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<p>This study proposes a novel computational method, the plane wave expansion/finite element (<i>PWE/FE</i>) method, to solve the governing equations of <i>PC</i> beams under multi-physics field coupling across multiple scales. The proposed method integrates the theoretical foundations of the plane wave expansion and finite element methods, exploiting the structural periodicity to decompose the displacement field. By incorporating Bloch's theorem, the approach is implemented using the partial differential equation module in COMSOL Multiphysics 6.2, a widely used finite element software. Rigorous validation through comparative numerical simulations and experimental measurements confirms the method's accuracy. By way of example analysis, it is found that an increase of one order of magnitude in the height of the beam will correspondingly increase the frequency band where the bandgap is located by one order of magnitude, and the applied voltage required to change the bandgap frequency band needs to be increased by several orders of magnitude. The <i>PWE/FE</i> analysis reveals significant dependencies of bandgap properties in piezoelectric <i>PC</i> and nanoscale <i>PC</i> structures on three key factors: piezoelectric coupling coefficients, size-dependent effects at the nanoscale and dimensional parameters.</p>

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PWE/FE: a novel approach tailored for investigating the structure of coupled phononic crystal beams with multiple physical fields at multiple scales

  • 期刊论文

  • 发表日期：

    2025年7月6日

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  • Denghui Qian,
  • Guoqing Liu,
  • Feiyang He

摘要

This study proposes a novel computational method, the plane wave expansion/finite element (PWE/FE) method, to solve the governing equations of PC beams under multi-physics field coupling across multiple scales. The proposed method integrates the theoretical foundations of the plane wave expansion and finite element methods, exploiting the structural periodicity to decompose the displacement field. By incorporating Bloch's theorem, the approach is implemented using the partial differential equation module in COMSOL Multiphysics 6.2, a widely used finite element software. Rigorous validation through comparative numerical simulations and experimental measurements confirms the method's accuracy. By way of example analysis, it is found that an increase of one order of magnitude in the height of the beam will correspondingly increase the frequency band where the bandgap is located by one order of magnitude, and the applied voltage required to change the bandgap frequency band needs to be increased by several orders of magnitude. The PWE/FE analysis reveals significant dependencies of bandgap properties in piezoelectric PC and nanoscale PC structures on three key factors: piezoelectric coupling coefficients, size-dependent effects at the nanoscale and dimensional parameters.