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Overview: The elastic particles are deviated from the equilibrium position under the elastic force. The stress in the particle changes or produces vibration. This change at the same time leads to a stress change and vibration of the surrounding particles. The mechanism of the elastic wave is more complicated than that of the electromagnetic wave, because its propagation relies on medium. This is a typical inverse question. 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). The elastic is widely used in many domains. In some space, the special demand is presented, such as the cloak. The objects enclosed inside this region cannot be impinged by the illumination light and hence are invisible to the outside observers. The concentrator is also applied to control the energy concentrated in a special zone, in order to highlight this domain. 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. It is a way and a tool in the evaluation of the elastic wave device design. The size of the scattering phenomenon marks the design effect. In some case, this is judged by our eyes. It is qualitative. Usually, the scattering wave is a variable frequency signal. The fractional Fourier transform (FRFT), which has good focusing characteristic, is adaptive to analyze frequency variation signal. It is a new attempt to transform the time and frequency domain to spatial frequency. The spatial signal in the propagation direction also has the same characters as the signal of time. The result of this transformation has turned the scattering problem into a signal analysis and processing problem. As this, the method of signal can be used to process these questions, such as the wavelet transform, Gabor transform and FRFT. Especially the FRFT, the focusing characters to the chirp signal, which can be used to analyses the spatial signal. The frequency change rate provides a quantitative description method of elastic scattering wave propagation control. With the FRFT, it reduces the blindness of scattering degree of cognitive, simplifying the dielectric become evaluation of design. This method is suitable for the signal of frequency changes, in many cases, the scattering is also complex, and it needs to analyze the reasons and characters of these phenomena and the corresponding method are brought.
Mapping method for spatial transformation of energy concentrator
The computational domain of the elastic wave concentrator transformation method
Results of displacement and energy distribution obtained by two design methods of elastic wave energy concentrato. (a), (b) are the displacement distribution that designed by spatial coordinate transformation and continuous medium coordinate method, respectively; (c), (d) are the energy density distribution results of the above two methods, respectively
Fitting effect of FRFT and short - time Fourier transform of polynomial. (a) Original signal; (b) Fitting result of short-time Fourier transform; (c) Fitting result of FRF
Intermediate position signal of the design material. (a) Spatial wave of coordinate transformation; (b) Spatial wave of continuous medium
Spatial frequency domain diagram under different conditions. (a), (b) Three dimensional energy distribution of FRFT for spatial signal; (c), (d) Maximum order of FRFT