基于蝶形准零刚度弹簧的双梁超材料低频带隙研究

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

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。

Here,to reduce low-frequency vibration and noise of transformers in residential areas and promote environmental protection of transformers to meet the related standards,a twin-beam metamaterial with butterfly quasi-zero stiffness spring periodically configured was proposed to reduce vibration and noise of transformers.By establishing the static theoretical model of butterfly quasi-zero stiffness spring,analytical expressions for restoring force-displacement and stiffness-displacement relations of butterfly quasi-zero stiffness spring were derived,and its quasi-zero stiffness characteristics at equilibrium position were analyzed.Mechanical properties of butterfly quasi-zero stiffness spring were verified with finite element simulation.Then,based on Euler-Bernoulli beam theory,the cellular dynamic model of twin-beam metamaterial composed of periodic interaction of butterfly quasi-zero stiffness spring with a silicon steel sheet beam and a duralumin alloy beam was established.Combined with continuous boundary conditions and periodic Bloch theorem,the dispersion relation of bending vibration of twin-beam metamaterial was deduced,and the form mechanism of its low frequency band gap was studied.Low frequency band gap characteristics of twin-beam metamaterial were simulated and analyzed.The results showed that the twin-beam metamaterial composed of periodic elastic interaction of butterfly quasi-zero stiffness spring with a silicon steel sheet beam and a duralumin alloy beam can generate a low frequency band gap for efficiently suppressing low frequency vibration and noise of transformer core silicon steel sheet,and the low frequency band gap is generated based on the hybrid mechanism of Bragg scattering and local resonance;the study results can provide a new idea for control of low frequency vibration and noise of transformers.