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<p>This study investigates the band gap properties and topology optimization of one-dimensional piezoelectric–elastic and piezoelectric–viscoelastic phononic crystal rods using the finite element method (FEM) and a genetic algorithm (GA). The FEM is used to compute the dispersion curves, and the results are validated against the plane wave expansion method (PWEM) and published results. The effects of electrical boundary conditions on band gap width are analyzed. The introduction of viscoelasticity further modifies the band gap characteristics, while the modulus ratio and relaxation time are identified as key parameters governing the band gap behavior. To maximize the first band gap, a GA-based topology optimization scheme is implemented. The optimized designs significantly widen the first band gap to about five times that of the initial configurations under both electrical boundary conditions. Specifically, under short-circuit and open-circuit conditions, the band gap width of the&#xa0;piezoelectric–elastic rod increases from 4.1 to 20.4&#xa0;kHz and from 4.4 to 24.2&#xa0;kHz, respectively, and that of the&#xa0;piezoelectric–viscoelastic rod increases from 4.3 to 21.5&#xa0;kHz and from 5.5 to 25.4&#xa0;kHz, respectively, both indicating a larger band gap widening under the open-circuit condition, thus demonstrating the effects of piezoelectricity on band gap. The optimized sandwich-like layout, with piezoelectric phases at both ends and elastic/viscoelastic phases in the middle, shows superior wave suppression capability. This work establishes a dual strategy framework for phononic crystal design which integrates material property modulation with topology optimization and provides a theoretical tool for developing tunable phononic crystals in intelligent vibration and acoustic filtering applications.</p>

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Band gap optimization of viscoelectroelastic phononic crystal rods based on genetic algorithm

  • 期刊论文

  • 发表日期：

    2026年5月27日

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  • Xiaohua Wu,
  • Mengyuan Gao,
  • Guannan Wang,
  • Zhelong He,
  • Sandro Luis Vatanabe,
  • Emílio Carlos Nelli Silva

摘要

This study investigates the band gap properties and topology optimization of one-dimensional piezoelectric–elastic and piezoelectric–viscoelastic phononic crystal rods using the finite element method (FEM) and a genetic algorithm (GA). The FEM is used to compute the dispersion curves, and the results are validated against the plane wave expansion method (PWEM) and published results. The effects of electrical boundary conditions on band gap width are analyzed. The introduction of viscoelasticity further modifies the band gap characteristics, while the modulus ratio and relaxation time are identified as key parameters governing the band gap behavior. To maximize the first band gap, a GA-based topology optimization scheme is implemented. The optimized designs significantly widen the first band gap to about five times that of the initial configurations under both electrical boundary conditions. Specifically, under short-circuit and open-circuit conditions, the band gap width of the piezoelectric–elastic rod increases from 4.1 to 20.4 kHz and from 4.4 to 24.2 kHz, respectively, and that of the piezoelectric–viscoelastic rod increases from 4.3 to 21.5 kHz and from 5.5 to 25.4 kHz, respectively, both indicating a larger band gap widening under the open-circuit condition, thus demonstrating the effects of piezoelectricity on band gap. The optimized sandwich-like layout, with piezoelectric phases at both ends and elastic/viscoelastic phases in the middle, shows superior wave suppression capability. This work establishes a dual strategy framework for phononic crystal design which integrates material property modulation with topology optimization and provides a theoretical tool for developing tunable phononic crystals in intelligent vibration and acoustic filtering applications.