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<p>Metamaterials’ design and development are a fast-growing field with unlimited potential in aircraft, acoustics, and telecommunications. Adding a gradient to materials could change wave behavior, making them useful for wave control. This study examines the impact of graded material distribution on dynamic wave transmission in 2D lattice structures. Three distinct lattice configurations, regular diamond, chiral, and triangular layouts, are used in the investigation. All lattices’ unit cell is represented using a Timoshenko beam with axial extension. Material inhomogeneity in the cell elements is represented through functionally graded properties, incorporated using three gradation schemes: Power law, exponential, and trigonometric distributions. The stiffness matrix is formulated using the dynamic stiffness method combined with the Floquet–Bloch theorem, and the resulting eigenvalue system is solved using the Wittrick–Williams algorithm. This investigation shows that modifying the material property along the thickness direction does not affect the shapes of the dispersion curves but uniformly scales the frequency magnitudes in all three lattice structures. Iso-frequency contours show that increased material inhomogeneity indicates enhanced anisotropy and direction-dependent wave propagation. The velocity charts illustrate that wave-propagation’s phase speed decreases across all lattices as index of material gradient increases. Validating all dispersion curves with finite element analysis verifies the results’ accuracy and reliability. This work highlights the use of functionally graded materials in lattice structures to tailor wave-propagation characteristics.</p>

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Tunable wave propagation and band gap characteristics in functionally graded lattices with multiple topologies via dynamic stiffness and Floquet–Bloch formulation

  • 期刊论文

  • 发表日期：

    2026年3月30日

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  • Mudit Mishra,
  • Sandeep Kumar,
  • Ambuj Sharma

摘要

Metamaterials’ design and development are a fast-growing field with unlimited potential in aircraft, acoustics, and telecommunications. Adding a gradient to materials could change wave behavior, making them useful for wave control. This study examines the impact of graded material distribution on dynamic wave transmission in 2D lattice structures. Three distinct lattice configurations, regular diamond, chiral, and triangular layouts, are used in the investigation. All lattices’ unit cell is represented using a Timoshenko beam with axial extension. Material inhomogeneity in the cell elements is represented through functionally graded properties, incorporated using three gradation schemes: Power law, exponential, and trigonometric distributions. The stiffness matrix is formulated using the dynamic stiffness method combined with the Floquet–Bloch theorem, and the resulting eigenvalue system is solved using the Wittrick–Williams algorithm. This investigation shows that modifying the material property along the thickness direction does not affect the shapes of the dispersion curves but uniformly scales the frequency magnitudes in all three lattice structures. Iso-frequency contours show that increased material inhomogeneity indicates enhanced anisotropy and direction-dependent wave propagation. The velocity charts illustrate that wave-propagation’s phase speed decreases across all lattices as index of material gradient increases. Validating all dispersion curves with finite element analysis verifies the results’ accuracy and reliability. This work highlights the use of functionally graded materials in lattice structures to tailor wave-propagation characteristics.