A lattice-reinforced sandwich structure with cavities was presented, which had prospects of the integration of both mechanical and acoustic properties. In order to predict the equivalent modulus of lattice-reinforced core materials with cavities, a multi-level equivalent micromechanical mathematical model was built, which was made up of cavities, lattice reinforcements and foam matrices. With the reinforcements and cavities distributing periodically in the core, the representative unit of the equivalent model was established. Based on the Mori-Tanaka method, the single-phase inclusion equivalent was performed twice and the equivalent modulus of lattice-reinforced core materials with cavities were obtained which agree well with the experimental results and those determined using the FEM method. The numerical simulation was then conducted via the ANSYS code package to obtain the bending deformations and the natural frequencies of both the actual model and the equivalent mode, and the equivalent modulus of the core was used as the material parameter of the core of the equivalent model. The simulation results conform highly with each other and the relative errors of both the bending deformation displacements and the natural frequencies at low frequency are less than 2%, which satisfy the precision requirement in engineering.On this premise, further research was conducted to investigate the effects of reinforcements and cavities volume ratio on the equivalent modulus of the core. The results indicate that the above method can predict equivalent modulus of lattice-reinforced core materials with cavities accurately and quickly with a clear mathematical mode and simple formulas.
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