# The Vibration Isolation Design of a Re-Entrant Negative Poisson's Ratio Metamaterial
## 1 Introduction
To achieve significant tunable bandgaps in conventional rigid materials, [PERSON] et al. [34] proposed a novel metamaterial with the use of soft materials and granular systems, which can avoid excessive pre-stress and enhance tunable phononic crystals. [PERSON] et al. [35] developed a gradient-based topology optimization method to maximize the bandgap width and demonstrated successful application in achieving wide bandgaps in a sample case. Additionally, [PERSON] et al. [36] demonstrated that the magneto-tunability of phononic bandgaps in a periodic hard-magnetic soft laminated composite and found that the first bandgap width was maximized when the volume fraction of the hard phase exceeded that of the soft phase. Furthermore, [PERSON] et al. [37] designed highly nonlinear isolators and diodes for the clean separation of highly deformable solitary waves by using highly deformable metamaterials. As a material that can be designed artificially, metamaterials show potential advantages in the regulation and optimization of various mechanical and physical properties. [PERSON] et al. have done much work on the regulation and optimization of metamaterials [38; 39; 40]. They proposed a novel unit cell configuration composed of two periodic locally resonant peace-logo planar metamaterial (PLPM) patterns, which can control the coupling and resonant frequency by the rotation of the bottom PLPM pattern. Moreover, [PERSON] et al. also proposed metamaterial structures to enhance the gain and reduce the mutual coupling of microstrip multiple-input multiple-output (MIMO) antennas. By vertically embedding modified peace-logo planar metamaterial (MPLPM) structures into the antenna substrate, the directivity and gain of the antenna can be increased, and placing two-sided MPLPM (TSMPLPM) structures between the antenna elements can improve isolation. Moreover, in their work, a millimeter-wave power divider (MWPD) was introduced, achieving high isolation in the millimeter-wave frequency range, specifically for mmWave applications, such as 5G, without the need for isolation resistors. [PERSON] et al. [41] proposed and verified a systematic inverse design framework for constructing multi-stable mechanical metamaterials with programmable gradients, and offered a new paradigm for developing precisely tailored and programmable mechanical metamaterials. [PERSON] et al. [42] proposed a multi-layered symmetric metamaterial design for C- and X-band applications,and the proposed metamaterial design accomplished the miniaturization concept by arranging unit cells in a multi-layer structure and possesses unique properties, such as a highly effective medium ratio and left-handed characteristics. It is evident that metamaterials possess a higher degree of designability compared to traditional materials, and incorporating assembly techniques into metamaterial design can enhance their versatility and designability. As a class of artificially designed materials, metamaterials offer significant advantages in structural lightweight while simultaneously addressing various other performance requirements. In the aerospace applications of metamaterials, there are three main requirements that need to be met simultaneously: structural lightweight requirements, adequate strength and stiffness, and good vibration properties. Extensive research has been conducted in this area. This work presents an assembly-based approach to design a re-entrant negative Poisson's ratio metamaterial by introducing circular rings as connecting nodes to conventional NPR metamaterials and a 300% increase in the bearing capacity of the novel structure compared to traditional structural metamaterials. The introduction of the metal pins and metal particles increases the density of the metamaterial structure, so the resonance frequencies of the overall structure will move in the low-frequency direction, and the corresponding resonant vibration amplitude may indeed be larger than that of the original structure, which can be suppressed by damping.