## 4 Conclusions  
This paper explores the negative Poisson's ratio of re-entrant hexagonal cells, and the main conclusions are as follows:  
1. The Poisson's ratio of re-entrant hexagon is changed by changing the re-entrant angle and the ratio of vertical and hypotenuse angles of re-entrant hexagon. Its natural frequency is analyzed, and the energy band analysis of re-entrant hexagon with different Poisson's ratio is carried out. The research shows that: the re-entrant hexagonal cell structure has a good vibration isolation effect in the vertical direction to the vibration of the unique frequency, and the vibration isolation bandwidth frequency of cell structure with different Poisson ratio is different.
2. By analyzing the different Poisson's ratio of re-entrant hexagon natural frequency vibration isolation performance of the cell structure, based on re-entrant hexagonal cell structure of cellular base, and different laying methods are used. Through the study, the structure of the honeycomb base has a good vibration isolation performance at a specific frequency, and it has a better vibration isolation performance when use the different Poisson's ratio cell to lay the base.
3. By adding mass blocks to the inner or surrounding corners angles of the basic re-entrant hexagonal cell, the vibration isolation performance of the honeycomb base frequencies can be changed. When the circular mass blocks of different sizes are added to the inner corner, the vibration isolation effect of the honeycomb base is much better in the middle and high frequencies. Meanwhile, when the mass blocks are added to the surrounding corners, the vibration isolation performance of the honeycomb base is better in the high frequencies.
4. When the side thickness of the cell structure is \(\tau~{}=~{}0.2\) cm, adding mass block to the cell structure has little effect on the vibration isolation performance. When the cell structure side thickness is \(\tau~{}=~{}0.1\) cm, the vibration isolation performance of the abnormity concave structure honeycomb base is superior to the ordinary inner re-entrant structure of honeycomb base, and the vibration isolation performance of the re-entrant structure honeycomb base with side thickness \(\tau~{}=~{}0.1\) cm is better than that of the re-entrant structure honeycomb base with side thickness \(\tau~{}=~{}0.2\) cm when the side thickness on the whole.
5. The honeycomb base composed of re-entrant hexagons has a lighter mass, and the lightweight nature can effectively reduce the mass of the ship base, which can effectively reduce the load of the ship and reduce transportation costs.  
According to the research and calculation results, considering the quality and vibration isolation performance of honeycomb base comprehensively, the re-entrant hexagonal honeycomb base has good vibration isolation performance and lower quality, and the manufacturing difficulty is relatively low, so it is more suitable for practical engineering application. Therefore, the base of the negative Poisson's ratio base can make military ships and cargo ships effectively reduce the large power equipment on the ship or motor vibration, and the base only depend on its structure and material selection and design to meet the different frequency isolation, no additional installation vibration isolator.  
Writing--original draft, S.Z.; Writing--review & editing, K.P., J.D. and W.Z. All authors have read and agreed to the published version of the manuscript.  
The authors gratefully acknowledge the support of National Natural Science Foundation of China (NNSFC) through Grant Nos. 11772166, 12172186, 11832002, and 11672188, and The APC was funded by 11772166, the Funding Project for Academic Human Resources Development in Institutions of Higher Learning under the Jurisdiction of Beijing Municipality (PHRIHLB).  
The data that support the findings of this study are available from the corresponding author upon reasonable request.  
The authors declare that there is no conflict of interest regarding the publication of this paper.