Simulation Study of Low-Frequency Bandgap for Triple Helix Beam Phononic Crystal

doi:10.16553/j.cnki.issn1000-985x.2025.0138

Abstract

Abstract: To mitigate low-frequency vibrational disturbances in engineering applications， this study proposes a triple-helix beam phononic crystal configuration， comprehensive finite element analysis and equivalent modeling demonstrating its superior low-frequency vibration attenuation characteristics. The results indicate that the phononic crystal exhibits a complete bandgap in the range of 47~99 Hz. Within this bandgap， the effective mass became negative， confirming the full reflection vibration isolation mechanism. Transmission loss simulations further corroborate substantial vibration energy attenuation across the bandgap frequencies. Additionally， the phononic crystals demonstrate robust vibration isolation performance under diverse loading conditions， including distributed， concentrated， and torsional loads. The parametric optimization study reveals that precise adjustment of the helix plate thickness， groove width and cylindrical oscillator radius enabled the realization of the band structure with lower frequency and significantly greater bandwidth. This study provides valuable insights and practical engineering significance for low-frequency vibration mitigation.

Key words: phononic crystal; local resonance; low-frequency vibration reduction; bandgap characteristic; equivalent quality; transmission loss

CLC Number:

O735

XUE Jingyi, HU Qiguo, YAN Zhaoqiang, LIU Ying, ZHANG Pizhu. Simulation Study of Low-Frequency Bandgap for Triple Helix Beam Phononic Crystal[J]. Journal of Synthetic Crystals, 2025, 54(12): 2127-2135.

Figures/Tables 11

Fig.1 Schematic diagram of a three-helix beam phononic crystal. （a） Axial view；（b） top view；（c） structural schematic diagram

Table 1 Geometrical parameters of the crystal cell

Geometric parameter	a	h	R	r	n	w	r_z	t_p	t_s
Value/mm	40	30	18.6	11.5	0.8	1	4	2	1

Fig.2 First irreducible Brillouin zone

Table 2 Material parameters of the crystal cell

Material	Density/（kg·m^-3）	Elastic modulus/Pa	Poisson ratio
Lead	11 600	4.08×10¹⁰	0.369
Epoxy resin	1 180	4.35×10⁹	0.367

Fig.3 Energy band structure diagram

Fig.4 Local resonance modes for different wave numbers k

Fig.5 Spring-mass diagram

Fig.6 Equivalent negative mass diagram

Fig.7 Transmission loss curves

Fig.8 Numerical simulation of phononic crystal plates under different operating conditions. （a） Line load；（b） front end line load；（c） point load；（d） torque

Fig.9 Effect of geometric parameter variations on bandgap. （a） Effect of helix plate thickness tp on band gap；（b） effect of cylindrical vibrator radius rz on band gap；（c） effect of helix groove width w on band gap

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