Theory of complex-coordinate transformation acoustics for non-Hermitian metamaterials

Transformation acoustics(TA)has emerged as a powerful tool for designing several intriguing conceptual devices,which can manipulate acoustic waves in a flexible manner,yet their applications are limited in Hermitian materials.In this work,we propose the theory of complex-coordinate transformation acoustics(CCTA)and verify the effectiveness in realizing acoustic non-Hermitian metamaterials.Especially,we apply this theory for the first time to the design of acoustic parity-time(PT)and antisymmetric parity-time(APT)metamaterials and demonstrate two distinctive examples.First,we use this method to obtain the exceptional points(EPs)of the PT/APT system and observe the spontaneous phase transition of the scattering matrix in the transformation parameter space.Second,by selecting the Jacobian matrix's constitutive parameters,the PT/APT-symmetric system can also be configured to approach the zero and pole of the scattering matrix,behaving as an acoustic coherent perfect absorber and equivalent laser.We envision our proposed CCTAbased paradigm to open the way for exploring the non-Hermitian physics and finding application in the design of acoustic functional devices such as absorbers and amplifiers whose material parameters are hard to realize by using the conventional transformation method.

Acoustic Multi Emission Lens via Transformation Acoustics

Based on transformation acoustic methodology, we propose an algorithm for designing acoustic non-resonant lens antenna, which is competent to generate multiple directive beams that are pointing at the desired direction.Unattainable with previous works, the present approach is capable of adjusting the directivity of each radiated beam individually, which is of the utmost importance in several acoustic applications such as in sonar systems. A linear transformation function is intentionally used for eliminating the inhomogeneity of the obtained materials and to pave the way towards more general acoustic patterns. Several numerical simulations are performed to show the capability of the proposed method in manipulating the acoustic waves. To authenticate the concept,a structure that can generate four beams with different directivities is realized with non-resonant meta-fluid bi-layered structure through effective medium theory.

A novel design scheme for acoustic cloaking of complex shape based on region partitioning and multi-origin coordinate transformation

Acoustic cloaking is an important application of acoustic metamaterials.This article proposes a novel design scheme for acoustic cloaking based on the region partitioning and multi-origin coordinate transformation.The cloaked region is partitioned into multiple narrow strips.For each strip,a local coordinate system is established with the local origin located at the strip center,and a coordinate transformation in the local coordinate system is conducted to squeeze the material along the strip length direction to form the cloaked region.To facilitate the implementation of the acoustic cloak,the multilayer effective medium is used to approximate the non-uniform anisotropic material parameters.The effectiveness of the proposed coordinate transformation method is verified by comparing the results from our method with those in the literature.Firstly,the results of a circular acoustic cloak in the literature are reproduced by using our finite element(FE)simulations for validation.Then,a comparison is made between the traditional coordinate transformation scheme and our new scheme for simulating an elliptical acoustic cloak.The results indicate that the proposed multi-origin coordinate transformation method has a better cloaking effect on the incident wave along the ellipse minor axis direction than the traditional method.This means that for the same object,an appropriate transformation scheme can be selected for different incident wave directions to achieve the optimal control effect.The validated scheme is further used to design an arch-shaped cloak composed of an upper semicircular area and a lower rectangular area,by combining the traditional single-centered coordinate transformation method for the semicircular area and the proposed multi-origin method for the rectangular area.The results show that the designed cloak can effectively control the wave propagation with significantly reduced acoustic pressure level.This work provides a flexible acoustic cloak design method applicable for arbitrary shapes and different wave incident directions,enriching the theory of acoustic cloaking based on coordinate transformation.

Layered and isotropic acoustic cloak design based on conformal transformation acoustics

The acoustic cloak can manipulate sound waves in surprising ways and enable us to guide the trajectories of waves at will.In contrast to the existing approaches for designing such devices that need exotic material parameters,here we demonstrate how to design a layered and isotropic acoustic cloak based on conformal transformation acoustics.A petal-shaped layered acoustic cloak is designed from the reduction of material parameters of an approximate rectangular cloak.The resultant material parameters span a narrow range,thus strongly facilitating the implementation.The invisibility performance of the cloak for different shapes of acoustic wavefront is verified using a full-wave finite-element analysis.

Achieving acoustic cloak by using compressible background flow

We propose a scheme of acoustic spherical cloaking by means of background irrotational flow in compressible fluid.The background flow forms a virtual curved spacetime and directs the sound waves to bypass the cloaked objects. To satisfy the laws of real fluid, we show that spatially distributed mass source and momentum source are necessary to supply. The propagation of sound waves in this system is studied via both geometric acoustics approximation and full wave approach.The analytic solution of sound fields is obtained for plane wave incidence. The results reveal the effect of phase retardation（or lead） in comparison with the ordinary transformation-acoustic cloak. In addition, the ability of cloaking is also evaluated for unideal background flows by analyzing the scattering cross section.

PARAMETERS OPTIMIZATION OF CONTINUOUS WAVELET TRANSFORM AND ITS APPLICATION IN ACOUSTIC EMISSION SIGNAL ANALYSIS OF ROLLING BEARING

Morlet wavelet is suitable to extract the impulse components of mechanical fault signals. And thus its continuous wavelet transform （CWT） has been successfully used in the field of fault diagnosis. The principle of scale selection in CWT is discussed. Based on genetic algorithm, an optimization strategy for the waveform parameters of the mother wavelet is proposed with wavelet entropy as the optimization target. Based on the optimized waveform parameters, the wavelet scalogram is used to analyze the simulated acoustic emission （AE） signal and real AE signal of rolling bearing. The results indicate that the proposed method is useful and efficient to improve the quality of CWT.

Implementation of a Novel Algorithm on Acoustic Doppler Current Profiler Signal Processing System

Acoustic Doppler current profiler （ADCP） uses acoustic energy directed along narrow beams for current measurement. In conventional method, the quantity of sampling affects the precision of fast Fourier transform （FFT） algorithm, and the algorithm needs a large amount of data to process. A novel frequency estimator.enhanced least mean square （ELMS） algorithm for a single complex sinusoid in complex white Gaussian noise, is proposed in ADCP system. As sampling frequency equals 120 krad/s and the sampling number equals 240. the minimum resolving is 0. 5 krad/s. All variances keep 11.11%. ELMS algorithm needs less data than FFT. And the robust algorithm can estimate the spectrum true value to 99.9% when the signal to noise ratio （SNR） is equal to 0 dB. Experiments prove that the estimation values will diverge much from the ideal when SNR is less than -6 dB.

Sound-transparent anisotropic media for backscattering-immune wave manipulation

The scattering behavior of an anisotropic acoustic medium is analyzed to reveal the possibility of routing acoustic signals through the anisotropic layers with no backscattering loss. The sound-transparent effect of such a medium is achieved by independently modulating the anisotropic effective acoustic parameters in a specific order, and is experimentally observed in a bending waveguide by arranging the subwavelength structures in the bending part according to transformation acoustics. With the properly designed filling structures, the original distorted acoustic field in the bending waveguide is restored as if the wave travels along a straight path. The transmitted acoustic signal is maintained nearly the same as the incident modulated Gaussian pulse. The proposed schemes and the supporting results could be instructive for further acoustic manipulations such as wave steering, cloaking and beam splitting.

On the application of wavelet transform to the solution of integral equations for acoustic radiation and scattering

The application of wavelets is explored to solve acoustic radiation and scattering problems. A new wavelet approach is presented for solving two-dimensional and axisymmetric acoustic problems. It is different from the previous methods in which Galerkin formulation or wavelet matrix transform approach is used. The boundary quantities are expended in terms of a basis of the periodic, orthogonal wavelets on the interval. Using wavelet transform leads a highly sparse matrix system. It can avoid an additional integration in Galerkin formulation, which may be very computationally expensive. The techniques of the singular integrals in two-dimensional and axisymmetric wavelet formulation are proposed. The new method can solve the boundary value problems with Dirichlet, Neumann and mixed conditions and treat axisymmetric bodies with arbitrary boundary conditions. It can be suitable for the solution at large wave numbers. A series of numerical examples are given. The comparisons of the results from new approach with those from boundary element method and analytical solutions demonstrate that the new techique has a fast convergence and high accuracy.