Energy-equivalent homogenization for efficient modal prediction of periodic composite sandwich structures

Abstract

This study proposes an energy-equivalent homogenization method for efficient prediction of the out-of-plane modal response of periodic composite sandwich structures based on Hamilton’s principle. The original grid-stiffened composite sandwich core is replaced by an equivalent orthotropic continuum whose parameters are derived from the strain-energy and kinetic-energy equivalence of a representative unit cell. The concept of effective participating deformation volume is used to accurately determine the main deformation regions of the unit cell under different generalized deformation modes, thereby simplifying the energy expressions while maintaining the accuracy of the equivalent model. The equivalent parameters can be directly implemented using the built-in orthotropic material model in ABAQUS, without user subroutines. Compared with the out-of-plane modal analysis of the original model, the equivalent model reduces the degrees of freedom by 88.88% and the wall-clock solution time from 444 s to 25 s, while the natural-frequency errors remain below 5% and the Modal Assurance Criterion (MAC) values are higher than 0.99. Parametric studies show that the main factor affecting the equivalent accuracy is the ratio between modal wavelength and unit-cell size. Numerical comparisons also indicate that the proposed method maintains good predictive accuracy for the investigated structures with continuously varying curvature.