## 2 Establishment and Verification of an FE Model for HVB-LA-DLTL Systems
### Modal Analysis  
Modes are the inherent vibration characteristics of a structure and the specific inherent frequency, damping ratio, and modal vibration pattern of each mode can be obtained by calculation or experiment. The vibrator experiment is a common method for structural modal analysis [22]. Building up a database of the real forcing functions applied by a vibrodyne plays a key role when conducting dynamical tests on a composite structure. \begin{table}
\begin{tabular}{c c c c c c} \hline \hline
**Part Name** & **Material** & \begin{tabular}{c} **Elastic Modulus** \\ **(GPa)** \\ \end{tabular}  & \begin{tabular}{c} **Poisson’s** \\ **Ratio** \\ \end{tabular}  & \begin{tabular}{c} **Element Type** \\ \end{tabular}  & \ \begin{tabular}{c} **Mesh Density** \\ **(mm)** \\ \end{tabular}  \\ \hline Down Conductor System & Aluminum & 50 & 0.33 & Solid186 & 50 \\ Clamps on High-Voltage & Aluminum & 70 & 0.33 & Solid186 & 10 \\ Bushing &
\begin{tabular}{c} **J**rans \\  
Modal analysis is the basic method for studying the dynamic properties (vibration pattern, frequency, etc.) of a structure and is also the basis for other dynamic analyses such as time-distance analysis. Through modal analysis, the vibration response of the system can be predicted when it is subjected to an applied dynamic excitation. To further analyze the influence of the force on the performance of the high-voltage casing lead structure system, the \"\(\lambda\)\"-shaped lead structure system is used as an example, and the effects of the lower electrical and the specific modal vibration characteristics are shown in Tables 3 and 4. According to the modal analysis results above, the natural frequencies of vibration of the HVB-LA-DLTL systems in this paper are lower than those in the literature. The model in the literature [19] contains only the upper span line, lead wire, and connection gold specific system. Given that the upper span line and lead wire are considered fixed ends, the overall stiffness of the system is high. The model in this paper is closer to actual engineering applications. Compared with the literature, [23] shows that HVB-LA-DLTL systems and substation boxes have a large impact on the overall system stiffness. Thus, the overall stiffness of the system decreases, the natural frequencies of vibration become lower, and the dynamic effect of the system under dynamic load is greater, which is consistent with the characteristics of the lead structure system in the actual substation. Due to space limitations, Figure 6 shows the first six orders of the vibration pattern of the model modal analysis in this paper. \begin{table}
\begin{tabular}{c c c} \hline \hline
**Mode** & **The Natural Frequency of Vibration (Hz)** & **Characteristics of the Mode of Vibration** \\ \hline
1 & 1.2827 & The upper jumper bends along the negative Z-axis \\
2 & 1.4931 & The arrester bends along X positive axis \\
3 & 1.5538 & The arrester bends along Z negative axis \\
4 & 1.8996 & The upper jumper twists along the X-axis \\
5 & 2.4006 & The HV bushing bends along the positive X-axis \\
6 & 2.4715 & The HV bushing bends along the positive Z-axis \\ \hline \hline \end{tabular}
\end{table} 
Table 4: Natural frequencies of vibration and characteristics of the first 6 modes of the FE model for the HVB-LA-DLTL systems.