一种圆柱壳类声子晶体振动带隙及振动特性研究

A study on the vibration band gap and vibration characteristics of a cylindrical shell phononic crystal

圆柱壳类结构在结构设计中应用广泛,其振动噪声问题十分普遍。基于二维板类声子晶体提出了一种基于布拉格散射机理的圆柱壳类声子晶体模型。该模型利用圆柱壳的动力学方程理论和Bloch周期条件,建立其结构有限元模型并分析其振动特性。针对一半径为0.1 m的圆柱壳声子晶体结构,利用有限元法计算能带结构,并分析其振动带隙的特性。为了验证带隙准确性,利用有限元法对多个周期结构圆柱壳模型进行了振动传递分析,获得的振动传递函数曲线与能带带隙相匹配,同时给出了带隙外和带隙内的两个不同频率点的位移场分布。结果表明,与板类结构相似,圆柱壳声子晶体同样具有良好的沿轴线和圆柱环两个方向的带隙或全禁带隙,其振动传递损失也验证该结论。

A cylindrical shell structure is widely used in structure design but its vibration noise problem commonly exists. Based on the theory of two-dimensional plate phononic crystal and the mechanism of Bragg scattering, this work presents a cylindrical shells phononic crystal model. According to the dynamic equation theory of cylindrical shell and Bloch periodic condition, the vibration characteristic of this structure was studied with an established finite element model. This research took a phononic crystal structure with a radius of 0.1m as an example, calculated its band structure, and analyzed its vibration characteristics. To verify the accuracy of the calculated band gap, the vibration transfer of cylinder shell models with multiple periodic structures was analyzed through the finite element method (FEM). The result shows that the vibration transfer function curve match the band gap well. It indicates that, similar to the plate structure, cylindrical shell phonon crystals also have quite good band gap and total forbidden band gap along the axial line and direction of cylinder ring.