Objectives  In order to study the natural vibration characteristics of the lattice reinforced sandwich structure with cavities, whose core layer contains multiple components, an analysis method for the natural vibration of the sandwich structure is discussed here.

  Methods  Firstly, frustum cone-like cavities are approximated as cylinder-like ones in the principle of volume average. the multi-level homogenization is adopted, the complex core layer of the sandwich structure is taken as orthotropic material, and the single-phase inclusions are performed twice by using Mori-Tanaka method to obtain the equivalent elastic modulus of the core layer. Then the equation of motion is established based on first-order shear deformation theory, and then combined with the resultant equivalent elastic modulus of the core layer so as to figure out the natural frequency of the four-sided simply supported lattice reinforced sandwich structure with cavities by using double Fourier series. On this basis, the influences of core panel modulus ratio, lattice-enhanced cylinder volume ratio and cavity volume ratio on the natural frequency of the lattice reinforced sandwich structure with cavities are discussed.

  Results  By comparing with the finite element calculation results, the relative error of the natural frequency is less than 3%, and the correctness of this method is verified.

  Conclusions  The method discussed in this paper can calculate the natural vibration characteristics at medium and low frequencies of the lattice reinforced sandwich structure with cavities accurately and quickly by using clear mathematical models and simple formulas, which helps to study the law of the natural vibration characteristics easily.