弹性波能量集中器散射效应的FRFT分析

Scattering effect analysis of elastic wave concentrator based on FRFT

由于弹性波传播动力学方程较复杂,若通过材料参数设计控制弹性波的传播路径,难以获得准确的设计结果。通常在对弹性波材料进行设计时,需要根据实际情况(如高频条件),对动力学方程进行简化或者近似才可以设计出基于弹性波的相应器件。由于这种设计方法的阻抗匹配和介质材料的无损要求难以满足,使得在设计弹性波传播器件过程中出现散射现象,而且往往散射的波形还是频变的信号,因此,在评价弹性波器件设计优劣时,散射现象的大小标志着设计效果的好坏,成为评价设计的手段和工具。但是,散射现象往往仅根据肉眼观察,难以准确地描述,无法给出定量的结果进行说明。为此,本文提出的分数阶Fourier变换(FRFT)对频变信号具有良好的聚焦特性,可利用频率变化的调频率,定量描述散射效应的大小,给出弹性波传播控制散射效应的一种定量的描述方法,降低散射程度认知的盲目性,为简化材料介质参数的设计提供依据。

The propagation equation of the elastic wave is more complicated than that of the electromagnetic wave. It is difficult to design medium parameters when controlling the direction of the elastic wave. In order to obtain precise results of elastic wave propagation, the equations were simplified or approximated to achieve the design effect, depending on the actual situation（such as high frequency）. Therefore, as impedance matching and lossless dielectric material requirements are difficult to meet, the scattering phenomenon appears in the design of elastic wave propagation in the process of the device. Usually, and the scattering wave is variable frequency signal. It is a way and a tool in the evaluation of elastic wave device design, the size of the scattering phenomenon marks the design effect. The fractional Fourier transform（FRFT）, which has good focusing characteristic, is adaptive to analyze frequency variation signal. The frequency change rate provides a quantitative description method of elastic scattering wave propagation control. This reduces the blindness of scattering degree of cognitive, simplifying the dielectric become evaluation of design.