Abstract
To describe the elastic wave scattering, which reflects the performance of propagation control materials, the approximate directional cloaks of an elastic wave are designed using the zero- and first-order approximation coordinate transformation method. Because the convergence features of fractional Fourier transform (FRFT) are more acute and sensitive to the frequency change than those of short time Fourier transform, the spatial signals in the designed materials are transformed in the FRFT domain. The spatial frequency changes of elastic waves through inhomogeneous materials are quantitatively analyzed under several circumstances. The provided time-frequency analysis method with FRFT can support the design evaluation of the material parameters.
Highlights
Due to zero- and first-order approximation method itself and the impedance mismatch in the materials, the scattering phenomena, which refers to the frequency changes as waves pass through the media, is caused in the material design of wave propagation control.[5]
Based on the fractional Fourier transform (FRFT) analysis of scattering phenomena, we established the correspondence between the maximum matching order of transformation and the scattering, and provided the basis for assessing the material design of elastic wave propagation control
The material parameters of elastic waves vary in accordance with the above equations, and the corresponding linear change materials can be obtained by the transformation method
Summary
The coordinate transformation method, proposed for electromagnetic waves controlling and manipulating metamaterials by Leonhardt and Pendry et al, has been extended to elastic waves in recent years.[1,2,3,4] Due to zero- and first-order approximation method itself and the impedance mismatch in the materials, the scattering phenomena, which refers to the frequency changes as waves pass through the media, is caused in the material design of wave propagation control.[5] Generally, the operating mechanism of elastic waves is more complicated and difficult to control than electromagnetic waves.[3] according to the existing control theory of wave propagation, some assumptions about the characteristics of the material, such as the anisotropy of the medium parameters, the continuity in the radial direction, and lossless dielectric are necessary but difficult to implement in practice. Based on the FRFT analysis of scattering phenomena, we established the correspondence between the maximum matching order of transformation and the scattering, and provided the basis for assessing the material design of elastic wave propagation control
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