## 1 Introduction  
Lattice structures have been extensively investigated for vibration isolation, primarily focusing on two mechanisms: bandgap-based isolation [1, 2, 3] and conventional passive vibration isolation [4, 5, 6, 7]. With the advancement of additive manufacturing, the fabrication of metal lattice structures has become relatively mature. By designing the parameters of metal lattice structures, their stiffness and damping characteristics can be adjusted; therefore, they can be used as traditional vibration isolation and shock resistance components. Metal lattice structures should operate within their linear elastic regime to make them possible for repeated long-term use for traditional vibration isolation and shock resistance applications. The stronger radiation resistance and corrosion resistance of metal lattice structuresexhibit their potential for application in extreme environments, such as high radiation and strong radiation conditions, compared to rubber vibration isolators. However, the metal lattice's low intrinsic damping leads to pronounced resonance peaks and inadequate shock attenuation, ultimately limiting its vibration isolation and shock resistance applications. Therefore, it is imperative to develop a damping enhancement approach that improves the damping performance of metal lattice structures, which should also maintain the capacity of resisting radiation and corrosion. The addition of viscoelastic layers is an effective method to enhance structural damping [8], mainly including two forms: base/viscoelastic/base platens with confined layer damping [9] and viscoelastic/base platens with free layer damping [10]. Polyurea, a viscoelastic material, exhibits inherent radiation and corrosion resistance [11; 12; 13]. Extensive research on its ballistic penetration resistance and blast mitigation capabilities further highlights its exceptional energy absorption properties [14; 15; 16; 17; 18; 19]. These multifunctional characteristics suggest significant potential for using polyurea in vibration isolation systems for large equipment in harsh environments, including radiation exposure, corrosive media, or combined extreme conditions, to enhance system damping performance. Three structural configurations incorporating polyurea layers into the metal panels of lattice sandwich structures were proposed to enhance damping performance. Modal vibration tests were conducted to evaluate the natural frequencies and damping loss factors of the first three modes [20]. Subsequently, the structural optimization design was investigated in further detail [21]. The damping performance of honeycomb structures could be enhanced by filling the pores with viscoelastic materials [22; 23; 24; 25], offering valuable insights for improving the damping of lattice structures. The damping properties of 316L BCC lattice structures incorporating different filler materials were examined [26]. Modal testing results indicate that while the composite structures exhibited an increased damping ratio compared to the unfilled lattice, the maximum attainable ratio remained limited to 0.007. A hybrid approach was proposed [27] to enhance the damping performance of pyramidal lattice structures by simultaneously incorporating both viscoelastic damping layers and filler materials. The damping and stiffness efficiency of the composite structures were evaluated through combined modal and quasi-static compression tests. However, adding a viscoelastic damping layer to the surface of the metal lattice structure cover plate formed a series combination of the metal lattice and the viscoelastic structure, whose load-bearing capacity was limited by the relatively weak viscoelastic damping layer, resulting in insufficient load-bearing capacity. When damping materials are filled internally, it is constrained by the fixed pore structure. The ability to achieve the desired optimal damping characteristics through adjustments to the shape and size of the damping materials is limited.