A Homogenization-Enabled Analytical Solution Framework for Free Vibration of Lattice Sandwich Panels

Lightweight lattice sandwich panels combine high stiffness-to-weight ratios with tailored vibration performance, making them ideal for aerospace structures. However, exact dynamic analysis of these structures remains computationally intensive and is frequently constrained by simplified boundary condition assumptions. This study proposes a novel solution framework that combines the asymptotic homogenization method (AHM) with the finite integral transform (FIT) method. The framework (1) uses the AHM to model a periodic lattice sandwich panel as an equivalent orthotropic thin plate, and (2) derives analytical natural frequency and mode shape solutions under non-Lévy-type boundary conditions via the FIT method. Comprehensive experimental and numerical validation demonstrates the accuracy and reliability of the AHM when applied to equivalent property prediction of lattice sandwich structures. All FIT-based analytical results achieve convergence to 5 significant digits within 15 terms, and demonstrate a maximum error of less than 1% when compared with the results from the finite element method-based equivalent model.