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Aims <p>Conventional noise control materials and structures are often limited by narrow effective frequency ranges, insufficient low-frequency attenuation, and bulky configurations, which makes them increasingly insufficient for meeting the rising demands on acoustic environmental quality. The incorporation of fractal geometry into phononic crystals provides a new pathway for sound insulation design.</p> Method <p>In this work, a three-dimensional phononic crystal based on a Menger sponge fractal core (MSPC) is proposed, in which multiple local resonant cavity are formed through the coupling between the fractal core and the surrounding shell. The band structures and sound transmission loss (STL) of both two-dimensional and three-dimensional MSPCs are analyzed using a finite-element method based on Bloch theory. The effects of key structural parameters on bandgap characteristics are systematically examined via parametric scanning, and the underlying bandgap formation mechanisms are interpreted through acoustic impedance analysis. In addition, prototype samples are fabricated, and impedance tube experiments based on the dual-load method are conducted for experimental validation.</p> Results <p>The results demonstrate that the proposed MSPC can generate multiple acoustic bandgaps accompanied by a significant enhancement of STL over the corresponding frequency ranges. The characteristic size of the Menger sponge core has the most pronounced influence on the bandgap boundaries, while variations in channel length and fractal factor induce systematic frequency shifts. Impedance analysis reveals that near-resonant conditions lead to near-zero real impedance at side-branch entrances and maximum transmission impedance, effectively suppressing acoustic wave propagation. Experimental measurements show good agreement with numerical predictions.</p> Conclusions <p>By exploiting multiple Helmholtz-type resonance mechanisms, the Menger sponge fractal phononic crystal enables efficient broadband noise insulation and provides a promising structural strategy for advanced noise control applications.</p>

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Bandgap Analysis and Experiment Investigation of Phnonic Crystals with Menger Sponge Fractal Geometry Core

  • 期刊论文

  • 发表日期：

    2026年5月29日

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  • Lv Haiting,
  • Chen Changzheng,
  • Zhang Dacheng,
  • Li Xuelai,
  • Sun Lulu

摘要

Aims

Conventional noise control materials and structures are often limited by narrow effective frequency ranges, insufficient low-frequency attenuation, and bulky configurations, which makes them increasingly insufficient for meeting the rising demands on acoustic environmental quality. The incorporation of fractal geometry into phononic crystals provides a new pathway for sound insulation design.

Method

In this work, a three-dimensional phononic crystal based on a Menger sponge fractal core (MSPC) is proposed, in which multiple local resonant cavity are formed through the coupling between the fractal core and the surrounding shell. The band structures and sound transmission loss (STL) of both two-dimensional and three-dimensional MSPCs are analyzed using a finite-element method based on Bloch theory. The effects of key structural parameters on bandgap characteristics are systematically examined via parametric scanning, and the underlying bandgap formation mechanisms are interpreted through acoustic impedance analysis. In addition, prototype samples are fabricated, and impedance tube experiments based on the dual-load method are conducted for experimental validation.

Results

The results demonstrate that the proposed MSPC can generate multiple acoustic bandgaps accompanied by a significant enhancement of STL over the corresponding frequency ranges. The characteristic size of the Menger sponge core has the most pronounced influence on the bandgap boundaries, while variations in channel length and fractal factor induce systematic frequency shifts. Impedance analysis reveals that near-resonant conditions lead to near-zero real impedance at side-branch entrances and maximum transmission impedance, effectively suppressing acoustic wave propagation. Experimental measurements show good agreement with numerical predictions.

Conclusions

By exploiting multiple Helmholtz-type resonance mechanisms, the Menger sponge fractal phononic crystal enables efficient broadband noise insulation and provides a promising structural strategy for advanced noise control applications.