Wave Propagation in Functionally Graded Re-Entrant Lattice Structures Using the Dynamic Stiffness Method and Wittrick–Williams Algorithm

Abstract

Functionally graded materials (FGMs) enhance the mechanical performance of homogeneous materials, while architected periodic structures enable lightweight designs with superior properties. This study investigates wave propagation in functionally graded re-entrant lattice (FG-RL) structures, combining the advantages of FGMs and architected lattices. The unit cell comprises three Timoshenko beam elements made of FGMs, incorporating axial deformation material properties varying through the thickness according to power-law, exponential, and trigonometric gradation profiles. Wave propagation analysis is carried out using the dynamic stiffness method (DSM) coupled with the Floquet–Bloch theorem, and the resulting eigenvalue problem is solved via the Wittrick–Williams algorithm. Two modeling approaches are explored: assigning identical power-law indices to all beams, and using different indices for each beam. Results reveal that increasing the power-law index reduces wave speed and shifts the frequency range without altering the overall shape of the dispersion curves. Additionally, material heterogeneity within the unit cell introduces bandgaps. The accuracy of the proposed method is validated through comparisons with FEM and COMSOL Multiphysics results. This work highlights the effectiveness of FGMs in tuning wave propagation behavior and offers a reliable framework for the design of advanced lattice structures with customizable dynamic characteristics.