基于蝶形准零刚度弹簧的双梁超材料低频带隙研究

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振动与冲击 ›› 2023, Vol. 42 ›› Issue (17) : 61-69.

论文

陈晓刚1，赵凯美2，聂京凯3，吴雪峰2，黄晓峰2，何强3

作者信息 +

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

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

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文章历史 +

摘要

为降低居民区变压器的低频振动噪声并促使变压器环保达标，提出一种采用周期性配置蝶形准零刚度弹簧的双梁超材料，以期实现变压器本体减振降噪。通过建立蝶形准零刚度弹簧的静力学理论模型，推导了蝶形准零刚度弹簧的回复力-位移、刚度-位移解析表达式，分析了其在平衡位置处的准零刚度特性，并采用有限元仿真验证了蝶形准零刚度弹簧的力学性能；以此为基础，基于欧拉-伯努利梁理论建立了由蝶形准零刚度弹簧周期性耦合硅钢片梁和硬铝合金梁构成的双梁超材料的元胞动力学模型，结合连续边界条件和周期性Bloch定理推导了双梁超材料的弯曲振动色散关系，研究了其低频带隙形成机理，仿真分析了双梁超材料的低频带隙特性。结果表明，通过蝶形准零刚度弹簧周期性弹性耦合硅钢片梁与硬铝合金梁形成的双梁超材料可产生应用于变压器铁芯硅钢片低频振动噪声高效抑制的低频带隙，且该低频带隙由布拉格散射-局域共振混合机制产生，为变压器低频振动噪声控制提供了一种崭新的思路。

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.

导出引用

陈晓刚1，赵凯美2，聂京凯3，吴雪峰2，黄晓峰2，何强3. 基于蝶形准零刚度弹簧的双梁超材料低频带隙研究[J]. 振动与冲击, 2023, 42(17): 61-69

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

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