Low frequency band gap of twin-beam metamaterial based on butterfly quasi-zero stiffness spring

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Journal of Vibration and Shock ›› 2023, Vol. 42 ›› Issue (17) : 61-69.

CHEN Xiaogang1, ZHAO Kaimei2, NIE Jingkai3, WU Xuefeng2, HUANG Xiaofeng2, HE Qiang3

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Abstract

To reduce the low frequency vibration and noise of transformers in residential areas and promote the environmental protection of transformers, a double-beam metamaterial with periodic configuration of Belleville quasi-zero stiffness spring (BQZSS) is proposed to achieve vibration and noise reduction for transformers. By establishing the theoretical model of statics of BQZSS, the analytical expressions of its restoring force-displacement and stiffness-displacement are deduced, and the quasi-zero stiffness characteristics at equilibrium position are analyzed as well. The mechanical properties of the BQZSS are verified through finite element simulation. On this basis, using Euler-Bernoulli beam theory, the cellular dynamics model of the double-beam metamaterial composed of BQZSS periodically coupled with silicon steel sheet and aluminum alloy beams is established. According to the continuous boundary conditions and Bloch theorem, the dispersion relation of the bending vibrations of double-beam metamaterial is derived, and its corresponding low frequency bandgap mechanism is investigated. Finally, the low frequency bandgap characteristics of the double-beam metamaterial are simulated and analyzed. The results show that the double-beam metamaterial formed by periodically coupling silicon steel sheet and aluminum alloy beams with BQZSSs can yield low frequency bandgap for suppression of low-frequency vibration and noise of transformers, and these bandgaps benefit from both Bragg scattering and local resonance mechanisms, which provides a new control strategy for low-frequency vibration and noise of transformers.

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quasi-zero stiffness / double-beam metamaterial / Bragg scattering / local resonance / vibration attenuation

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CHEN Xiaogang1, ZHAO Kaimei2, NIE Jingkai3, WU Xuefeng2, HUANG Xiaofeng2, HE Qiang3. Low frequency band gap of twin-beam metamaterial based on butterfly quasi-zero stiffness spring[J]. Journal of Vibration and Shock, 2023, 42(17): 61-69

References

[1] 王成芳,杜天苍.城市变电站选址面临的尴尬及其对策思考[J].规划师,2008,24(2):42-44.
WANG Cheng-fang, DU Tian-cang. A Reflection on the Embarrassment of City Substation Addressing and Its Countermeasure [J]. Management, 2008, 24(2): 42-44.
[2] 汲胜昌, 师愉航, 张凡, 陆伟锋. 电力变压器振动与噪声及其控制措施研究现状与展望[J]. 高压电器, 2019, 55(11): 1-17.
JI Sheng-chang, SHI Yu-hang, ZHANG Fan, LU Wei-feng. Review on Vibration and Noise of Power Transformer and Its Control Measures [J]. High Voltage Apparatus, 2019, 55(11): 1-17.
[3] 刘姜涛. 电力变压器有源降噪的关键技术研究[D]. 武汉大学, 2012.
LIU Jiang-tao. Research on the Key Technology of Active Noise Control for Power Transformer [D]. Wuhan University, 2012.
[4] 王瑜, 赵建网. 油浸式电力变压器的噪声源及降噪对策[J].电力环境保护, 2008(3): 45-47.
WANG Yu, ZHAO Jian-wang. Analysis of oil—immersed power transformers noise and its countermeasure[J]. Power environmental protection, 2008(3): 45-47.
[5] 胡静竹, 刘涤尘, 廖清芬, 晏阳, 梁姗姗. 变电站声屏障降噪效果及影响因素分析[J]. 武汉大学学报, 2017, 50(1): 75-80.
HU Jing-zhu, LIU Di-chen, MIU Qing-fen, YAN Yang, LIANG Shan-shan. Substation noise reduction effect of barrier and analysis of influencing factors[J]. Engineering Journal of Wuhan University, 2017, 50(1): 75-80.
[6] 刘姜涛, 刘震宇, 应黎明, 李靖. 基于广义FIR滤波器的电力设备有源噪声控制[J]. 电网技术, 2012, 36(6): 250-255.
LIU Jiang-tao, LIU Zhen-yu, YING Li-ming, LI Jing. Active Noise Control of Power Equipments Based on Generalized Finite Impulse Response Filter [J]. Power System Technology, 2012, 36(6): 250-255.
[7] 张玉兰. 橡胶隔振器在实现变压器减振降噪中的应用[J]. 职业, 2013(20): 109.
ZHANG Yu-lan. Application of Rubber Vibration Isolator in Realizing Transformer Vibration and Noise Reduction [J]. occupation, 2013(20): 109.
[8] 刘玉成, 何强, 罗永利, 王鹏浩, 聂京凯, 董光旭. 变压器准零刚度隔振平台非共振响应[J]. 应用力学学报, 2020, 37(6): 2463-2469.
LIU Yu-cheng, HE Qiang, LUO Yong-li, WANG Peng-hao, NIE Jing-kai, DONG Guang-xu, HE Qiang. Nonresonant response of quasi-zero stiffness platform for power transformer [J]. Chinese journal of applied mechanics, 2020, 37(6): 2463-2469.
[9] 李文鹏, 刘海波, 曹春诚, 段炼, 聂京凯, 董光旭, 何强. 双非线性变压器基础隔振降噪研究[J]. 机械科学与技术, 2020, 39(12): 1836-1843.
LI Wen-peng, LIU Hai-bo, CAO Chun-cheng, DUAN Lian, NIE Jing-kai, DONG Guang-xu, HE Qiang. Investigation on the Vibration Isolation and Noise Reduction of Dual- nonlinear Isolation System for Transformer [J]. Mechanical Science and Technology for Aerospace Engineering, 2020, 39(2): 1836-1843.
[10] Cao H , Chang Y , Zhou J , et al. High-Efficiency Vibration Isolation for a Three-Phase Power Transformer by a Quasi-Zero-Stiffness Isolator [J]. Shock and Vibration, 2021: 1-11.
[11] 王天正, 张超, 赵欣哲, 亢银柱, 刘国强, 唐保国. 基于电力变压器噪声特性的声学超材料降噪方法[J]. 高压电器, 2019, 55(11): 277-282.
WANG Tian-zheng, ZHANG Chao, ZHAO Xin-zhe, KANG Yin-zhu, LIU Guo-qiang, TANG Bao-guo. Niose Reduction Method with Acoustic Metamaterials Based on Noise Characteristics of Power Transformer[J]. High Voltage Apparatus, 2019, 55(11): 277-282.
[12] 赵欣哲, 刘国强, 夏东. 混合盘绕型声学超材料在低频隔声中的应用[J]. 陕西师范大学学报, 2019, 47(6): 100-104.
ZHAO Xin-zhe, LIU Guo-qiang, XIA Dong. Application of hybrid coiled acoustic metamaterials in low frequency sound insulation [J]. Journal of Shananxi Normal University, 2019, 47(6): 100-104.
[13] Sharafkhani N. A Helmholtz Resonator-Based Acoustic Metamaterial for Power Transformer Noise Control [J]. Acoustics Australia, 2021: 1-7.
[14] 张嵩阳, 陈勇勇, 王广周,王磊磊,王小鹏. 两边支撑声学超材料板的低频宽带隔声性能研究[J]. 振动与冲击, 2020, 39(9):254-266.
ZHANG Song-yang, CHEN Yong-yong, WANG Guang-zhou, WANG Lei-lei, WANG Xiao-peng. Low frequency broadband sound insulation performance of an acoustic metamaterial panel supported on two sides[J]. Journal of Vibration and Shock, 2020, 39(9):254-266.
[15] Mastricola N P, Dreyer J T, Singh R. Analytical and experimental characterization of nonlinear coned disk springs with focus on edge friction contribution to force-deflection hysteresis[J]. Mechanical Systems and Signal Processing, 2017, 91: 215-232.
[16] Wang M Y, Wang X. Frequency band structure of locally resonant periodic flexural beams suspended with force–moment resonators[J]. Journal of Physics D: Applied Physics, 2013, 46(25): 255502.