一种具有动态磁负刚度薄膜声学超材料的低频隔声特性

Low-frequency sound insulation performance of novel membrane acoustic metamaterial with dynamic negative stiffness

为提升薄膜/板状结构的低频隔声特性,本文提出一种具有动态磁负刚度的新型准零刚度薄膜声学超材料.首先,应用等效磁荷理论推导了动态磁负刚度;然后,基于伽辽金法建立了有限尺寸下薄膜/板结构的隔声理论模型.通过理论分析、数值仿真及实验测试相结合的方法,从结构模态、振动模式、平均速度、相位曲线、等效质量密度和等效弹簧-质量动力学模型等多个角度对其低频(1—1000 Hz)隔声机理开展了研究.结果表明:在初始薄膜张力一定时,减小磁间隙或增大剩余磁通密度均可增大动态磁负刚度,进而减小隔声峰值频率,增加隔声带宽,实现了较宽频段下的有效低频隔声;进一步,当磁间隙大于第二临界磁间隙小于第一临界磁间隙时,结构的一阶模态共振消失,对应隔声谷值大幅提升,显示出超宽频段的隔声效果.这种利用动态磁负刚度改善模态共振导致的低频隔声谷值的方法对薄膜/板型低频隔声超材料的设计具有重要的理论指导价值.

For improving the low-frequency sound insulation properties of membrane/plate structures,a new quasizero stiffness membrane acoustic metamaterial with dynamic magnetic negative stiffness is proposed.When the equivalent magnetic charge theory is used to investigate the dynamic magnetic negative stiffness,a theoretical model of proposed metamaterial with finite dimension is established based on the Galerkin method.Through a combination of theoretical analysis,numerical simulation and experimental measurement,the low-frequency(1–1000 Hz)sound insulation performance of the metamaterial is investigated from several perspectives,including structural modality,vibration mode,average velocity,phase curve,equivalent mass density,and equivalent spring-mass dynamics model.The results show that at a certain initial membrane tension,the decreasing of the magnetic gap or the increasing of the residual flux density can increase the dynamic magnetic negative stiffness.This in turn leads the peak frequency to decrease and the bandwidth of sound insulation to increase,thus achieving effective low-frequency sound insulation over a wide frequency band.Further,when the magnetic gap is larger than the second critical magnetic gap and smaller than the first critical magnetic gap,the first-order modal resonance of the metamaterial disappears,and the corresponding value of sound insulation valley increases significantly,thus demonstrating superior sound insulation effect in a wide frequency band.The proposed method of using dynamic magnetic negative stiffness to improve low-frequency sound insulation valleys due to modal resonance provides useful theoretical guidance for designing membrane/plate type lowfrequency sound insulation metamaterials.