\).  
Figure 6a shows the vibration transmissibility curves of the BI-DSVI with different transverse spring stiffness \(k_{d}\). The values of \(l_{d}\) and \(\varphi_{d0}\) are set to 0.4 m and \(\pi/4\), respectively. It is obvious that with the increase in \(k_{d}\), both the first and second peaks of the vibration transmissibility curves increase. In the given frequency band (2-12 Hz), as \(k_{d}\) increases, the overall vibration transmissibility curve shifts to the right, which indicates that the effective vibration isolation bandwidth becomes narrower.  
\begin{table}
\begin{tabular}{c c c c c c} \hline \hline
**Initial Phase of the Base Excitation** & \(l_{d}\) & \(k_{d}\) & \(\varphi_{d0}\) & \(a\) & \(b\) \\ \hline \(\phi_{01}=\phi_{02}=\phi_{03}=\phi_{04}=0\) & 0.4 & 5000 & \(\pi/6\) & 0.10 & 0.10 \\ \(\phi_{01}=\phi_{02}=0\), \(\phi_{03}=\phi_{04}=\pi\) & 0.4 & 5000 & \(\pi/6\) & 0.20 & 0.10 \\ \(\phi_{01}=\phi_{04}=0\), \(\phi_{02}=\phi_{03}=\pi\) & 0.4 & 5000 & \(\pi/6\) & 0.21 & 0.21 \\ \hline \hline \end{tabular}
\end{table}
Table 2: The optimal design parameters of the three different base excitations.  
Figure 6: Vibration transmissibility \(T\) of the BI-DSVI with different structural parameters of the bio-inspired isolator: (**a**) the transverse spring stiffness \(k_{d}\), (**b**) the connecting rod length \(l_{d}\), (**c**) the initial assembly angle \(\varphi_{d0}\).  
Figure 6b shows the vibration transmissibility curves of the BI-DSVI with different connecting rod lengths \(l_{d}\). The values of \(k_{d}\) and \(\varphi_{d0}\) are set to 6000 N/m and \(\pi/4\), respectively. Near the first resonant frequency, the vibration transmissibility slightly decreases with the increase in \(l_{d}\), which is suitable for vibration isolation. However, in the other frequency regions, \(l_{d}\) has no effect on the vibration transmissibility.  
Figure 6c shows the vibration transmissibility curves of the BI-DSVI with different initial assembly angles \(\varphi_{d0}\). The values of \(l_{d}\) and \(k_{d}\) are set to 0.4 m and 6000 N/m, respectively. With the angle \(\varphi_{d0}\) varying from \(\pi/6\) to \(\pi/3\), both the first and the second resonant frequencies increase significantly. Moreover, the peak values of the first and second resonant frequencies also increase significantly. The results indicate that a small initial assembly angle \(\varphi_{d0}\) may lead to better vibration isolation performance, including a wider effective vibration isolation bandwidth and lower resonance peak.  
Through the above parameter analysis, it can be seen that the vibration isolation performance is significantly influenced by the following structural parameters: the transverse spring stiffness \(k_{d}\) and the initial assembly angle \(\varphi_{d0}\). The connecting rod length \(l_{d}\) also has a slight effect on the vibration isolation performance. The vibration isolation performance is better when using a smaller \(k_{d},\varphi_{d0}\) and longer \(l_{d}\). This conclusion validates the optimization results in Section 3.