中文摘要：

为减少弹性波动力学方程在传播控制材料设计应用中的复杂性，以弹性波特征方程的一阶和0阶阶近似的方法，由于设计方法本身的近似性，以及材料在阻抗匹配、对介质材料的无损要求等方面的原因，使得弹性波在设计材料里的传播过程中产生散射现象。以弹性波近似设计的匀质定向斗篷为研究对象，借助于分数阶傅里叶变换（FRFT）对频率变化的敏感性，将设计材料中传播的空间波形信号变换到分数阶域，直观、定量的反映了散射效应引起的频率变化，减少了对散射程度认知的盲目性，为简化材料介质参数的设计、降低散射效应的影响提供了依据。

英文摘要：

In order to reduce the complexity of designing control material of elastic wave mechanics equation with the transfor-mation method,the first and the zero order approximation method of elastic wave mechanics equation is used.Due to the approxi-mate design method itself,and the impedance matching material parameters,and requirements of dielectric materials those are kept intact,etc,the scattering effect is produced when the elastic wave makes the spread in the design of material.The design directional cloak of homogeneous elastic wave approximation is as the research object,with fractional Fourier transform （FRFT） on the sensitivity of the frequency change,the waveform signal in material is transmitted from the space to the fractional domain. This could intuitively,quantitatively reflect the frequency variation that caused by scattering effect,and reduce the blindness of the cognition of the degree of scattering,and provide the basis for the design the material medium parameters simplify.