Research on low-frequency sound insulation characteristics of metamaterials based on coupling of local resonance and Helmholtz resonators

Wenmin  Zhang; Shangshuai  Jia; Xinli  Zhao; Lixin  Zheng; Cai  Zeng

doi:10.59400/sv3676

Research on low-frequency sound insulation characteristics of metamaterials based on coupling of local resonance and Helmholtz resonators

Wenmin Zhang
CRRC Tangshan Co., Ltd., Tangshan 064099, China
Shangshuai Jia
CRRC Tangshan Co., Ltd., Tangshan 064099, China
Xinli Zhao
CRRC Tangshan Co., Ltd., Tangshan 064099, China
Lixin Zheng
State Key Laboratory of Rail Transit Vehicle System, Southwest Jiaotong University, Chengdu 610031, China
Cai Zeng
School of Electrical Engineering, Southwest Jiaotong University, Chengdu 610031, China

Article ID: 3676

DOI: https://doi.org/10.59400/sv3676

Keywords: acoustic metamaterials; local resonance; Helmholtz resonator; impedance tube testing

Abstract

This study addresses the challenge of low-frequency noise control by proposing a novel composite acoustic metamaterial that synergistically couples a multilayer locally resonant acoustic metamaterial (MLRAM) with a dual-cavity Helmholtz resonator. The research systematically investigates the sound insulation performance through an integrated approach combining theoretical analysis, finite element simulation, and impedance tube experimentation. Results demonstrate that while the MLRAM structure generates a significant sound insulation peak of 44.5 dB at 214 Hz, it is accompanied by a pronounced insulation valley of 6.4 dB at 228 Hz. To mitigate this limitation, a dual-cavity Helmholtz resonator was designed, achieving near-perfect absorption (α > 0.99) and corresponding insulation peaks at 236 Hz and 316 Hz. The integrated composite structure effectively elevates the original insulation valley by 3.0 dB and introduces a new insulation peak of 32.0 dB at 311 Hz. Parametric studies reveal that the resonance frequencies can be precisely tuned by adjusting the neck geometry, and increasing the number of cavities broadens the effective bandwidth at the expense of peak amplitude. After optimization, the composite structure achieves a remarkable valley improvement of up to 10.8 dB and an average sound transmission loss of 21.0 dB, significantly enhancing broadband low-frequency sound insulation performance. This work provides a validated strategy for active "valley compensation" in acoustic metamaterials.

Published

2025-10-29

How to Cite

Zhang, W., Jia, S., Zhao, X., Zheng, L., & Zeng, C. (2025). Research on low-frequency sound insulation characteristics of metamaterials based on coupling of local resonance and Helmholtz resonators. Sound & Vibration, 59(5). https://doi.org/10.59400/sv3676

Download Citation

Issue

Vol. 59 No. 5 (2025)

Section

Article

This work is licensed under a Creative Commons Attribution 4.0 International License.

References

[1]Thompson DJ, Hemsworth B, Vincent N. Experimental validation of the TWINS prediction program for rolling noise, part 1: Description of the model and method. Journal of Sound and Vibration. 1996; 193(1): 123–135.

[2]Feng T, Wang YH, Wang J, et al. Progress in research and application of structural acoustic metamaterials. Journal of Vibration and Shock. 2021; 40(20): 150–157. (in Chinese)

[3]Liu ZY, Chan CT, Sheng P. Analytic model of phononic crystals with local resonances. Physical Review B. 2005; 71(1): 014103.

[4]Fang N, Xi DJ, Xu JY, et al. Ultrasonic metamaterials with negative modulus. Nature Materials. 2006; 5: 452–456.

[5]Deng K, Ding YQ, He ZJ, et al. Graded negative index lens with designable focal length by phononic crystal. Journal of Physics D: Applied Physics. 2009; 42(18): 185505.

[6]Wang G, Wen XS, Wen JH, et al. Quasi-one-dimensional periodic structure with locally resonant band gap. Journal of Applied Mechanics. 2006; 73(1): 167–170.

[7]Janssen S, Van Belle L, de Melo Filho NGR, et al. Improving the noise insulation performance of vibro-acoustic metamaterial panels through multi-resonant design. Applied Acoustics. 2023; 213: 109622.

[8]Oudich M, Li Y, Assouar MB, et al. A sonic band gap based on locally resonant phononic plates with stubs. New Journal of Physics. 2010; 12(8): 083049.

[9]Oudich M, Senesi M, Assouar MB, et al. Experimental evidence of locally resonant sonic band gap in two-dimensional phononic stubbed plates. Physical Review B. 2011; 84(16): 165136.

[10]Xiao Y, Wen JH, Wen XS. Sound transmission loss of metamaterial-based thin plates with multiple subwavelength arrays of attached resonators. Journal of Sound and Vibration. 2012; 331(25): 5408–5423.

[11]Ho KM, Cheng CK, Yang Z, et al. Broadband locally resonant sonic shields. Applied Physics Letters. 2003; 83(26): 5566–5568.

[12]Naify CJ, Chang CM, McKnight G, et al. Transmission loss of membrane-type acoustic metamaterials with coaxial ring masses. Journal of Applied Physics. 2011; 110(12): 124903.

[13]Naify CJ, Chang CM, McKnight G, et al. Scaling of membrane-type locally resonant acoustic metamaterial arrays. Journal of the Acoustical Society of America. 2012; 132: 2784–2792.

[14]Zhang YG, Wen JH, Zhao HG, et al. Sound insulation property of membrane-type acoustic metamaterials carrying different masses at adjacent cells. Journal of Applied Physics. 2013; 114(6): 063515.

[15]Wang XP, Chen YY, Zhou GJ, et al. Synergetic coupling large-scale plate-type acoustic metamaterial panel for broadband sound insulation. Journal of Sound and Vibration. 2019; 459: 114867.

[16]Ingard U. On the radiation of sound into a circular tube with an application to resonators. Journal of the Acoustical Society of America. 1948; 20(5): 665–682.

[17]Selamet A, Lee I. Helmholtz resonator with extended neck. Journal of the Acoustical Society of America. 2003; 113(4): 1975–1985.

[18]Zhang WT, Xin FX. Broadband low-frequency sound absorption via Helmholtz resonators with porous material lining. Journal of Sound and Vibration. 2024; 578: 118330.

[19]Sun P, Xu SQ, Wang XL, et al. Sound absorption of space-coiled metamaterials with soft walls. International Journal of Mechanical Sciences. 2024; 261: 108696.

[20]Bi SH, Wang ES, Shen XM, et al. Enhancement of sound absorption performance of Helmholtz resonators by space division and chamber grouping. Applied Acoustics. 2023; 207: 109352.

[21]Li HM, Wu JW, Yan SL, et al. Design and study of broadband sound absorbers with partition based on micro-perforated panel and Helmholtz resonator. Applied Acoustics. 2023; 205: 109262.

[22]Yamamoto T. Acoustic metamaterial plate embedded with Helmholtz resonators for extraordinary sound transmission loss. Journal of Applied Physics. 2018; 123(21): 215110.

[23]Laly Z, Mechefske C, Ghinet S, et al. Sound attenuation analysis of a honeycomb structure with extended necks. In: Proceedings of the 2023 International Congress on Noise Control Engineering; 20–23 August 2023; Tokyo, Japan.

[24]Langfeldt F, Khatokar AJ, Gleine W. Plate-type acoustic metamaterials with integrated Helmholtz resonators. Applied Acoustics. 2022; 199: 109019.

[25]Gu JT, Tang YH, Wang XL, et al. Laminated plate-type acoustic metamaterials with Willis coupling effects for broadband low-frequency sound insulation. Composite Structures. 2022; 292: 115689.

[26]Yang XH, Kang YZ, Xie XX, et al. Multilayer coupled plate-type acoustic metamaterials for low-frequency broadband sound insulation. Applied Acoustics. 2023; 209: 109399.

This paper introduces a universal framework for understanding the vibration responses of systems subjected to harmonic excitation. By examining a simplified cylinder-spring-damper model, the study refurbishes traditional scaling methods for the excitation frequency ratio and critical damping ratio. The findings indicate that in damped systems, the maximum amplitude of vibration does not align with the natural frequency. This observation leads to the introduction of a new scaling method for reduced frequency. This new approach aligns resonance peaks at the new reduced velocity of 1.0 across different damping ratios, providing a consistent characterization of vibration behavior. A new critical damping ratio of 0.707 is identified for an excited system as opposed to the traditional damping ratio of 1.0 for an unexcited system. Key properties such as maximum amplitude, phase lag, bandwidth, and quality factor are analyzed, demonstrating that the proposed reduced frequency and critical damping ratio effectively capture the dynamics of both damped and undamped excited systems. The findings offer significant insights for practical applications in engineering and various scientific fields.

This study makes significant contributions to the field of ultrasonic testing (UT) by offering a novel approach to the identification of artificially introduced defects within Japanese cedar wood (Cryptomeria japonica). The findings are of particular relevance for the heritage conservation and construction sectors, where non-invasive defect detection is paramount. The study establishes a robust framework for assessing the structural integrity of timber by correlating ultrasonic wave velocity reductions with defect size and distribution. Big-sized defects led to more substantial decreases in wave velocity. The study establishes a robust framework for assessing the structural integrity of historical timber by correlating ultrasonic wave velocity reductions with defect size and distribution. This framework has the potential to be applicable to diverse wood species and defect types.

The control of vehicle interior noise has become a critical metric for assessing noise, vibration, and harshness (NVH) in vehicles. During the initial phases of vehicle development, accurately predicting the impact of road noise on interior noise is essential for reducing noise levels and expediting the product development cycle. In recent years, data-driven methods based on machine learning have gained significant attention due to their robust capability in navigating complex data mapping relationships. Notably, surrogate models have demonstrated exceptional performance in this domain. Numerous researchers have integrated diverse intelligent algorithms into the study of vehicle noise, leveraging advantages such as the elimination of precise modeling requirements, extensive solution space exploration, continuous learning from data, and robust algorithmic versatility. However, in NVH engineering applications, data-driven models face inherent limitations, particularly in interpretability and stability. To address these issues, this paper introduces an improved Long Short-Term Memory (LSTM) network that combines knowledge and data. Inspired by the physical information neural network concept, this approach incorporates values calculated through empirical formulas into the neural network as constraints. Comparative assessments with traditional LSTM networks highlight the advantages of this deep learning model. By integrating empirical formulas constraints, the model not only enhances interpretability but also achieves robust generalization with fewer data samples. The proposed method is validated on a specific vehicle model, showing significant improvements in prediction accuracy and efficiency.