## 1 Introduction  
Consisting of two thin panels attached to each side of a thick core, the sandwich structure is a special structure of composite materials. The sandwich structure has been widely used in aviation, aerospace, transportation, ocean engineering and other fields due to its light weight, high rigidity and high strength [1, 2, 3, 4, 5, 6, 7, 8, 9]. When the sandwich structure is subjected to a bending load, its panel will bear plane compression and tensile loads, and the core material will bear shear loads. The mechanical properties of the sandwich structure can be obtained by selecting different panel and core material configurations simultaneously. Sandwich structures of foam [10, 11] and honeycomb materials [12, 13] have been widely used as traditional sandwich structures due to their high rigidity and weight ratio, which can significantly reduce weight while maintaining mechanical properties. However, the conventional sandwich structure cannot be universally used, as it is not compatible with closed-cell foam or a honeycomb core. The space lattice sandwich structure with various types of 3D periodic lattice cores, including pyramidal [14, 15, 16, 17, 18], tetrahedral [19, 20], Kagome [21, 22] and corrugated lattice core [23, 24], has been proved to be stronger and more rigid than traditional sandwich structures due to its opening structure with high node connectivity [25]. Based on the developmental trend of recent years, the three-dimensional periodic lattice core has been considered the best direction for multifunctional ultra-light structure design. The space lattice sandwich structure is often dynamically stimulated by the working environment load in practical engineering applications. Therefore, for design purposes, it is of great significance to understand the vibration response mechanism of space lattice sandwich structures. In recent years, a great deal of research has been conducted on the vibration mechanism of space lattice sandwich structures. The most common approach is to transform the sandwich structure as an equivalent homogeneous layer, and then use different panel and shell theories for modeling and calculation analyses. [PERSON] et al. [26] studied the free vibration and dynamic vibration responses of composite sandwich beams and discussed their influence on transverse shear deformation and rotational inertia. By treating pyramidal truss cores as a continuous homogeneous material, [PERSON] et al. [27] discussed the free vibration characteristic of a sandwich beam under the simply supported boundary condition and verified the calculation results with Abaqus, the finite element analysis software. In order to obtain more a accurate sandwich beam response, [PERSON] et al. [28] introduced a modified piecewise function to establish an analytical model for studying the free vibration response of composite lattice sandwich beams under several typical boundary conditions. Considering the different uncertainties of materials and structures, [PERSON] and [PERSON] [29] analyzed the free vibration mechanism and studied the structural optimization of two kinds of space lattice sandwich beams with different core types. [PERSON] et al. [30] selected different panel theories to study the vibration characteristics of composite lattice sandwich panels with three truss cores. By using [PERSON]'s principle and the assumed mode method and setting up a piezoelectric actuator and sensor on the upper and lower panels of the lattice sandwich beam, [PERSON] and [PERSON] [31] analyzed the vibration control problem of the beam under a simply supported boundary condition. [PERSON] et al. 's work was extended by [PERSON] et al. [32], who studied the vibration response for a multi-span lattice sandwich beam with a Kagome lattice core and a pyramidal truss core. By applying the Rayleigh-Ritz method, [PERSON] and his collaborators [33] established an analytical method to study the natural frequency of lattice sandwich beams with a composite gradual corrugated core.