压电分流阵列板复能带结构计算的ES-FEM方法  

ES-FEM Method for Complex Energy Band Structure Calculation of Piezoelectric Shunt Array Plates

作　　者：杨兴家 杨会松 王刚[1] YANG Xingjia;YANG Huisong;WANG Gang(College of Mechanical Engineering,Hebei University of Technology,Tianjin 300401,China)

机构地区：[1]河北工业大学机械工程学院,天津300401

出　　处：《噪声与振动控制》2023年第1期43-49,共7页Noise and Vibration Control

基　　金：国家自然科学基金资助项目(12072099,11832011);河北省自然科学基金资助项目(A2021202023)。

摘　　要：为了提高压电分流阵列板复能带结构的计算精度,构造一种基于Mindlin假设的边光滑有限元法(ES-FEM)数值模型。以单个原胞为研究对象,采用三角形单元对其进行离散。基于背景单元的各条边,进一步构造相应的光滑域,依托梯度光滑技术(GST)建立光滑应变场。最后通过建立离散系统方程并结合Bloch定理对复能带结构进行求解,并进一步探究电学参量对带隙的影响规律。研究结果表明:ES-FEM方法能够有效提高压电分流阵列板复能带结构的计算精度;电阻和电感等参数分别对局域共振带隙的衰减峰值和位置有显著影响,而对布拉格带隙则影响较小。In order to improve the calculation accuracy of complex energy band structure of piezoelectric shunt array plates, a numerical model of edge-based smoothed finite element method(ES-FEM) based on Mindlin hypothesis is constructed. A single cell is taken as the research object which is discretized with triangular elements. Based on the edges of the background elements, the corresponding smoothing domain is further constructed, and the gradient smoothing technique(GST) is performed over each smoothing domain to construct the smoothed strain field. Finally, combined with Bloch theorem, the discrete system equations are established and the complex energy band structure is calculated. The influence of electrical parameters on the band gap is further explored. The results show that the ES-FEM method can effectively improve the calculation accuracy of the complex energy band structure of piezoelectric shunt array plates;Parameters such as resistance and inductance have a significant influence on the attenuation peak and position of the local resonance band gap,but have a small influence on the Bragg band gap.

关 键 词：振动与波 压电分流阵列板 边光滑有限元法 梯度光滑技术 复能带结构 带隙调控规律 

分 类 号：O241.82[理学—计算数学]