Synergistic design of ultra-wide low-frequency continuous bandgap metastructure for audible noise attenuation

doi:10.1007/s10483-026-3361-7

摘要/Abstract

Abstract:

Local resonant acoustic metamaterials have broad applications in sound insulation, yet their single-configuration designs often exhibit limited and discontinuous bandgap widths, hindering full-frequency noise attenuation across the human auditory range. This study presents a double-phase fidget-spinner-shaped acoustic metamaterial (DFAM), specifically designed to achieve an ultra-broad, low-frequency continuous bandgap by means of synergistic structural optimization, enabling effective and robust control of audible noise. Based on Bloch’s theorem and the finite element method, the dispersion relation of the DFAM structure is calculated and verified by the transmission loss curves. The propagation characteristics of sound waves within the structure are further analyzed for noise frequencies that fall within the passband. The influence of the geometric and physical parameters on the bandgap is investigated, and the corresponding transmission loss in the propagation direction is further calculated. A hybrid collaborative design strategy, leveraging multi-parameter optimization and bandgap complementarity, is developed to construct a metastructure with continuous bandgap coverage from 20 Hz to 1 000 Hz. The resulting metastructure demonstrates exceptional broadband noise attenuation, achieving a total bandgap width of 876.3 Hz (87.63% of the target range) with the transmission loss up to -762.78 dB in a three-periodic arrangement. The simulation and experimental results for the transmission loss of the DFAM metastructure show strong agreement in the low-frequency range. This work provides a novel framework for designing ultra-wide low-frequency continuous bandgap metastructures, offering significant potential for noise mitigation in complex environments.

Key words: acoustic metastructure, local resonance, continuous bandgap, noise attenuation, synergistic design

中图分类号:

TB53

. [J]. Applied Mathematics and Mechanics (English Edition), 2026, 47(3): 473-496.

Dongxu GUO, Xiaolong ZHANG, Ruilan TIAN, Xiangyang LI, Minghao WANG. Synergistic design of ultra-wide low-frequency continuous bandgap metastructure for audible noise attenuation[J]. Applied Mathematics and Mechanics (English Edition), 2026, 47(3): 473-496.

图/表 17

Structure	Disc material	a/mm	p/mm	t/mm	$θ / (∘)$	r/mm
DFAM-65-C-12	Copper	80	16	0.5	65	12
DFAM-65-S-2.5	Steel	80	16	0.5	65	2.5
DFAM-65-S-1.5	Steel	80	16	0.5	65	1.5
DFAM-40-S-12	Steel	80	16	0.5	40	12

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No.	Bandgap location	Lower boundary/Hz	Upper boundary/Hz	Bandgap wide/Hz
1	3rd-4th	5.03	6.05	1.02
2	7th-8th	20.24	27.77	7.53
3	9th-10th	37.15	45.96	8.81
4	10th-11th	46.59	112.74	66.15
5	12th-13th	112.95	136.55	23.61
6	14th-15th	224.53	312.03	87.50
7	16th-17th	312.12	599.68	287.56
8	18th-19th	599.93	906.12	306.19
9	20th-21st	906.27	994.20	87.93