# Design Methodology and Application Dynamics of Compact Quasi-Zero Stiffness Isolators
## 3 Compact Design of QZS Isolation
### Metamaterials-Based Type  
Metamaterials are artificially engineered materials that attain unique physical properties through microstructural design. The uniqueness of such materials lies in the fact that their properties originate from the layout of the internal crystal structure. In recent years, the development of metamaterials theory has opened up new research directions in many engineering fields. By precisely designing the microstructure of metamaterials, it is possible to integrate multiple functional properties in the same material. [PERSON] et al. [74] focused on metamaterial lattice structures possessing high-static and low-motion properties and summarized the design strategies for lattice metamaterials with this feature. This chapter provides an overview of compactly designed metamaterial structures. Figure 13 illustrates several typical approaches to the design of metamaterials. [PERSON] et al. [75] proposed an arrayed lattice core sandwich beam design embedded in a 3D printed quasi-zero stiffness resonator, which exhibits broadband vibration isolation far beyond the corresponding linear object bandgap. [PERSON] et al. [76] proposed the lightweight design of 3D QZS meta structures with beam-like monoclinic cells, which used an optimized design approach to enable vibration isolation meta structures to achieve customizable QZS properties in complex operating environments. [PERSON] et al. [77] proposed a structural unit consisting of an elastic ring with two cross-bent beams, which can be realized by structural design to achieve metamaterials with multilevel QZS regions. [PERSON] et al. [78] fabricated a metamaterial with quasi-zero stiffness properties inspired by Miura origami by laser powder bed fusion printing technique, which shows great potential in longitudinal vibration. [PERSON] et al. [79] Inspired by the honeycomb morphology structure with negative Poisson's ratio characteristics, a symmetric concave thin-walled structure is used to provide the main load-carrying capacity, and the staggered arrangement of the load-carrying units is used to design a lightweight, compact mechanical metamaterial configuration with a low initial load and a large densification strain. [PERSON] et al. [80] proposed a class of customized  
Figure 12: Bionic beetle vibration isolator proposed by [PERSON] et al. [73]: **(a)** Model of vibration isolator; **(b)** Experimental and simulation transmissibility comparison, where the corresponding time histories of the load platform and the base plate at 15 Hz. mechanical metamaterials containing specific geometrically shaped bending beams to provide the QZS characteristics. In the compression test, the bending beam reaches the preset operating range sequentially, forming a customized stepped force-displacement curve with multiple working ranges. [PERSON] et al. [81] proposed a topology optimization scheme for the reverse design of QZS meta-structures with smooth boundaries, which resulted in a compact superstructure with smooth boundaries and no post-processing, integrating lightweighting, load-carrying capacity, and vibration isolation. [PERSON] et al. [82] implemented the optimization of trajectories at the center of the cross-section of bent beams with the help of a genetic algorithm. Through this operation, customizable stiffness and load-carrying capacity were successfully achieved, and multiple QZS regions were constructed. The optimized design was proven to be effective in isolating vibrations with frequencies above 4.67 Hz, and its mass was only 3.2% of the load-carrying capacity. [PERSON] et al. [83] proposed a one-dimensional bandgap-tunable QZS metamaterial consisting of a single unit centered on a truncated conical shell. Compared with conventional vibration isolation structures, the material significantly reduces the weight and decreases the size, and the onset frequency is reduced to 15.01 Hz, which is 46.6%.