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<p>Inspired by the hierarchical multi-periodic structures ubiquitous in nature, a three-dimensional (3D) hierarchical phononic crystal is proposed. The diverse band gap generation mechanisms within these complex 3D periodic configurations are investigated, and vibration attenuation is achieved through the exploitation of these band gap characteristics. In the proposed 3D hierarchical phononic crystal, variable cross-section cylinders with varying radii are adopted as the fundamental micro-unit cells. Through periodic arrangement of these micro-unit cells, the macroscopic unit cell is constructed. Dispersion band curves are computed via finite element numerical simulation incorporating Bloch periodic boundary conditions. The energy band structure exhibits tortuous and relatively flat energy band curves, corresponding respectively to macro- and micro- unit cell vibration modes. The influence of structural parameters on tortuous and flat band gaps is investigated. It is demonstrated that the vibration characteristics of the macro- and micro-unit cells are pivotal in regulating diverse band gap types. Furthermore, the vibration attenuation properties of a 2 × 2 × 2 periodic 3D hierarchical phononic crystal model are analyzed across various directions and positions. Effective vibration attenuation is observed even with a limited number of periods. An experimental prototype is fabricated via additive manufacturing (3D printing) and validated through vibration testing. The experimentally observed vibration suppression performance is found to be in good agreement with the numerical predictions. This study advances the understanding of band gap mechanisms in hierarchical periodic structures and elucidates the design principles for regulating band gaps via different substructures.</p>

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Research on Multi-type Band Gaps and Vibration Reduction Characteristics of Three-Dimensional Hierarchical Phononic Crystals

  • 期刊论文

  • 发表日期：

    2026年7月20日

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  • Jiping Jing,
  • Zhijing Wu

摘要

Inspired by the hierarchical multi-periodic structures ubiquitous in nature, a three-dimensional (3D) hierarchical phononic crystal is proposed. The diverse band gap generation mechanisms within these complex 3D periodic configurations are investigated, and vibration attenuation is achieved through the exploitation of these band gap characteristics. In the proposed 3D hierarchical phononic crystal, variable cross-section cylinders with varying radii are adopted as the fundamental micro-unit cells. Through periodic arrangement of these micro-unit cells, the macroscopic unit cell is constructed. Dispersion band curves are computed via finite element numerical simulation incorporating Bloch periodic boundary conditions. The energy band structure exhibits tortuous and relatively flat energy band curves, corresponding respectively to macro- and micro- unit cell vibration modes. The influence of structural parameters on tortuous and flat band gaps is investigated. It is demonstrated that the vibration characteristics of the macro- and micro-unit cells are pivotal in regulating diverse band gap types. Furthermore, the vibration attenuation properties of a 2 × 2 × 2 periodic 3D hierarchical phononic crystal model are analyzed across various directions and positions. Effective vibration attenuation is observed even with a limited number of periods. An experimental prototype is fabricated via additive manufacturing (3D printing) and validated through vibration testing. The experimentally observed vibration suppression performance is found to be in good agreement with the numerical predictions. This study advances the understanding of band gap mechanisms in hierarchical periodic structures and elucidates the design principles for regulating band gaps via different substructures.