Truncation Boundary Research Articles

Numerical Simulation of Electromagnetic Nondestructive Testing Technology for Elasto-Plastic Deformation of Ferromagnetic Materials Based on Magneto-Mechanical Coupling Effect.

A numerical tool for simulating the detection signals of electromagnetic nondestructive testing technology (ENDT) is of great significance for studying detection mechanisms and improving detection efficiency. However, the quantitative analysis methods for ENDT have not yet been sufficiently studied due to the absence of an effective constitutive model. This paper proposed a new magneto-mechanical model that can reflect the dependence of relative permeability on elasto-plastic deformation and proposed a finite element-infinite element coupling method that can replace the traditional finite element truncation boundary. The validity of the finite element-infinite element coupling method is verified by the experimental result of testing electromagnetic analysis methods using TEAM Problem 7. Then, the reliability and accuracy of the proposed model are verified by comparing the simulation results under elasto-plastic deformation with experimental results. This paper also investigates the effect of elasto-plastic deformation on the transient magnetic flux signal, a quantitative hyperbolic tangent model between Bzpp (peak-peak value of the normal component of magnetic flux signal) and elastic stress, and the exponential function relationship between Bzpp and plastic deformation is established. In addition, the difference and mechanism of a magnetic flux signal under elasto-plastic deformations are analyzed. The results reveal that the variation of the transient magnetic flux signal is mainly due to domain wall pinning, which is significantly affected by elasto-plastic deformation. The results of this paper are important for improving the accuracy of quantitative ENDT for elasto-plastic deformation.

A new seismic wave input method for canyon sites based on the finite element method-indirect boundary integral equation method

The seismic input is the basis for the seismic safety analysis of dams, but current seismic input methods have not reasonably considered the influence of canyon scattering effects on the dynamic response of dams. In this paper, the total motion field of the canyon is deconstructed into the free field of a uniform half space and the scattering field of the canyon and they are obtained separately. The indirect boundary integral equation method (IBIEM) is used to determine the scattering field of the canyon, which is superimposed with the free field to obtain the seismic ground motion field (total motion field) of the canyon. The accuracy of the total motion field of the canyon is verified through reference solutions. In the finite element analysis of seismic ground motion field in the canyon, the total motion field at the truncation boundary of the canyon foundation is transformed into the equivalent seismic input loads and the interior of the canyon are simulated using the finite element method (FEM). Then, based on the wave input for the free field combined with the viscoelastic artificial boundary, a new wave input method for the total motion field combined with the viscoelastic artificial boundary is established. The seismic wave input method based on the finite element-indirect boundary integral equation method is applied to numerically determine the seismic response of a trapezoidal canyon. The differences in the seismic response of the canyon under free-field input and total motion field input are discussed. The results show that there is a certain deviation between the displacement and waveform obtained from the free-field input and the solutions obtained from the indirect boundary integral equation method. There is a large error for a large angle of incidence, and the errors increase with increasing seismic wave frequency. When the incident angle is 60°, the maximum error in the frequency domain reaches 92.3 %, and the maximum error in the time domain reaches 250 %. The displacement amplitude and waveform of the canyon obtained from the total motion field input showed agreement with the results of the indirect boundary integral equation method. The wave input method established in this paper has high calculation accuracy and reasonably considers the scattering effect of canyons, which provides a basis for more accurate predictions of the seismic response of dams on canyon foundations.

Segment-based wall treatment model for heat transfer rate in smoothed particle hydrodynamics

We propose a new smoothed particle hydrodynamics (SPH) model that applies a segment-based wall boundary treatment method (SBWM) for heat transfer applications. We begin by focusing on natural convection simulations, where accurately modeling heat-transferring wall boundaries is crucial as they are the energy source driving the flow. A conventional SPH approach that handles such tasks is the boundary particle (BP) method, which constructs wall boundaries by placing multiple layers of particles on and behind the walls. Despite its capability of imposing accurate boundary conditions, the BP approach becomes a non-trivial task when the fluid domain involves complex boundaries. Moreover, computational costs may significantly increase because of the increased number of SPH particles necessary for modeling walls. Therefore, we utilize the recent development of SBWM to efficiently model energy-transferring wall boundaries. Specifically, SBWM is applied to the energy conservation equation for the wall heat transfer model, using the boundary truncation terms derived in this work. The SBWM-SPH method is verified in various numerical examples, comparing the results with BP-SPH and finite volume method as well as experimental data in the literature. Our study finally extends to investigating a heat exchanger with an optimized shape, demonstrating how SBWM-SPH effectively handles practical issues associated with the BP method while providing accurate heat transfer calculations for the wall.

Polarization-independent Spatial Kramers-Kronig medium for omnidirectional reflectionless absorption of unpolarized light

Spatial Kramers-Kronig (KK) media offer a possible route to obtain omnidirectional light absorption within a thin layer of material. However, the experimental realizations are typically limited to a specific polarization, i.e., either transverse electric (TE) or transverse magnetic (TM), hence lacking specific implementations for the absorption of unpolarized light. In this work, we propose theoretically and demonstrate experimentally a polarization-independent KK medium which performs omnidirectional reflectionless absorption for both TE and TM polarized waves. Our design makes use of a special matryoshka metamaterial, whose electric and magnetic responses can be independently controlled with minimized crosstalk. To extend the absorption spectrum, the inner truncation boundary of the KK medium is set at a position far away from the spatial Lorentz resonance, where the constitutive parameter of the metamaterial remains unitary over a broad frequency band. A mini anechoic chamber, 6.83-wavelength in diameter, is constructed using the designed annulus-shaped KK medium. The measured fields for both TE and TM polarizations confirm the polarization-independent omnidirectional and nearly reflectionless absorption in a broadband frequency range.

Prismatic-element SBPML coupled with SBFEM for 3D infinite transient wave problems

In this paper, an enhanced prismatic-element scaled boundary perfectly matched layer (SBPML) is developed, which is a novel time-domain artificial boundary method for 3D infinite wave problems. The SBPML permits the utilization of an artificial boundary with general geometry and can consider planar physical surfaces and interfaces extending to infinity. Moreover, this enhancement enables the seamless integration with surface meshes of arbitrary polygonal faces (such as triangles, quadrangles, pentagons, heptagons, octagons, etc.) at the truncation boundaries. The interior domain can be modelled by polyhedrons formulated by the scaled boundary finite element method (SBFEM). The geometric shape of the SBPML elements in the proposed method, within the local coordinate system, takes the form of a regular prism with regular polygonal top and bottom faces. Consequently, it is referred to as the Prismatic-element SBPML. Local scaled boundary coordinates based on the polygonal shape function are firstly introduced into the truncated infinite domain to describe its general geometry properties and provide the coupled capabilities with arbitrary polygonal face meshes at the truncation boundaries of numerical models. Then, a complex stretching function from PML is applied to radial direction of the local scaled boundary coordinates to map the physical space onto the complex space, resulting in a SBPML domain. Upon spatial discretization, the proposed method is formulated using a 2nd-order mixed displacement-stress unsplit-field formulation, allowing seamless coupling with FEM and SBFEM originally designed for the interior computational domain. Finally, three benchmark examples of wave propagation problems in unbounded domains and two soil-structure interaction problems of engineering problems are presented to demonstrate the accuracy and robustness of the Prismatic-element SBPML.

3D isogeometric indirect BEM solution based on virtual surface sources on the boundaries of Helmholtz acoustic problems

A solution for 3D Helmholtz acoustic problems is introduced based on an indirect boundary element method (indirect BEM) coupled with isogeometric analysis (IGA). The novelty of this work arises from using virtual surface sources placed directly on the scatterer boundaries, producing robust results. These virtual surface sources are discretized by the same Non-Uniform Rational B-Splines (NURBS) approximating the scatterer CAD model. This allows modeling of general irregular geometries. The proposed solution has the same features of BEM approaches, which do not need any domain discretization or truncation boundaries at the far-field. It shows an additional merit by arranging the linear system of equations directly depending on a single coefficient matrix, consuming less computational time compared to other BEM methods. A Greville abscissae collocation scheme is proposed with offsets at C0\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$C^0$$\\end{document}-continuities. This collocation scheme allows for easy evaluation for both free-terms and normals at the collocation points. The performance of the proposed solution is discussed on 3D numerical exterior problems and compared against other BEM methods. Then, the practical interior muffler problem with internal extended thin tubes is studied and the obtained results are compared against other numerical methods in addition to the available experimental data, showing the capability of the proposed solution in handling thin-walled geometries.

An unsplit-field viscoelastic complex-frequency-shifted perfectly matched layer for analysis of transient waves in heterogeneous media based on an efficient voxel element method

Wave propagation analysis of heterogeneous unbounded media employing domain discretization methods necessitates truncation of the finite computational domain at its truncation boundaries. The Perfectly Matched Layer (PML) is a robust absorbing boundary condition, which is extensively employed to favorably absorb outgoing scattered waves from the interior computational domain, regardless of frequencies and directions of outgoing waves. Nonetheless, most available PMLs are developed for elastic domains, while their developments in domain discretization methods, which consider damping using the Rayleigh damping formulation, are insufficient. In this study, a viscoelastic PML formulation is developed that accommodates the Rayleigh-type damping. The PMLs are basically developed from a coordinate transformation concept using a complex stretching function. Suitable stretching functions can efficiently control the absorptive properties and the spectral character of the PML. Besides, the stretching functions play a crucial role in the long-time stability of transient wave simulations. The standard stretching function usually results in spurious reflections, especially when propagating waves incident to the truncation boundary at near-grazing incidence. On the other hand, the complex-frequency-shifted (CFS) stretching function has been shown to mitigate long-time instability. Therefore, the proposed viscoelastic PML in the time-domain and frequency-domain are derived using the CFS stretching function for the first time. Comprehensive formulations of the proposed viscoelastic CFS-PML are given, where the displacement field is represented as the sole unknown variable of the problem. Hence, the proposed CFS-PML can be incorporated into any domain discretization method. However, the proposed CFS-PML is further developed in the context of the voxel element method, where element-by-element iterative strategies are implemented to solve the governing equations without storing global matrices in the computer memory. Comprehensive numerical experiments are conducted to demonstrate the validity and efficiency of the proposed viscoelastic CFS-PML formulation in analyzing soil profiles with various damping ratios and properties. Moreover, long-time stability for problems involving waveguides and near-grazing wave incidence is studied, where no instabilities are detected.

Nonlinear seismic response and damage evolution of a mountain tunnel: Multi-scale simulation by IBEM-FEM coupled method

Studying dynamic response and damage assessment of mountain tunnels is paramount in earthquake engineering. This paper proposed a novel method, the indirect boundary element method-finite element method (IBEM-FEM) coupled method, aimed to concurrently simulate the amplification effect of kilometer-scale mountain topography and the damage evolution in a centimeter-scale lining tunnel section. The proposed method involves two fundamental steps. Initially, the input motion on the truncation boundary within the mountain is accurately determined using the indirect boundary element method (IBEM). Subsequently, the nonlinear dynamic behavior of the tunnel structure and its adjacent area is analyzed by the finite element method (FEM) based on the results from the previous step. This study numerically simulates the seismic damage and failure mechanisms of a mountain tunnel considering three influence factors: incident wave types, incident wave intensities, and surrounding rock mass grades. The results indicate that mountain topography amplifies the seismic response, thereby affecting the dynamic behavior of the tunnel. Under the incidence of SV-waves and P-waves, the dynamic damage distribution patterns of the tunnel lining are significantly different. Moreover, as seismic wave intensity increases, the peak values of tunnel stress exhibit a non-monotonic increasing trend. The surrounding rock mass grade also significantly affects the dynamic response and damage distribution of the mountain tunnel. Overall, the proposed IBEM-FEM coupled method can effectively consider complex mountain topography and is applicable for evaluating the nonlinear seismic response of mountain tunnels.

Analysis of the absorbing boundary condition for the Maxwell fluid flow over a semi-infinite plate with considering the magnetic field

In this paper, we analyze the flow mechanism of the Maxwell fluid over a semi-infinite plate. To handle the semi-infinite boundary, the artificial boundary method is employed and the absorbing boundary condition in the form of convolution is derived. Besides, the stability of the absorbing boundary condition is analyzed. Solutions are obtained numerically using the finite difference method and the accuracy is verified by introducing a source term to construct the exact solution. To demonstrate the validity and reasonableness of the absorbing boundary condition, a comparison with the direct truncation boundary is discussed. Our study examines the effects of the magnetic field, relaxation parameter, oscillation frequency and plate amplitude on the velocity distribution and flow mechanism of the Maxwell fluid.

ADMM-inspired image reconstruction forterahertz off-axis digital holography.

Image reconstruction in off-axis terahertz digital holography is complicated due to the harsh recording conditions and the non-convexity form of the problem. In this paper, we propose an inverse problem-based reconstruction technique that jointly reconstructs the object field and the amplitude of the reference field. Regularization in the wavelet domain promotes a sparse object solution. A single objective function combining the data-fidelity and regularization terms is optimized with a dedicated algorithm based on an alternating direction method of multipliers framework. Each iteration alternates between two consecutive optimizations using projections operating on each solution and one soft thresholding operator applying to the object solution. The method is preceded by a windowing process to alleviate artifacts due to the mismatch between camera frame truncation and periodic boundary conditions assumed to implement convolution operators. Experiments demonstrate the effectiveness of the proposed method, in particular, improvements of reconstruction quality, compared to two other methods.

Tidal Truncation of Circumplanetary Disks Fails above a Critical Disk Aspect Ratio

We use numerical simulations of circumplanetary disks to determine the boundary between disks that are radially truncated by the tidal potential and those where gas escapes the Hill sphere. We consider a model problem, in which a coplanar circumplanetary disk is resupplied with gas at an injection radius smaller than the Hill radius. We evolve the disk using the Phantom smoothed particle hydrodynamics code until a steady state is reached. We find that the most significant dependence of the truncation boundary is on the disk aspect ratio H/R. Circumplanetary disks are efficiently truncated for H/R ≲ 0.2. For H/R ≃ 0.3, up to about half of the injected mass, depending on the injection radius, flows outward through the decretion disk and escapes. As expected from analytic arguments, the conditions (H/R and Shakura–Sunyaev α) required for tidal truncation are independent of planet mass. A simulation with larger α = 0.1 shows stronger outflow than one with α = 0.01, but the dependence on transport efficiency is less important than variations of H/R. Our results suggest two distinct classes of circumplanetary disks: tidally truncated thin disks with dust-poor outer regions, and thicker actively decreting disks with enhanced dust-to-gas ratios. Applying our results to the PDS 70 c system, we predict a largely truncated circumplanetary disk, but it is possible that enough mass escapes to support an outward flow of dust that could explain the observed disk size.

Analysis of the absorbing boundary conditions for anomalous diffusion in comb model with Cattaneo model in an unbounded region

A fractional governing equation is derived from the two-dimensional anomalous diffusion in the comb model with the Cattaneo model by using rigorous derivation. One strategy to deal with the unbounded region is to create acceptable truncation. We abandon the traditional method of approximating infinite boundaries by enormous value and use the artificial boundary method to construct absorbing boundary conditions using the Laplace transform. The absorbing boundary conditions with the Mittag-Leffler function are obtained, and the stability is demonstrated. We discretise the governing equation by using the finite difference method, and the accuracy of the numerical method is confirmed by comparing with the exact solution, which is generated by introducing a source term. The particle distributions and the mean square displacement under the absorbing boundary conditions are in good agreement with the exact expressions which are superior to the conventional direct truncation boundary conditions. Additionally, the particle distributions under different parameters are examined and explained graphically.

Time harmonic analysis of concrete gravity dam-reservoir systems by mixed High order-Wavenumber approach for general reservoir bottom condition

Recently, mixed HO-WN (i.e., High order-Wavenumber) method was introduced for dynamic analysis of concrete gravity dam-reservoir systems. This is formulated by FE-(FE-TE) approach (i.e., Finite Element-(Finite Element-Truncation Element)). In this technique, dam and reservoir are discretized by plane solid and fluid finite elements. Moreover, the mixed HO-WN (i.e., High order-Wavenumber) condition is imposed at the reservoir truncation boundary. This task is formulated by employing a truncation element at that boundary. The method is derived by combining the High-order and Wavenumber approaches. The present study is an extension of mixed HO-WN approach which allows it to be effectively utilized in the case of absorptive as well as fully reflective reservoir bottom condition. The formulation is initially explained in details and three alternatives are presented for this method. Subsequently, the response of an idealized triangular dam-reservoir system is studied for an absorptive reservoir condition due to horizontal and vertical ground motions. For each alternative, responses are evaluated from accuracy point of view by comparing them against exact solutions for three different values of normalized reservoir length (i.e., L/H ratio). It should be emphasized that a very low value of L/H = 0.2 is also considered for this investigation which makes it a very challenging test for any kind of truncation boundary condition. Moreover, it is worthwhile to stress that although time harmonic analysis is adopted in the present study, the main part of formulation is explained in the context of time domain. Therefore, the approach can easily be extended for transient type of analysis.

Artificial boundary condition for Klein-Gordon equation by constructing mechanics structure

An innovative local artificial boundary condition is proposed to numerically solve the Cauchy problem of the Klein-Gordon equation in an unbounded domain. Initially, the equation is considered as the axial wave propagation in a bar supported on a spring foundation. The numerical model is then truncated by replacing the half-infinitely long bar with an equivalent mechanical structure. The effective frequency-dependent stiffness of the half-infinitely long bar is expressed as the sum of rational terms using Pade approximation. For each term, a corresponding substructure composed of dampers and masses is constructed. Finally, the equivalent mechanical structure is obtained by parallelly connecting these substructures. The proposed approach can be easily implemented within a standard finite element framework by incorporating additional mass points and damper elements. Numerical examples show that with just a few extra degrees of freedom, the proposed approach effectively suppresses artificial reflections at the truncation boundary and exhibits first-order convergence.

Insight into the significance of absorbing boundary condition for the flow mechanism analysis of fractional Maxwell fluid over a semi-infinite plate

Viscoelastic fluids have many applications in engineering, and studying the complex fluidity of viscoelastic fluids can improve their applicability. Based on the flow caused by the pressure or the moving plate with various velocities, the aim of this paper is to deeply study the significance of absorbing boundary condition for the flow mechanism analysis of the fractional Maxwell fluid, of which the constitutive relation is formulated by introducing the relaxation parameter and the fractional parameter with considering the memory characteristics. For treating the model in a semi-infinite boundary domain, the artificial boundary method is applied to transfer it to a problem in a bounded domain with absorbing boundary condition, which is solved numerically by the finite difference method combined with the L1 formula and verified by numerical examples. The difference of the flow characteristics is subject to the direct truncation boundary condition and the absorbing boundary condition is compared and the effectiveness and rationality are analyzed graphically, and the influences of the dynamic parameters on the velocity and the flow mechanism are also discussed. The main findings of this research are that the larger relaxation parameter plays a role in a stronger delay effect, a larger fractional parameter refers to the stronger memory characteristics of the delay effect, and the smaller Reynolds number leads to the larger viscous force, all of which lead to a slower flow process.

3D finite element modeling techniques and application to underwater target scattering

Underwater acoustic target scattering measurements rely on high fidelity modeling for experimental comparison and understanding. Three-dimensional (3D) finite element models are well suited for this purpose, as they can account for arbitrary or unknown target properties and configurations/orientations within complex and asymmetrical seafloor environments. High acoustic frequencies and large physical distances associated with in situ scattering measurements pose challenges to 3D modeling efforts in terms of model sizes and runtimes. Certain model considerations must be made to keep the 3D model computationally efficient, yet accurate in predictive capability. Numerically determined Green’s functions are demonstrated to permit 3D model reduction, while still preserving far-field scattering prediction capability through the Helmholtz-Kirchhoff integral. By determining Green’s functions within the model, they need not be known or estimated for complex ocean environments a priori. Nontraditional scattering formulations and a survey of boundary truncation methods also are explored and implemented for maximal accuracy within small 3D computational domains. Model results for canonical elastic targets within varying seafloor environments are shown and compared to theory and experimentation. [This work has been supported by the Strategic Environmental Research and Development Program, and by the Office of Naval Research, Ocean Acoustics.]

Application of G-N high-order boundary condition on time harmonic analysis of concrete gravity dam-reservoir systems

PurposeThe response of an idealized triangular concrete gravity dam is studied due to horizontal and vertical ground motions for both fully reflective and absorptive reservoir bottom conditions. For each combination, in this paper different orders of Givoli-Neta (G-N) high-order truncation condition are aimed to be evaluated from accuracy point of view by comparing the results against corresponding exact solutions which relies on utilizing a two-dimensional fluid hyper-element.Design/methodology/approachIn present study, the dynamic analysis of concrete gravity dam-reservoir systems is formulated by Finite Element (FE)-(FE-TE) approach. In this technique, dam and reservoir are discretized by plane solid and fluid finite elements. Moreover, the G-N high-order condition imposed at the reservoir truncation boundary. This task is formulated by employing a truncation element at that boundary. It is emphasized that reservoir far-field is excluded from the discretized model.FindingsIt was observed that trend in gaining accuracy with increase in the order of G-N condition were basically the same for both horizontal and vertical ground motions under full reflective reservoir bottom condition. Moreover, convergence rate increases for absorptive reservoir bottom condition cases in comparison with fully reflective cases. It is also noticed that in certain cases, the responses are hardly distinguishable from corresponding exact responses. This reveals that proposed FE-(FE-TE) analysis technique based on G-N condition is quite successful, and one may fully rely on that for accurate and efficient analysis of concrete gravity dam-reservoir systems.Originality/valueDynamic analysis of concrete gravity dam-reservoir systems are formulated by a new method. The salient aspect of the technique is that it utilizes G-N high-order condition at the truncation boundary. This is achieved by developing a special truncation element which its generalized matrices are derived for Finite Element Method (FEM) programmers. The method is discussed for all types of excitation and reservoir bottom conditions. It must be emphasized that although time harmonic analysis is considered in the present study, the main part of formulation is explained in the context of time domain. Therefore, the approach can easily be extended for transient type of analysis.

Isogeometric indirect BEM solution based on virtual continuous sources placed directly on the boundary of 2D Helmholtz acoustic problems

An indirect boundary element method (BEM) based on isogeometric analysis (IGA) is proposed for 2D Helmholtz acoustic problems using virtual continuous sources placed directly on the problem boundary. The virtual sources form a virtual boundary identical to the main problem boundary. The proposed solution couples the CAD model with the analysis model by approximating both the CAD model and the virtual continuous sources with the same non-uniform rational B-spline functions (NURBS). Moreover, neither domain discretization nor truncation boundaries at the far-field are required. This solution creates only one coefficient matrix by directly arranging the linear system of equations.The solution follows a collocation scheme on the boundaries based on Greville abscissae with offsets wherever C0 continuity is encountered to permit an easy prediction for the normal directions and the free-terms at the collocation points required in the cases of Neumann and Robin boundary conditions. It allows us also to treat all integrals with standard Gauss quadrature points.Several numerical examples for exterior and interior acoustic problems are discussed to verify the proposed solution with comparisons to analytical solutions and previously published numerical results. These examples prove the robustness of the proposed solution even for high wavenumbers, in contrast to the previous attempts which implemented extensive investigations to find out the optimum place of the sources outside the domain producing minimum errors. Furthermore, no fictitious eigenfrequency problem is observed for exterior acoustic problems.

Construction parameters of graded sand-gravel foundation on seismic response law of nuclear safety grade underground corridor

The treatment of soft soil foundation under nuclear safety grade corridors with graded sand and gravel materials has a good development prospect. It is of great engineering value to explore the influence of construction parameters of graded sand and gravel foundation on the seismic response of gallery structures. Taking the safety grade underground corridor of a nuclear power plant as the engineering background, the equivalent linear method is used to consider the nonlinear dynamic characteristics of graded sand and gravel. The energy transfer boundary is applied at the truncation boundary to simulate the dissipation effect of scattered wave fluctuation energy and the ground motion input. The thicknessless contact element is introduced to consider the contact effect between the corridor structure and the graded sand and gravel foundation, so as to establish the calculation model of the dynamic interaction between the graded sand and gravel foundation and the corridor structure. Furthermore, the influence of the relative compactness and the foundation treatment depth on the seismic response of the corridor structure is studied, and the calculation results of the acceleration response spectrum and relative displacement of the corridor structure are analyzed. The calculation results show that the two construction parameters have different degrees of influence on the seismic response of corridor structure. The research results can provide reference for the engineering design and construction of underground corridors, and provide technical support for the application of graded gravel materials in soft soil foundation treatment.

Probing Two Distinct Types of Topological Rainbow Concentrators Related to the Acoustic Valley Hall Insulator in Synthesized Three-Dimensional Space

Synthesized three-dimensional space provides us with a platform to explore the intriguing acoustic valley Hall insulator. In this paper, a rotational degree of freedom is introduced to construct a synthetic three-dimensional space. Based on simulations, our results show that Weyl points and Fermi arcs and topologically nontrivial edge modes appear in a synthetic space. Not only rotational operation but also boundary truncation can modulate the frequencies of nontrivial edge states, which result in two completely different edge states at the upper and lower boundaries. Using frequencies of edge states protected by Weyl points, we devise two different acoustic topological rainbow devices. The two devices are able to trap states with different frequency components at different spatial positions: one device is capable of capturing low-frequency components at close range, while the other has the ability to confine low-frequency components at long distances. This work may boost further the development of topological rainbow devices in a synthetic space related to the acoustic valley Hall insulator.