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<p>This paper investigates the influence of material property gradients on the wave propagation characteristics of 2D square lattice structures. The unit cell is modeled using three functionally graded Timoshenko beam elements, incorporating axial extension. The beam elements are composed of Functionally Graded Material (FGM) with a transverse power-law distribution. The dynamic stiffness method, in combination with the Floquet–Bloch theorem, is used to formulate the stiffness matrix, while the Wittrick–Williams algorithm is applied as the solution technique. Three distinct approaches are explored in this study: assigning a uniform power-law index to all elements within the unit cell, assigning a variable power-law index to each element, and maintaining a uniform power-law index while assigning different cross-sectional properties to each element. Results show that altering the material gradient scales frequency magnitudes uniformly without affecting the shapes of dispersion curves. A decrease in wave propagation speed is observed as the power-law index increases. Additionally, the band diagram highlights the emergence of band gaps when the unit cell elements have distinct cross-sections and gradients. Validation through the&#xa0;finite element method and COMSOL Multiphysics confirms accuracy. This study highlights the potential of FGMs in tailoring wave propagation properties and offers a design framework for advanced lattice structures.</p>

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Analysis of Wave Propagation in Functionally Graded Square Lattice Structures Using the Dynamic Stiffness Method Combined with the Wittrick–Williams Algorithm

  • 期刊论文

  • 发表日期：

    2025年6月4日

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  • Mudit Mishra,
  • Sandeep Kumar

摘要

This paper investigates the influence of material property gradients on the wave propagation characteristics of 2D square lattice structures. The unit cell is modeled using three functionally graded Timoshenko beam elements, incorporating axial extension. The beam elements are composed of Functionally Graded Material (FGM) with a transverse power-law distribution. The dynamic stiffness method, in combination with the Floquet–Bloch theorem, is used to formulate the stiffness matrix, while the Wittrick–Williams algorithm is applied as the solution technique. Three distinct approaches are explored in this study: assigning a uniform power-law index to all elements within the unit cell, assigning a variable power-law index to each element, and maintaining a uniform power-law index while assigning different cross-sectional properties to each element. Results show that altering the material gradient scales frequency magnitudes uniformly without affecting the shapes of dispersion curves. A decrease in wave propagation speed is observed as the power-law index increases. Additionally, the band diagram highlights the emergence of band gaps when the unit cell elements have distinct cross-sections and gradients. Validation through the finite element method and COMSOL Multiphysics confirms accuracy. This study highlights the potential of FGMs in tailoring wave propagation properties and offers a design framework for advanced lattice structures.