功能梯度声子晶体中SH波带隙结构的精确解

Exact solution for band gap structures of SH waves in functionally graded phononic crystals

【目的】以精确方法分析研究具有指数分布特性的功能梯度弹性声子晶体中斜入射剪切水平(shear horizontal,SH)波的带隙结构。【方法】首先,利用应力变换并结合Snell定理和状态空间法,精确地获得了斜入射SH波的位移、应力解及显式特解;然后,根据应力、位移连续条件和Bloch理论,应用传递矩阵法,导出了带隙结构的特征值方程。【结果】通过计算特征值方程得到了色散曲线,并与层合模型和传输率结果进行比对后验证了本研究方法的准确性;在数值算例中,指数梯度和入射角对带隙宽度及频率中心的影响规律表明,单梯度声子晶体对带隙调谐具有更好的性能。【结论】本研究给出的精确解析解可作为各类近似解与数值解的检验基准。

[Objective]The precise methods are aimed at probing into the bandgap structure of oblique shear horizontal(SH)waves in functionally graded elastic phononic crystals with exponential distribution characteristics.[Method]Firstly,by utilizing stress transformation and combining Snell\s theorem and state space method,the displacement,stress solution,and explicit characteristic solution of obliquely incident SH waves were accurately obtained;then,based on the continuity conditions of stress and displacement and Bloch theory,the transfer matrix method was applied to derive the eigenvalue equation of the band gap structure.[Result]The dispersion curve has been obtained by calculating the eigenvalue equation,and the accuracy of this research method has been verified by comparing it with the laminated model and transmission rate results;in numerical examples,the influence of exponential gradient and incident angle on band gap width and frequency center indicates that single gradient phononic crystals have better performance in band gap tuning.[Conclusion]The exact analytical solution provided in this study can serve as a benchmark for testing various approximate and numerical solutions.