Impedance Boundary Research Articles

On Computing Impulse Responses from Frequency-Domain Finite Element Solutions

In acoustics, knowledge of the impulse response of a system is often important. While impulse responses may be measured, they may also be predicted using numerical methods. This work considers the generation of impulse responses from frequency-domain finite element solutions. It is shown that these impulse responses, obtained by inverse Fourier transformation, are noncausal. Through error analysis, it is demonstrated that the noncausality can be reduced by increasing the duration of a source signal used to excite a simulated system. It is found that increasing the source signal duration increases the dispersion-related phase error present in the simulated impulse responses. The findings of this study are used to simulate an impulse response for a system with a nonuniform, frequency-dependent, complex impedance boundary condition.

A Numerical Study on Heat Transfer Performance in a Straight Microchannel Heat Sink with Standing Surface Acoustic Waves

There has been a remarkably increasing interest in applying acoustofluidics in micro-electro-mechanical systems and lab-on-a-chip systems in the past decades. This paper investigated the heat transfer performance in a straight microchannel heat sink which applies standing surface acoustic waves (SSAW) to disturb the flow. Two-dimensional numerical simulations of the SSAW-driven flow are performed by employing perturbation theory on basis of COMSOL platform. The elasticity of microchannel material is taken into account by applying the impedance boundary conditions. Parametric effects on heat transfer performance including the SSAW wavelength and the dimensions of microchannel heat sink are investigated. It is found that the introduction of SSAW can greatly enhance the overall heat transfer. Moreover, with a constant channel height, shorter SSAW wavelength and narrower microchannel are found to be more beneficial to the overall thermal performance. Keeping both the microchannel width and the SSAW wavelength unchanged, a “wide” configuration of the microchannel cross section is recommended to achieve higher heat transfer efficiency. Finally, we elucidate the underlying mechanisms of heat transfer enhancement peculiar to the excitation of SSAW in microchannel, which is attributed to the appearance of acoustic vortices and the disruption of thermal boundary layer induced by acoustic streaming.

Tunable surface waves supported by graphene-covered left-handed material structures

The active tuning of surface waves supported by left-handed materials (LHMs) is a major challenge for their practical applications and usability, and graphene has been proposed as an agent for the active tuning of surface waves. In this study, tunable surface waves supported by graphene-layered LHM structures are investigated theoretically. The analytical and numerical results are computed for transverse electric (TE) and transverse magnetic (TM)-polarized surface waves. According to the spectral range, two configurations of LHMs (i.e., gigahertz (GHz)-LHM and terahertz (THz)-LHM) are discussed. The physical modeling of graphene is done using the conductivity model based on random phase approximation-based Kubo formalism. The split ring resonator (SRR) model and Kramers–Kronig relations-based causality principle are used for the physical realization of LHMs. To simulate the graphene-layered LHM interface, impedance boundary conditions (IBCs) are applied. Numerical results are computed for dispersion curves, effective wave numbers, and field profiles of surface waves supported by graphene-covered GHz-LHM and THz-LHM. The influence of graphene parameters on the resonance frequency, dispersion curves, and confinement characteristics of surface waves is analyzed for both configurations of LHMs. It is concluded that the graphene-covered GHz-LHM structure supports the tunable surface waves as surface plasmon polaritons (SPPs) support TM-polarized waves. However, with the TE-polarized surface wave, the structure supports the surface polaritons, which do not depend upon the graphene parameters. For the case of the graphene-covered THz-LHM structure, it is concluded that the structure supports the plasmon modes for both polarized waves and the resonance frequency ranges from THz to infrared (IR). The confinement of the TE-polarized surface waves on the graphene layer can be enhanced up to fourfold as compared to the suspended monolayer graphene by using a THz-LHM substrate. Further, the numerical results are found to be consistent with the literature under special conditions. The proposed graphene-layered LHM structure may have potential uses in the active tuning of surface waves, near-field communication and imaging devices, surface waveguide design, and LHM-based metasurfaces.

Chassis Influence on the Exposure Assessment of a Compact EV during WPT Recharging Operations

In this study, the external magnetic field emitted by a wireless power transfer (WPT) system and the internal electric field induced in human body models during recharging operations of a compact electric vehicle (EV) are evaluated. The magneticfield is calculated with a hybrid scheme coupling the boundary element method with the surface impedance boundary conditions in order to fit the multiscale open-boundary characteristics of the problem. A commercial software is then used to perform numerical dosimetry. Specifically, two realistic anatomical models, both in a driving position and in a standing posture, are considered, and the chassis of the EV is modeled either as a currently employed aluminum alloy and as a futuristic carbon fiber composite panel. Aligned and misaligned coil configurations of the WPT system are considered as well. The analysis of the obtained results shows that the International Commission on Non-Ionizing Radiation Protection (ICNIRP) reference levels are exceeded in the driving position, especially for the carbon fiber chassis, whereas the system is compliant with the basic restrictions, at least for the considered scenarios.

Phase field-based topology optimization of metallic structures for microwave applications using adaptive mesh refinement

An important issue in the metallic structure design for microwave applications is the skin depth which may significantly degrade the intended performance. In order to address the skin depth issue, a perfect electric conductor or an impedance boundary condition can be imposed on the outer surface of the metallic structure. However, it is hard to impose such boundary conditions in topology optimization-based design because clear boundary definition with the best performance is difficult in ordinary topology optimization. To overcome such difficulties, this study proposes the phase field-based topological design process of the metallic structure using the adaptive mesh refinement for improved boundary representation. The reaction-diffusion equations combined with the double-well potentials are used as the update scheme. An exponential function using logarithmic interpolation with penalization is used for electrical conductivity definition of gray materials to replace the PEC boundary conditions for the metallic structure with the adaptive mesh refinement. The design process consists of two steps; the first step derives a roughly optimized shape which is used for the initial shape in the next step, where the finally optimized shape is derived using adapted mesh with respect to the material distribution. The validity of the proposed approach is confirmed through three numerical examples.

Electromagnetic Energy Surface Modes in Metamaterial-Filled Bi-layer Graphene Structures

This paper presents a theoretical study on the propagation of electromagnetic surface waves supported by the metamaterial-filled bi-layered graphene structure. The effective surface conductivity approach based upon the Kubo’s formalism is used to model the atomically thick graphene layer, while the analytical modeling of the metamaterials used the framework of causality principle-based Kramers-Kroing relations. With respect to the index of refraction, the two configurations of metamaterials have been considered—i.e., double positive (DPS) and double negative (DNG). The impedance boundary conditions (IBCs) have been employed at the interface for the computation of characteristics equations of odd and even surface modes under DPS and DNG configurations. The numerical results regarding the dispersion relations, effective mode index, and phase speed for the odd and even modes of electromagnetic surface waves supported by each configuration of structure have been presented. Further, the influence of chemical potential and thickness of metamaterial filling in parallel graphene layers on the wave propagation characteristics has been analyzed. To check the accuracy of the numerical results, special conditions were employed, which converge to the published results. The proposed work may have potential applications in plasmonic based logic designs, renewable energy devices, THz surface wave guides, and near-field communication devices.

Time-dependent acoustic scattering from generalized impedance boundary conditions via boundary elements and convolution quadrature

Abstract Generalized impedance boundary conditions are effective approximate boundary conditions that describe scattering of waves in situations where the wave interaction with the material involves multiple scales. In particular, this includes materials with a thin coating (with the thickness of the coating as the small scale) and strongly absorbing materials. For the acoustic scattering from generalized impedance boundary conditions, the approach taken here first determines the Dirichlet and Neumann boundary data from a system of time-dependent boundary integral equations with the usual boundary integral operators, and then the scattered wave is obtained from the Kirchhoff representation. The system of time-dependent boundary integral equations is discretized by boundary elements in space and convolution quadrature in time. The well-posedness of the problem and the stability of the numerical discretization rely on the coercivity of the Calderón operator for the Helmholtz equation with frequencies in a complex half-plane. Convergence of optimal order in the natural norms is proved for the full discretization. Numerical experiments illustrate the behaviour of the proposed numerical method.

Propagation of Hybrid Surface Waves in Ferrite Anisotropic Plasma Planar Structures

This manuscript presents a theoretical analysis of hybrid surface wave propagation at the ferrite–anisotropic plasma planar interface. Maxwell’s equations in differential forms and impedance boundary conditions are used to solve the problem. The influence of the plasma frequency, cyclotron frequency, and the different permittivities of ferrite films on the dispersion curve are analyzed. Moreover, the propagation length, normalized phase speed, and normalized field distribution are also analyzed. The presented work may have potential applications in surface waveguide control, optical sensing, and wave propagation in the terahertz frequency range such as measurement of electron bunches, remote sensing, material characterization, medical and biological imaging.

An Inverse Mixed Impedance Scattering Problem in a Chiral Medium

An inverse scattering problem of time-harmonic chiral electromagnetic waves for a buried partially coated object was studied. The buried object was embedded in a piecewise isotropic homogeneous background chiral material. On the boundary of the scattering object, the total electromagnetic field satisfied perfect conductor and impedance boundary conditions. A modified linear sampling method, which originated from the chiral reciprocity gap functional, was employed for reconstruction of the shape of the buried object without requiring any a priori knowledge of the material properties of the scattering object. Furthermore, a characterization of the impedance of the object’s surface was determined.

Parametric speaker analysis in acoustic space with impedance boundary by using concentrated mass model

Parametric speaker analysis in acoustic space with impedance boundary by using concentrated mass model

Inverse Time-Harmonic Electromagnetic Scattering from Coated Polyhedral Scatterers With a Single Far-Field Pattern

It is proved that a convex polyhedral scatterer of impedance type can be uniquely determined by the electric far-field pattern of a non-vanishing incident field. The incoming wave is allowed to bean electromagnetic plane wave, a vector Herglotz wave function or a point source wave incited by some magnetic dipole. Our proof relies on the reflection principle for Maxwell's equations with the impedance (or Leontovich) boundary condition enforcing on a hyper-plane. We prove that it is impossible to analytically extend the total field across any vertex of the scatterer. This leads to a data-driven inversion scheme for imaging an arbitrary convex polyhedron.

Simultaneous Reconstruction of Conductivity, Boundary Shape, and Contact Impedances in Electrical Impedance Tomography

The objective of electrical impedance tomography (EIT) is to reconstruct the internal conductivity of a physical body based on current and voltage measurements at the boundary of the body. In many medical applications the exact shape of the domain boundary and contact impedances are not available. This is problematic as even small errors in the boundary shape of the computation domain or in the contact impedance values can produce large artifacts in the reconstructed images which results in a loss of relevant information. A method is proposed that simultaneously reconstructs the conductivity, the contact impedances and the boundary shape from EIT data. The approach consists of three steps: first, the unknown contact impedances and an anisotropic conductivity reproducing the measured EIT data in a model domain are computed. Second, using isothermal coordinates, a deformation is constructed that makes the conductivity isotropic. The final step minimizes the error of true and reconstructed known geometric properties (like the electrode lengths) using conformal deformations. The feasibility of the method is illustrated with experimental EIT data, with robust and accurate reconstructions of both conductivity and boundary shape.

An Inverse Parameter Problem with Generalized Impedance Boundary Condition for Two-Dimensional Linear Viscoelasticity

We analyze an inverse boundary value problem in two-dimensional viscoelastic media with a generalized impedance boundary condition on the inclusion via boundary integral equation methods. The model...

Variational Methods for Acoustic Radiation in a Duct with a Shear Flow and an Absorbing Boundary

Related DatabasesWeb of Science You must be logged in with an active subscription to view this.Article DataHistorySubmitted: 3 December 2020Accepted: 23 August 2021Published online: 13 December 2021Keywordsacoustics, time-harmonic radiation, fluid in motion, impedance boundary condition, variational methods, Fredholm alternativeAMS Subject Headings35J20, 35J50, 35Q35, 76N10Publication DataISSN (print): 0036-1399ISSN (online): 1095-712XPublisher: Society for Industrial and Applied MathematicsCODEN: smjmap

Optimization of Bathymetry for Long Waves with Small Amplitude

This paper deals with bathymetry-oriented optimization in the case of long waves with small amplitude. Under these two assumptions, the free-surface incompressible Navier-Stokes system can be written as a wave equation where the bathymetry appears as a parameter in the spatial operator. Looking then for time-harmonic fields and writing the bottom topography as a perturbation of a flat bottom, we end up with a heterogeneous Helmholtz equation with impedance boundary condition. In this way, we study some PDE-constrained optimization problem for a Helmholtz equation in heterogeneous media whose coefficients are only bounded with bounded variation. We provide necessary condition for a general cost function to have at least one optimal solution. We also prove the convergence of a finite element approximation of the solution to the considered Helmholtz equation as well as the convergence of discrete optimum toward the continuous ones. We end this paper with some numerical experiments to illustrate the theoretical results and show that some of their assumptions could actually be removed.

One‐dimensional consolidation of layered soils under ramp load based on continuous drainage boundary

AbstractThe traditional drainage boundary regards the drainage boundary as completely permeable or completely impervious. However, the drainage boundary is an impeded drainage boundary between completely permeable and impervious in engineering practice. In view of this, a new drainage boundary, namely the continuous drainage boundary, is introduced in this paper to study the consolidation problem of layered soils. First, the governing equations for the one‐dimensional consolidation problem of layered soils subjected to a ramp load are established. Then, the analytical solution of excess pore water pressure and average consolidation degree is derived by means of Laplace transform and matrix transfer method. The present solution is verified by degenerating it and comparing with existing solutions. Based on the present solution, the consolidation behavior of the layered soils is investigated by conducting a detailed parametric study. The results show that, both the interface parameters of boundaries and the stratification of the layered soils can heavily affect the distribution of the excess pore water pressure along the depth, thereby influence the plane of the maximum excess pore water pressure. Therefore, the interface parameters of boundaries and the soil stratification should be comprehensively considered in the optimization for the horizontal drains.

One-Dimensional Consolidation of Multi-Layered Unsaturated Soil with Impeded Drainage Boundaries

In geotechnical engineering, the consolidation of unsaturated soil is a common issue of great interest. Considering the multi-layered property and impeded drainage boundary condition of the soil stratum in real engineering, this study aimed to develop a general semi-analytical solution for assessing the one-dimensional (1D) consolidation behavior of multi-layered unsaturated soil that is subjected to a general impeded drainage boundary condition and a time-dependent loading. To achieve the final solution, the proposed consolidation system is firstly decoupled and solved in the Laplace domain. Then, the semi-analytical solutions for the excess pore-air pressure and excess pore-water pressures as well as the soil settlement are formulated. The Crump method is employed to provide their final results in the time domain. The correctness of the derived solutions was verified against the available analytical and numerical solutions, and excellent agreements were found for the two comparisons. Moreover, two studied examples are presented to illustrate the 1D consolidation behavior of multi-layered unsaturated soil and the influences stemming from the impeded drainage parameters are discussed.

A general analytical solution for two-dimensional plane strain consolidation of unsaturated soil incorporating lateral and vertical impeded drainage boundaries

In most practical consolidation problems, impeded drainage boundaries are a great concern. By simultaneously introducing the impeded drainage boundaries in the horizontal and vertical directions, this study attempts to constitute a general two-dimensional (2D) plane strain consolidation system of unsaturated soil. A newly analytical solution is developed to calculate the excess pore-air and pore-water pressures and average degree of consolidation. On the basis of the eigenfunction expansion method, the developed analytical solution is given as a product of three functions, including one variable of time, horizontal and vertical dimensions only. For the impeded drainage boundaries, the eigenfunctions and eigenvalues are derived in the horizontal and vertical dimensions. The Laplace transform technique is further adopted to solve the ordinary differential system in the time domain. The developed analytical solution is verified with the existing analytical/semi-analytical solutions and finite difference solution for several typical cases. Excellent agreements are obtained so that the correctness of the developed analytical solution is validated. Moreover, two worked examples are presented to show the superiority of the developed analytical solution and to assess the influences of the drainage parameters on the 2D plane strain consolidation behavior of unsaturated soil.

Domain decomposition preconditioners for high-order discretizations of the heterogeneous Helmholtz equation

Abstract We consider one-level additive Schwarz domain decomposition preconditioners for the Helmholtz equation with variable coefficients (modelling wave propagation in heterogeneous media), subject to boundary conditions that include wave scattering problems. Absorption is included as a parameter in the problem. This problem is discretized using $H^1$-conforming nodal finite elements of fixed local degree $p$ on meshes with diameter $h = h(k)$, chosen so that the error remains bounded with increasing $k$. The action of the one-level preconditioner consists of the parallel solution of problems on subdomains (which can be of general geometry), each equipped with an impedance boundary condition. We prove rigorous estimates on the norm and field of values of the left- or right-preconditioned matrix that show explicitly how the absorption, the heterogeneity in the coefficients and the dependence on the degree enter the estimates. These estimates prove rigorously that, with enough absorption and for $k$ large enough, GMRES is guaranteed to converge in a number of iterations that is independent of $k,p$ and the coefficients. The theoretical threshold for $k$ to be large enough depends on $p$ and on the local variation of coefficients in subdomains (and not globally). Extensive numerical experiments are given for both the absorptive and the propagative cases; in the latter case, we investigate examples both when the coefficients are nontrapping and when they are trapping. These experiments support (i) our theory in terms of dependence on polynomial degree and the coefficients; and (ii) the sharpness of our field of values estimates in terms of the level of absorption required.

Sensitivity analysis of rectangular waveguides with different anisotropic surface impedance boundaries using modal extended theory

This article presents a sensitivity analysis of rectangular waveguides loaded with anisotropic surface impedance boundaries on their vertical walls, by using modal extended theory (MET). Using this method, several dispersion diagrams are computed for various anisotropic impedance boundary conditions of the surface walls of the waveguides in order to assess how the slight changes on the surface impedance can affect on the bandwidth and the fundamental cutoff frequency of the waveguide. The results obtained with MET were validated by comparison with the commercial software ANSYS HFSS. The results show that small anisotropic variations of the surface wall impedances lead to variation on the fundamental cutoff frequency and the bandwidth of the waveguide. Most significantly, and compared to an isotropic metasurface case, the variation of the transverse impedance of the metasurface is the one that have more significant effect over the waveguide parameters. This is an useful information for the metasurface design in order to take into account the fabrication tolerance of these structures and how they can have an influence over the final constructed device.