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<p>The present work explores how material gradation influences the wave propagation behavior of two-dimensional hexagonal lattice structures with functionally graded properties. Each unit cell is represented by three Timoshenko beam elements incorporating axial deformation, where the material composition varies across the thickness according to a power-law profile. To analyze the frequency response, the dynamic stiffness framework is formulated in conjunction with the Floquet–Bloch periodicity conditions, and the Wittrick–Williams algorithm is employed to efficiently determine the eigenfrequencies. The study reveals that increasing the material gradient exponent in functionally graded hexagonal lattice (FG-HL) structures causes a non-monotonic decrease in frequency, with higher modes experiencing a more pronounced reduction. The dispersion and phase velocity plots demonstrate that higher material gradient exponents lead to increased wave hindrance and slower propagation speeds. Additionally, assigning different material gradient exponents to the beams within each unit cell leads to band gap widening due to enhanced wave reflections at the material junctions. The proposed framework effectively integrates geometric periodicity with functional grading in a planar functionally graded hexagonal lattice, allowing enhanced control over wave propagation mechanisms. The accuracy of the results is validated through Finite Element Method (FEM) simulations, and this validation is further confirmed using COMSOL Multiphysics. These findings offer valuable insights into the design of advanced lattice structures with optimized vibration and wave control properties, enabling applications such as vibration isolation, wave filtering, and energy harvesting.</p>

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Impact of material gradation on wave dynamics in hexagonal lattices

  • 期刊论文

  • 发表日期：

    2026年1月6日

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  • Mudit Mishra,
  • Sandeep Kumar

摘要

The present work explores how material gradation influences the wave propagation behavior of two-dimensional hexagonal lattice structures with functionally graded properties. Each unit cell is represented by three Timoshenko beam elements incorporating axial deformation, where the material composition varies across the thickness according to a power-law profile. To analyze the frequency response, the dynamic stiffness framework is formulated in conjunction with the Floquet–Bloch periodicity conditions, and the Wittrick–Williams algorithm is employed to efficiently determine the eigenfrequencies. The study reveals that increasing the material gradient exponent in functionally graded hexagonal lattice (FG-HL) structures causes a non-monotonic decrease in frequency, with higher modes experiencing a more pronounced reduction. The dispersion and phase velocity plots demonstrate that higher material gradient exponents lead to increased wave hindrance and slower propagation speeds. Additionally, assigning different material gradient exponents to the beams within each unit cell leads to band gap widening due to enhanced wave reflections at the material junctions. The proposed framework effectively integrates geometric periodicity with functional grading in a planar functionally graded hexagonal lattice, allowing enhanced control over wave propagation mechanisms. The accuracy of the results is validated through Finite Element Method (FEM) simulations, and this validation is further confirmed using COMSOL Multiphysics. These findings offer valuable insights into the design of advanced lattice structures with optimized vibration and wave control properties, enabling applications such as vibration isolation, wave filtering, and energy harvesting.