## 3 Cell Base Structure and Frequency Response Analysis
### Frequency Response Analysis Based on Heteromorphic Negative Poisson's Ratio Cell structure Base
Figure 11:4 The diagram of the cell structure and the analysis curve is given, (**a**) the heteromorphic negative Poisson’s ratio cell structure added circular mass blocks to the inner circle radius: 1.5 cm; around the corner circle radius: 1.5 cm; (**b**) tenth order natural frequency band diagram of a single cell structure, side thickness: \(\tau\ =\ 0.2\) cm, Poisson’s ratio: \(v\ =\ -1.11\). (**c**) a fixed displacement 1 m upper plane of the base. (**d**) frequency response curve of the honeycomb base. When the sideside thickness of the structure is \(\tau=0.1\) cm, from Figures 11-15, it can be seen that, when the Poisson's ratio of the structure is \(v=-0.47\), the value range of the band gap frequency of the structure shows an overall increasing trend with the increase of mass blocks in the inner and outer corner angles of the cell structure: according to the vertical coordinates of Figure 11d and Figure 12d, Figure 7c-Figure 9c, the vibration isolation performance of the structure is almost the same as the structure that the Poisson's ratio is \(v=-0.47\) and the side thickness is \(\tau=0.1\) cm. When the mass blocks added to the inner and outer angles are large, under the same Poisson ratio and side thickness, the vertical coordinates of Figures 13d-16d shows that the vibration isolation performance of the structure is better than that of the structures without mass blocks. When the Poisson's ratio of structure is \(v=-1.11\), side thickness \(\tau=0.1\) cm, from the Figure 17 to Figure 22 we can see that, when the inside and outside mass increases, the structure of the vibration isolation performance of the overall rise, especially when the quality of block size increases to a certain extent, such as Figures 21d and 22d, vibration isolation performance of the structure is more prominent, moreover, the vibration isolation effect of the structure is particularly outstanding at the frequency of 6000 Hz-8000 Hz. When the side thickness of the structure is \(\tau=0.2\) cm, it can be seen from Figures 23-28 that when the Poisson's ratio of the structure is \(v=-0.47\), with the increase of internal and external angle blocks, the vibration isolation performance of the structure is almost the same as that shown in Figure 7d without adding mass blocks, and occasionally presents a downward trend. When the Poisson's ratio of structure is \(v=-1.11\), it can be seen that from the Figure 29 to Figure 34, vibration isolation performance of the structure is almost unanimous, even in some size mass block will appear the situation of vibration isolation performance decline, but when quality block size is larger, as shown in Figures 31 and 34, The structure will have better vibration isolation performance at more frequencies compared without the quality block structure is Figure 8d. As can be seen from the overall comparison of Figures 11-22 and Figures 23-34, when the side thickness of the structure is \(\tau=0.1\) cm, the vibration isolation performance of the structure is better than that of the structure when the side thickness is \(\tau=0.2\) cm. By the overall comparison between the internal and external angles with mass blocks and those without mass blocks, that is, the overall comparison between Figures 11-34 and Figures 7-9, it can be concluded that the vibration isolation performance of the structure with mass blocks is generally better than that without mass blocks. In conclusion, when the side thickness is \(\tau=0.1\) cm, the vibration isolation performance of the structure is much better. The inner mass block is bigger, the performance is better, but if the mass block is too big, the vibration isolation performance gets worse. Adding the mass block to the outer corner can make the vibration isolation frequency more wide. However, when the side thickness is \(\tau=0.2\) cm, the vibration isolation performance of the structure with mass blocks added to the inner and outer angles is weaker than that without mass blocks.