# A New Top-Mounted Shear-Hinge Structure Based on Modal Theory and Rubber-Pad Damping Theory
## 4 Modal Analysis and Frequency-Response Analysis under Assembly Conditions
### Analysis of Shear-Hinge Frequency-Response Function When Rubber Padding Is Added  
In Section 4.2, it was demonstrated that the TMSH assembly's natural frequency is significantly reduced by adding a rubber bedding layer between the metal pad and the TMSH. In this section, the frequency-response function of the TMSH with rubber padding is analyzed, and the following figures show the frequency-response function curves of the TMSH's damage-prone areas.  
In Figure 14a, it can be seen that the sensitive peaks of transverse acceleration admittance at the connection point of the shear rod and sleeve are near the first (261.83 Hz)- and second (293.22 Hz)-order modes and the peak level is higher in the first order. In  
Figure 13: Vertical and lateral frequency-response analysis results for TMSH installed on the metal pad: (**a**) lateral acceleration admittance; (**b**) vertical acceleration admittance.  
Figure 14b, it can be seen that the shear rod has only one sensitive peak under vertical excitation, which is located near the third-order (313.73 Hz) mode. The peak transverse acceleration admittance values of the front-, middle-, and rear-end bolts are located near the first-order mode (261.83 Hz) and the second-order mode (293.22 Hz), indicating that the excitation of the first two order modes will mainly produce transverse displacement. In Figure 14b, it can be seen that the resonance peaks of the bolts in the vertical direction of the three positions are all in the third-order mode (313.73 Hz), which can be summarized as follows: the first- and second-order modes mainly produce transverse acceleration, and the third-order mode mainly produces vertical acceleration.  
The addition of rubber pads can isolate most of the high-frequency vibrations, but there are still some high frequencies that will be reduced due to the increase in the rubber pads, and they will fall into the higher region of the floating-slab excitation energy. Tables 9 and 10 show the response amplitudes of the easily damaged areas of the TMSH (shear rod, front-end bolt, mid-end bolt, rear-end bolt) in the higher region of floating-slab excitation energy of 400-3000 Hz under the two structures with metal pads and rubber pads.  
The rubber pad has strong vibration isolation performance and can greatly reduce the vibration amplitude. In Table 8, we can see that the transverse vibration amplitude of each easily damaged part was reduced by more than 30 dB, among which the transverse vibration energy of the shear rod was attenuated by 59.71 dB. This proves that the rubber pad can effectively reduce the problem of shear-rod fracture while suppressing the problems of bolt loosening and broken bolts.  
Figure 14: Results of frequency-response analysis of the TMSH installed on the rubber pad in the vertical and lateral directions: (**a**) lateral acceleration admittance; (**b**) vertical acceleration admittance.  
\begin{table}
\begin{tabular}{c c c c c} \hline \hline
**Work Conditions** & **Shear Rod** & **Rear-End Bolt** & **Mid-End Bolt** & **Front-End Bolt** \\ \hline Metal pad/dB & 161.29 & 129.54 & 122.28 & 134.32 \\ Rubber pad/dB & 101.58 & 95.56 & 87.96 & 87.23 \\ Improvement value/dB & 59.71 & 33.98 & 34.32 & 47.09 \\ \hline \hline \end{tabular}
\end{table}
Table 9: Comparison of the magnitudes of the frequency responses of the TMSHs placed on the metal pad and the rubber pad under lateral excitation.