考虑表/界面效应的微纳米压电声子晶体波传播特性研究

The project aims to investigate the wave propagation of the micro/nano scaled piezoelectric phononic crystals based on the boundary element method, and explore the significance of the surface/ interface effects and the reasonability of the calculation method. The main contents include: First, the band structures of the relatively simple two-dimensional piezoelectric phononic crystals with nanosized holes are calculated by using the boundary element method, the influence of the piezoelectric effect and the surface effect on the wave propagation are analyzed, and then the validity and the convergence of the boundary element method are discussed; on this basis, the band structures of the piezoelectric phononic crystals involved arbitrary inclusions with the consideration of the surface/interface effects are investigated, and the influences of the lattice structures, inclusion shapes, material parameters and the surface/interface parameters on the band gap characteristics are analyzed; further, the wave propagation of bulk waves in the micro/nano scaled piezoelectric phononic crystals with defects and the surface waves in the micro/nano scaled piezoelectric phononic crystals are studied by the boundary element method, on which the surface/interface effects are analyzed, and simultaneously the convergence of the algorithm is discussed; based on the above theoretical and numerical analysis, the relevant experiments are carried out to further verify the effectiveness of the boundary element method and the significant influences of the surface/interface effects on the wave propagation at the nanometer scale. The research will provide new ideas for the tuning and control of the phononic crystals, and provide a theoretical basis for the design of the acoustic functional devices based on the micro/nano scaled piezoelectric phononic crystals.

本项目基于边界元法研究微纳米压电声子晶体波的传播特性；探讨表/界面效应的影响以及计算方法的合理性。主要内容包括：首先针对较简单的二维纳米孔压电声子晶体，采用边界元法计算考虑表面效应时的能带结构，分析压电效应及表面效应对压电声子晶体波传播特性的影响，探索边界元法的有效性和收敛性等问题；在此基础上，研究考虑表/界面效应的含夹杂的压电声子晶体的能带结构，考察晶格结构、夹杂形式、材料参数、表/界面参数等对能带结构和带隙宽度的影响；进一步针对含有缺陷的微纳米压电声子晶体和微纳米压电声子晶体中的表面波，采用边界元法研究考虑表/界面效应时波的传播特性，同时分析算法的收敛性；结合上述理论和数值分析，开展相关的试验测试，来进一步验证计算方法的合理性及表/界面效应对波传播的重要影响。该项目的研究将为声子晶体带隙的调控提供新的思路，为微纳米压电声子晶体用于声学功能器件的设计提供理论依据。

声子晶体作为一种新型的声学功能材料，表现出许多独特的声学特性，在滤波器、声谐振器、声波换能器、波导、纳米传感器、声学透镜以及减震降噪控制等方面具有广阔的应用前景。本申请项目采用边界元法建立了各向异性的力-电耦合边界元方程，对各向异性声子晶体、含点和线缺陷的声子晶体进行了计算，分析了边界元法的计算特点及弹性波在这些结构中的传播特点，以及压电效应对弹性波传播的影响；并与其它方法进行了比较，验证了边界元法计算的合理性及准确性；将Dirichlet-to-Neumann(DtN) 映射法应用到含表/界面效应的声子晶体的计算中，分析了表/界面效应对声子晶体中弹性波传播的影响，结果表明考虑表/界面效应时，能带结构将发生变化，具体变化大小与表/界面材料影响参数有关；同时采用边界元法及DtN映射法分析了不同界面情况下弹性波传播的特性，表明这两种方法都可以有效的考虑界面连接条件，并且通过改变界面条件可以得到低频带隙；针对上述各种情况，探索了晶格结构形式、夹杂形式、不同材料参数及表/界面参数等对能带结构和带隙宽度的影响，以及弹性波的传播规律；发展了计算能带结构和传输谱的有效计算方法，探讨了各种算法的计算收敛性、计算速度及准确性。本项目从理论及计算为声带隙材料走向应用奠定了基础，为各种声学功能器件的设计与开发提供重要的理论指导意义。