宇称时间对称声子晶体纳米杆波动特性分析

Analysis of Wave Propagation Characteristics of Parity-time Symmetric Phononic-crystal Nanorods

提出一种宇称时间对称声子晶体纳米杆结构,并构建一种非局部有限元杆的波动力学模型,研究宇称时间对称声子晶体纳米杆中一些新颖的弹性波传播机理。研究结果表明宇称时间对称性声子晶体纳米杆的能带结构出现简并点,且简并点之前频率为实数,简并点之后频率则以复共轭的形式成对出现。虚部能带结构中正、负频率的成对出现表明结构中单色波传播呈现增强和衰减的效应。进一步研究尺寸效应对一维宇称时间对称声子晶体纳米杆结构中弹性波传播的影响,研究表明尺寸效应可以改变结构带隙频率所在位置及其宽度。该研究为宇称时间对称性声子晶体纳米结构在振动与弹性波控制领域的工程应用提供一定的理论指导。

A kind of parity-time symmetric phononic crystal nanorod(PTSPCN) structures is proposed, and a wave dynamical model based on nonlocal finite rod elements is constructed to study some novel elastic wave propagation mechanisms in the PTSPCN. Results show that there are degeneracy points in the band structure of the PTSPCN. Value of frequencies is real before the degeneracy points occur, and frequencies exhibit in imaginary pairs with complex conjugate after the appearance of the degeneracy points. Positive and negative frequencies in the imaginary energy band structure appear in pairs, which indicates that the monochromatic wave is enhanced and attenuated alternatively. Meanwhile, the influence of size effect on the propagation of elastic wave in one-dimensional PTSPCN structure is studied. Results shown that size effect can alter the location and width of band-gap frequency. This study may provide a theoretical guidance for the engineering application of PTSPCN structures in the field of vibration and elastic wave control.