基于压电分流的声学黑洞梁可调谐零反射设计

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振动与冲击 ›› 2025, Vol. 44 ›› Issue (9) : 223-230.

声学研究与应用

基于压电分流的声学黑洞梁可调谐零反射设计

安天鹏，王世龙，王作为*，张国渊

作者信息 +

Tunable zero reflection design of acoustic black hole beam based on piezoelectric shunt

AN Tianpeng, WANG Shilong, WANG Zuowei*, ZHANG Guoyuan

Author information +

文章历史 +

摘要

声学黑洞结构是同时满足轻量化、低功耗、高可靠性等振动控制性能要求的可行方案。实际声学黑洞结构尖端厚度截断会产生显著的波反射，导致能量耗散效率明显降低。声学黑洞结构临界耦合条件具有精确的零反射系数，可提高系统的能量耗散效率。本文设计了一种基于压电分流的声学黑洞梁结构，采用混合波基/瑞利-里兹方法推导了弯曲波反射系数半解析模型。通过改变电阻-电感分流电路参数，实现了声学黑洞梁结构单个和多重临界耦合条件。数值结果验证了提出的反射系数半解析模型有效性以及压电分流电路精确的临界耦合条件调谐能力。

Abstract

The acoustic black hole structure is a feasible scheme to meet the vibration control performance requirements of lightweight, low power consumption and high reliability simultaneously. The tip thickness truncation of acoustic black hole structures results in strong wave reflections which significantly reduce the energy dissipation efficiency. The critical coupling conditions of acoustic black hole structures can achieve accurate zero-reflection coefficients to improve the energy dissipation efficiency. In this paper, we design an acoustic black hole beam based on the piezoelectric shunting circuit. A semi-analytical model of reflection coefficients is derived for flexural waves using the hybrid wave-based/Rayleigh-Ritz method. Single and multiple critical coupling conditions are achieved by the parameter adjustment of the resistance-inductance shunt circuit. Numerical results demonstrate the validity of the semi-analytic model of reflection coefficients and the precise tuning ability of the piezoelectric shunting circuit in achieving critical coupling conditions.

导出引用

安天鹏, 王世龙, 王作为, 张国渊. 基于压电分流的声学黑洞梁可调谐零反射设计[J]. 振动与冲击, 2025, 44(9): 223-230

AN Tianpeng, WANG Shilong, WANG Zuowei, ZHANG Guoyuan. Tunable zero reflection design of acoustic black hole beam based on piezoelectric shunt[J]. Journal of Vibration and Shock, 2025, 44(9): 223-230

参考文献

[1] 黄薇, 季宏丽, 裘进浩, 等. 二维声学黑洞对弯曲波的能量聚集效应[J]. 振动与冲击, 2017, 36(09): 51-57+92.
HUANG Wei, JI Hongli, QIU Jinhao, et al. Energy focusing effect of two-dimensional acoustic black hole on flexural waves[J]. Journal of Vibration and Shock, 2017, 36(09): 51-57+92.
[2] 何璞, 王小东, 季宏丽, 等. 基于声学黑洞的盒式结构全频带振动控制[J]. 航空学报, 2020, 41(04): 134-143.
HE Pu, WANG Xiaodong, JI Hongli, et al. Full-band vibration control of box-type structure with acoustic black hole[J]. Acta Aeronautica et Astronautica Sinica, 2020, 41(04): 134-143.
[3] Zhang L, Sun X, Dietrich J, et al. Enhanced energy transfer and multimodal vibration mitigation in an electromechanical acoustic black hole beam[J]. Journal of Sound and Vibration, 2023, 561: 117841.
[4] 赵楠, 王禹, 陈林, 等. 分布式声学黑洞浮筏系统隔振性能研究[J]. 振动与冲击, 2022, 41(13): 75-80.
ZHAO Nan, WANG Yu, CHEN Lin. Vibration isolation performance of distributed acoustic black hole floating raft system[J]. Journal of Vibration and Shock, 2022, 41(13): 75-80.
[5] Pelat A, Gautier F, Conlon S C, et al. The acoustic black hole: A review of theory and applications[J]. Journal of Sound and Vibration, 2020, 476: 115316.
[6] Krylov V V, Tilman F. Acoustic ‘black holes’ for flexural waves as effective vibration dampers[J]. Journal of Sound and Vibration, 2004, 274(3-5): 605-619.
[7] Georgiev V B, Cuenca J, Gautier F, et al. Damping of structural vibrations in beams and elliptical plates using the acoustic black hole effect[J]. Journal of Sound and Vibration, 2011, 330(11): 2497-2508.
[8] Ma L, Cheng L. Topological optimization of damping layout for minimized sound radiation of an acoustic black hole plate[J]. Journal of Sound and Vibration, 2019, 458: 349-364.
[9] Huang W, Zhang H, Inman D J, et al. Low reflection effect by 3D printed functionally graded acoustic black holes[J]. Journal of Sound and Vibration, 2019, 450: 96-108.
[10] Cheer J, Hook K, Daley S. Active feedforward control of flexural waves in an Acoustic Black Hole terminated beam[J]. Smart Materials and Structures, 2021, 30(3): 035003.
[11] Hook K, Cheer J, Daley S. Control of vibration in a plate using active acoustic black holes[J]. Smart Materials and Structures, 2022, 31(3): 035033.
[12] Raybaud G, Lee J Y, Jeon W, et al. On the control of the absorption of an Acoustic Black Hole by using attached point supports[J]. Journal of Sound and Vibration, 2023, 548: 117562.
[13] Leng J, Romero-García V, Pelat A, et al. Interpretation of the acoustic black hole effect based on the concept of critical coupling[J]. Journal of Sound and Vibration, 2020, 471: 115199.
[14] 彭飞, 张欣超, 张洪辉, 等. 声学黑洞铝型材板结构减振特性仿真研究[J]. 噪声与振动控制, 2024, 44(01): 75-79+141.
PENG Fei, ZHANG Xinchao, ZHANG Honghui, et al. Simulation Study on Vibration Reduction Characteristics of Acoustic Black Hole Aluminum Profile Plate Structures[J]. Noise and Vibration Control, 2022, 41(13): 75-80.
[15] Raybaud G, Pelat A, Ouisse M, et al. Zero reflections by a 1D acoustic black hole termination using thermally controlled damping[J]. Journal of Sound and Vibration, 2021, 510: 116282.
[16] Raybaud G, Ouisse M, Leng J, et al. Control of bending wave reflection at beam terminations by thermally tunable subwavelength resonators[J]. Journal of Sound and Vibration, 2022, 530: 116918.
[17] 万志威, 朱翔, 李天匀, 等. 含压电分流阻尼的声学黑洞梁振动特性研究[J]. 振动与冲击, 2022, 41(09): 113-119+135.
WAN Zhiwei, ZHU Xiang, LI Tianyun, et al. Vibration characteristics of acoustic black hole beam with piezoelectric shunt damping [J]. Journal of Vibration and Shock, 2022, 41(09): 113-119+135.
[18] 李宁, 张景绘. 连续梁的压电分流阻尼模型[J]. 应用力学学报, 2006, (03): 398-402+510.
LI Ning, ZHANG Jinghui. Piezoelectric shunt damping model for continuous beams[J]. Chinese Journal of Applied Mechanics, 2006, (03): 398-402+510.
[19] Deng J, Guasch O, Zheng L, et al. Semi-analytical model of an acoustic black hole piezoelectric bimorph cantilever for energy harvesting[J]. Journal of Sound and Vibration, 2021, 494: 115790.
[20] Thomas O, Deu J F, Ducarne J. Vibrations of an elastic structure with shunted piezoelectric patches: efficient finite element formulation and electromechanical coupling coefficients[J]. International Journal for Numerical Methods in Engineering, 2009, 80(2): 235-268.
[21] 付俊勇, 朱翔, 李天匀, 等. 含周期声学黑洞梁的板架结构振动特性[J]. 噪声与振动控制, 2023, 43(03): 21-26+33.
FU Junyong, ZHU Xiang, LI Tianyun, et al. Vibration Characteristics of Panel Structures Including Periodic Acoustic Black Hole Beams[J]. Noise and Vibration Control, 2023, 43(03): 21-26+33.
[22] Denis V, Gautier F, Pelat A, et al. Measurement and modelling of the reflection coefficient of an acoustic black hole termination[J]. Journal of Sound and Vibration, 2015, 349: 67-79.
[23] Ma L, Zhang S, Cheng L. A 2D Daubechies wavelet model on the vibration of rectangular plates containing strip indentations with a parabolic thickness profile[J]. Journal of Sound and Vibration, 2018, 429: 130-146.
[24] 曾鹏云, 郑玲, 左益芳, 等. 基于半解析法的一维圆锥形声学黑洞梁能量聚集效应研究[J]. 噪声与振动控制, 2018, 38(S1): 210-214.
ZENG Pengyun, ZHENG Ling, ZUO Yifang, et al. Analysis of the Energy Concentration Effect of Flexural Vibrations in Tapered Rods with Power-law Profile based on Semi-analytical Method [J]. Noise and Vibration Control, 2018, 38(S1): 210-214.
[25] Deng J, Zheng L, Zeng P, et al. Passive constrained viscoelastic layers to improve the efficiency of truncated acoustic black holes in beams[J]. Mechanical Systems and Signal Processing, 2019, 118: 461-476.
[26] Deng J, Gao N. Broadband vibroacoustic reduction for a circular beam coupled with a curved acoustic black hole via nullspace method[J]. International Journal of Mechanical Sciences, 2022, 233: 107641.
[27] 宋婷婷, 郑玲, 邓杰. 基于高斯展开法的周期声学黑洞宽频能量回收特性研究[J]. 振动与冲击, 2022, 41(10): 186-195.
SONG Tingting, ZHENG Ling, DENG Jie. Gaussian expansion method used in analysing the broadband energy harvesting characteristics of periodic acoustic black holes[J]. Journal of Vibration and Shock, 2022, 41(10): 186-195.
[28] 丁媛, 施凯耀, 郑玲. 基于高斯展开法的碟形声学黑洞宽频调谐减振机理研究[J]. 振动与冲击, 2024, 43(02): 291-298+342.
DING Yuan, SHI Kaiyao, ZHENG Ling. Semi-analytical modelling of a dish-shaped acoustic black hole coupling system based on the Gaussian expansion method and research on the vibration damping mechanism of broadband tuning[J]. Journal of Vibration and Shock, 2024, 43(02): 291-298+342.
[29] Wan Z W, Zhu X, Li T Y, Fu J Y. A method for improving wave suppression ability of acoustic black hole plate in low-frequency range[J]. Thin-Walled Structures, 2023, 182: 110327.