二自由度振子型的二维LR声子晶体弯曲振动带隙研究

为了抑制板件的低频振动，本文提出了一种由二自由度振子周期性排列的二维LR (Locally Resonant) 声子晶体，实现了低频范围内的双带隙。首先运用平面波展开法计算了该声子晶体结构的带隙特性，并通过有限元法和样件试验得到的振动传递特性验证了带隙计算结果的准确性。通过对含二自由度振子的元胞模态振型计算，进一步揭示了该结构低频双带隙的产生机理；振子的平动和转动的两种振型相互耦合作用可以形成两个低频弯曲波带隙，并根据简化模型推导出双带隙起始和截止频率计算方法；最后分析了弹簧刚度、弹簧距离、振子质量和转动惯量对双带隙的影响。结果表明，通过合理选择设计参数可以获得低频范围内的双带隙特性，为声子晶体在汽车板件多频减振的应用研究上提供了新的方法。
Abstract：In order to suppress the vibration of plate components in low frequency,a two-dimensional locally resonant phononic crystal with dual band gaps was proposed.The oscillators with two degrees of freedom were connected to the plate in a periodic arrangement.The plane wave expansion method (PWEM) was used to calculate the band structure.The finite element method (FEM) and experiments were also applied to acquire the vibration transmission spectrums and verify the accuracy of the theoretical calculation.The modal analysis based on a simplified model was carried out in order to reveal the mechanism of the dual band gaps in low frequency.The coupling action between the oscillators’ translation and rotation gives rise to form the dual flexural wave band gaps.Based on the simplified model,an approach was proposed to calculate the start and stop frequencies of band gaps.The results are consistent with the band gaps calculated by the PMEM.The influences of the spring’ s stiffness and interval,oscillators’ mass and moment of inertia on dual band gaps were investigated.The target dual band gaps can be obtained through selecting appropriate parameters of the model.The method provides references to the application of phononic crystals in vehicle panels.