半无限板类声子晶体带隙仿真的PWE/NS-FEM方法

PWE/NS-FEM for Band Structures Simulation of Semi-infinite Plate-like Phononic Crystals

声子晶体是一种具有弹性波带隙的周期性功能材料,可以对在介质中传播的弹性波起到衰减作用,因此,在汽车减振降噪方面有极大的应用价值。文章针对现有数值方法求解半无限板类声子晶体的能带结构时计算复杂和精度低的缺陷,在传统有限元法的基础上引入梯度光滑技术,结合空间傅里叶级数展开理论,构造了平面波展开/点光滑有限元法数值模型。数值算例表明,对于半无限板类声子晶体,所构造方法能够适当软化离散系统刚度,提供更加精确、高效的能带结构仿真结果,在工业应用中有较大潜力。

The phononic crystal is a kind of periodic functional material with elastic wave band gap,which can attenuate the elastic wave propagating in the medium, thus it has great application value in automobile vibration and noise reduction. In this paper, in order to solve the problems of complex calculation and low numerical accuracy in the existing methods for band structures simulation of semi-infinite plate-like phononic crystals, a theoretical framework of plane wave expansion/node-based smoothed finite element method is constructed by adopting the gradient smoothing technique and spatial fourier series. Numerical examples demonstrate that the nodebased gradient smoothing technique can soften the numerical model to a certain extent, thus the present plane wave expansion/node-based smoothed finite element method possesses higher computational accuracy for band structures simulation of semi-infinite plate-like PCs, which has great potential in industrial application.