###### Abstract
[24] found that the main factors affecting the mechanical impedance of the base are the thickness and the amplitude of its resonance response. [PERSON] and [PERSON] [25] used the micropole to study the dynamic deformation and performance of regular hexagonal honeycomb cell structure under vertical harmonic force excitation. [PERSON] et al. [26] studied the dynamic response of a chiral \"arrow\" negative Poisson's ratio material under bending load. [PERSON] et al. [27] used the equivalent continuum model to study the free vibration characteristics of honeycomb structures without excitation. [PERSON] et al. [28] studied the vibration characteristics of hexagonal inner negative Poisson's ratio honeycomb sandwich panels simply supported by four sides and analyzed the influence of geometric parameters of honeycomb cells on its natural frequency. [PERSON] et al. [29] used 3D printing technology to analyze and compare the in-plane axial compressive performance, impact deformation and failure mode of conventional honeycomb sandwich panels with the negative Poisson's ratio honeycomb sandwich panels and conventional-negative Poisson's ratio honeycomb hybrid sandwich panels. [PERSON] et al. [30] studied the response of cellular geometric parameters to the energy absorption of honeycomb sandwich structure under high-speed in-plane impact load, and it showed that the energy absorption rate was the highest when the honeycomb configuration presented negative Poisson's ratio. [PERSON] et al. [31] used analytical solutions to study the dynamic response and vibration of a double-curved flat shell with negative Poisson's ratio, and the honeycomb showed on an elastic foundation under explosion and damping loads. [PERSON] et al. [32] calculated the effective Poisson's ratio for different geometries to characterize the symmetry, and used finite element method to discuss the effect of effective elastic mesh characteristics in different loading directions on compression energy dissipation. [PERSON] et al. [33] proposes a topology optimization design method of metamaterials for improving the vibration reduction performance, and it showed that the novel designed meta-materials have at least 12% improvement in vibration reduction performance over the traditional honeycomb. [PERSON] et al. [34] studied the propagation of waves in phononic crystals, it consisted of a negative Poisson's ratio star-shaped honeycomb matrix. [PERSON] et al. [35] designed a three-dimensional (3D) star structure to construct meta-materials with both negative static and dynamic properties. The results showed that the 3D star structure formed a wide band gap at lower frequency and had a negative Poisson's ratio. [PERSON] et al. [36] developed a design framework, it integrated the topology optimization, parametric design and compression experiment for the GS mechanical meta-materials induced by the negative Poisson's ratio (NPR) property. [PERSON] et al. [37] investigated the vibration and damping properties of carbon fiber reinforced polymer (CFRP) 3D double-arrowhead (3D DAH) metamaterials, the negative Poisson's ratio effect of CFRP 3D DAH meta-materials was studied analytically by energy method. The literature reviews indicate that applying the negative Poisson's ratio structure to the honeycomb structure is highly meaningful. Studying the vibration damping performance of the structure is very important to the vibration base designs and analysis. Few analyses can be found on the vibration isolation performance of different special-shaped negative Poisson's ratio structures. In this paper, the vibration isolation performance of negative Poisson's ratio re-entrant structure was analyzed respectively. The Poisson's ratio calculation formula of negative Poisson's ratio re-entrant structure is derived according to the dimension angle of the structure. The band gap diagram of negative Poisson's ratio re-entrant structure was got, and the frequency response curve of the honeycomb structure was got, so the vibration isolation performance of the structure is analyzed.