Search

A new crack-tip finite element able to improve the accuracy of Finite Element Method (FEM) solutions for cracks growing along the Winkler-type spring interfaces between linear elastic adherents is proposed. The spring model for interface fracture, sometimes called Linear-Elastic (perfectly) Brittle Interface Model (LEBIM), can be used, e.g., to analyse fracture of adhesive joints with a thin adhesive layer. Recently an analytical expression for the asymptotic elastic solution with logarithmic stress-singularity at the interface crack tip considering spring-like interface behaviour under fracture Mode III was deduced by some of the authors. Based on this asymptotic solution, a special 5-node triangular crack-tip finite element is developed. The generated special singular shape functions reproduce the radial behaviour of the first main term and shadow terms of the asymptotic solution. This special element implemented in a FEM code written in Matlab has successfully passed various patch tests with spring boundary conditions. The new element allows to model cracks in spring interfaces without the need of using excessively refined FEM meshes, which is one of the current disadvantages in the use of LEBIM when stiff spring interfaces are considered. Numerical tests carried out by h-refinement of uniform meshes show that the new singular element consistently provides significantly more accurate results than the standard finite elements, especially for stiff interfaces, which could be relevant for practical applications minimizing computational costs. The new element can also be used to solve other problems with logarithmic stress-singularities. [ABSTRACT FROM AUTHOR]

IN THIS PAPER, THE EXISTENCE OF RAYLEIGH WAVES propagating in weakly nonlocal incompressible isotropic elastic half-spaces subject to the tangential impedance boundary condition (TIBC) (at the surface of half-spaces, the tangential stress is proportional to the horizontal displacement and the normal stress is zero) is investigated. It is shown that for the negative values of the dimensionless tangential impedance parameter and the values of the dimensionless nonlocality parameter belong to the interval (0, 0.5), there exist exactly two Rayleigh waves. The first wave is the counterpart of the Rayleigh wave in local incompressible isotropic elastic half-spaces and the second is a new Rayleigh mode appearing due to the presence of nonlocality. Formulae for their velocities have been derived. Remarkably, the second wave can travel with very high velocity. [ABSTRACT FROM AUTHOR]

We regard anisotropic Maxwell's equations as a boundary control and observation system on a bounded Lipschitz domain. The boundary is split into two parts: one part with perfect conductor boundary conditions and the other where the control and observation takes place. We apply a feedback control law that stabilizes the system in a semi-uniform manner without any further geometric assumption on the domain. This will be achieved by separating the equilibriums from the system and show that the remaining system is described by an operator with compact resolvent. Furthermore, we will apply a unique continuation principle on the resolvent equation to show that there are no eigenvalues on the imaginary axis. [ABSTRACT FROM AUTHOR]

A boundary value problem for Maxwell's equations in the frequency domain with impedance boundary conditions is considered. The problem is reduced to solving a system of two boundary integral equations containing weakly and strongly singular integrals. For the numerical solution of a system of integral equations, the paper presents a numerical solution method based on piecewise constant approximation and collocation methods. Thus, the original problem is reduced to solving a system of linear algebraic equations with a dense matrix. To effectively solve a system of linear equations, the method of mosaic-skeleton approximations of matrices is used. The specifics of applying the method of mosaic-skeleton approximations in this problem are analyzed. [ABSTRACT FROM AUTHOR]

In the cm-wave range, the skin depth is comparable to the micron radius of ferromagnetic wires and thus their magnetic and conductive properties will influence the scattered electromagnetic field. Solving the scattering problem by considering the complicated internal magnetic structure of the wire becomes unpractical. There is thus a need to develop hybrid methods when the external problem of scattering on an inclusion is solved together with the experimental impedance conditions on its surface. Herein, we propose an accurate broadband impedance measurement technique operating up to 15 GHz. The printed circuit board measurement and calibration cells designed in this work allow flexibility in choosing external stimuli such as magnetic field, tensile stress, and heat. The experimental impedance can be then used as the boundary condition in electromagnetic simulations making it possible to model, predict and design wire-based composites using numerical solvers such as CST Studio Suite. [ABSTRACT FROM AUTHOR]

Abstract The study investigates the H‐polarized plane wave diffraction by a slotted cylinder with different surface impedances employing an analytical‐numerical approach. The solution is obtained by expressing the current distribution on the obstacle with Gegenbauer polynomials considering the edge conditions. To obtain the field and current distribution on the surface, the Leontovich boundary condition on each side of the slotted cylinder is employed. The results are compared with Dirichlet and Neumann boundary condition cases obtained previously. It is observed that the resonant field amplitudes and the location at the resonances strongly depend on the impedance values.

Copyright of Systems Engineering & Electronics is the property of Journal of Systems Engineering & Electronics Editorial Department and its content may not be copied or emailed to multiple sites or posted to a listserv without the copyright holder's express written permission. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract. (Copyright applies to all Abstracts.)

We consider the time-harmonic Maxwell's equations in anisotropic media. The problem to be solved is an approximation of the diffraction problem, or scattering from bounded objects, that is usually set in some exterior domain in ℝ³. We consider perfectly conducting objects, so the equations are supplemented with a Dirichlet boundary condition on those objects, and we truncate the exterior domain by imposing an impedance condition on an artificial boundary, to model an approximate radiation condition. The resulting problem is then posed in a bounded domain, with Dirichlet and impedance boundary conditions. In this work, we focus on the mathematical meaning of the impedance condition, precisely in which function space it holds. This relies on a careful analysis of the regularity of the traces of electromagnetic fields, which can be derived thanks to the study of the regularity of the solution to second-order surface PDEs. Then, we prove well-posedness of the model, and we determine the a priori regularity of the fields in the domain and on the boundaries, depending on the geometry, the coefficients, and the data. Finally, the discretization of the formulations is presented, with an approximation based on edge finite elements. Error estimates are derived, and a benchmark is provided to discuss those estimates. [ABSTRACT FROM AUTHOR]

A time-harmonic electromagnetic wave is scattered by a buried object. We assume that the scattering object has an impedance boundary surface and it is embedded in a piecewise homogeneous isotropic background chiral medium. Using a chiral reciprocity gap operator and appropriate density properties of chiral Herglotz wave functions we solve an inverse scattering problem for reconstruction of the shape of the scatterer from the knowledge of the tangential components of electric and magnetic fields, without requiring any a priori information of the physical properties. Furthermore, a characterization of the surface impedance of the scattering object is proved. [ABSTRACT FROM AUTHOR]

The study investigates the H‐polarized plane wave diffraction by a slotted cylinder with different surface impedances employing an analytical‐numerical approach. The solution is obtained by expressing the current distribution on the obstacle with Gegenbauer polynomials considering the edge conditions. To obtain the field and current distribution on the surface, the Leontovich boundary condition on each side of the slotted cylinder is employed. The results are compared with Dirichlet and Neumann boundary condition cases obtained previously. It is observed that the resonant field amplitudes and the location at the resonances strongly depend on the impedance values. [ABSTRACT FROM AUTHOR]

To analyze a microstrip antenna consisting of a lossy metal, we proposed a scheme for a method of moments (MoM) to completely implement a zero-thickness impedance boundary condition (IBC). This model is more accurate for lossy metal than other boundary conditions, such as a resistive sheet model. The accuracy of the proposed scheme is numerically demonstrated by comparing antenna parameters, such as the scattering parameter, directivity, gain, and efficiency, computed by two commercial tools, FEKO and HFSS. These tools and the proposed scheme were applied to two microstrip antennas made from lossy metals with various conductivity.

Copyright of Technical Electrodynamics / Tekhnichna Elektrodynamika is the property of National Academy of Sciences of Ukraine, Institute of Electrodynamics and its content may not be copied or emailed to multiple sites or posted to a listserv without the copyright holder's express written permission. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract. (Copyright applies to all Abstracts.)

• Eccentric swirl inlet leads to additional efficiency and stall margin losses, resulting in a decrease in the compression capacity of the system. • Eccentric swirls generate localized over-loading, where abnormal prestall disturbances in the frequency range of 0.3-0.5 BPF amplify. • A novel casing treatment is proven to address the circumferential non-uniformity problem in the fan. • IBC CT enables the fan under an eccentric inlet to reach the stability boundary of the concentric inlet which has the same average loading. An eccentric inlet swirl, a source of circumferential non-uniformity in aero-engines, can compromise the stable operational range of the compression system and potentially jeopardize the safety of the entire flight vehicle. This study experimentally examined the additional effects of an eccentric inlet swirl on an axial fan in comparison with a concentric inlet condition. Then, the effectiveness of an impedance-boundary-controlled (IBC) casing treatment (CT) in extending the stable operating range of the fan under eccentric inlets is evaluated. Steady-state loading and prestall disturbance analyses were conducted using a five-hole probe and high-frequency response pressure transducers to elucidate the instability mechanisms of fans exposed to eccentric inlets. The findings indicate that the eccentric swirl generates localized over-loading regions around the circumference, where abnormal prestall disturbances amplify in amplitude across a frequency range of 0.3 to 0.5 times the blade passing frequency. These characteristics were mitigated when IBC CT was applied over the rotor tip, allowing the fan to operate under concentric inlet conditions. The IBC CT enhances the stall margin of the fan by 9.3–19.6% in response to a range of swirl inlet conditions, suggesting its potential to address the irregularity problems in fans/compressors. The mechanisms by which IBC CT extends the stall margin are discussed from the unique perspective of evaluating steady loading and system damping. [ABSTRACT FROM AUTHOR]

A boundary element method formulation coupled with the impedance boundary condition is proposed as an efficient way to compute the frequency-dependent impedance of axisymmetric air-core inductors. The formulation is based on the splitting of the magnetic vector potential into a source and an eddy current component in the axisymmetric field. The proposed technique is tested against standard finite element method results. [ABSTRACT FROM AUTHOR]

In this paper, we investigate shape inversion algorithms based on the computation of iterated topological derivatives for the detection of multiple particles coated by a complex surface impedance in two- and three-dimensional acoustic media. New closed-form formulae for the topological derivative of the misfit functional are derived when an approximate set of unknown particles has already been recovered. Proofs rely on the computation of shape derivatives followed by the topological asymptotic analysis of a boundary integral equation formulation of the forward and adjoint problems. The relevance of the theoretical results is illustrated by various 2D and 3D experiments using monochromatic imaging algorithms either fully or partially based on topological derivatives. [ABSTRACT FROM AUTHOR]

In this paper, we consider the reconstruction of the shape and the impedance function of an obstacle from measurements of the scattered field at a collection of receivers outside the object. The data is assumed to be generated by plane waves impinging on the unknown obstacle from multiple directions and at multiple frequencies. This inverse problem can be reformulated as an optimization problem: that of finding band-limited shape and impedance functions which minimize the L2 distance between the computed value of the scattered field at the receivers and the given measurement data. The optimization problem is highly non-linear, non-convex, and ill-posed. Moreover, the objective function is computationally expensive to evaluate (since a large number of Helmholtz boundary value problems need to be solved at every iteration in the optimization loop). The recursive linearization approach (RLA) proposed by Chen has been successful in addressing these issues in the context of recovering the sound speed of an inhomogeneous object or the shape of a sound-soft obstacle. We present an extension of the RLA for the recovery of both the shape and impedance functions of the object. The RLA is, in essence, a continuation method in frequency where a sequence of single frequency inverse problems is solved. At each higher frequency, one attempts to recover incrementally higher resolution features using a step assumed to be small enough to ensure that the initial guess obtained at the preceding frequency lies in the basin of attraction for Newton’s method at the new frequency. We demonstrate the effectiveness of this approach with several numerical examples. Surprisingly, we find that one can recover the shape with high accuracy even when the measurements are generated by sound-hard or sound-soft objects, eliminating the need to know the precise boundary conditions appropriate for modeling the object under consideration. While the method is effective in obtaining high-quality reconstructions for many complicated geometries and impedance functions, a number of interesting open questions remain regarding the convergence behavior of the approach. We present numerical experiments that suggest underlying mechanisms of success and failure, pointing out areas where improvements could help lead to robust and automatic tools for the solution of inverse obstacle scattering problems. [ABSTRACT FROM AUTHOR]

In this paper, we propose a reducedcomplexity finite difference time domain (FDTD) simulations of modulated metasurfaces with arbitrary unit cells. The three dimensional (3D) physical structure of the metasurface is substituted by a spatially varying surface impedance boundary condition (IBC) in the simulation; as the mesh size is not dictated by sub-wavelength details, considerable advantage in space- and time-step is achieved. The local parameters of the IBC are obtained by numerical simulation of the individual unit cells of the physical structure, in a periodic environment approximation, in the frequency domain. As the FDTD requires an appropriate time domain impulse-response, the latter is obtained by broad-band frequency simulations, and vector fitting to an analytic realizable time response. The approach is tested on metasurface structures with complex unit cells and extending over 10 -10 wavelengths, using a standard PC with 64GB RAM. [ABSTRACT FROM AUTHOR]

The well-posedness of the acoustic radiation in a 2D duct in the presence of both a fluid in flow and an absorbing wall described by the Myers boundary condition is studied using variational methods. Without flow the problem is found to be well-posed for any impedance value. The presence of a flow complicates the results. With a uniform flow the problem is proven to be always of the Fredholm type but is found to be well-posed only when considering a dissipative radiation problem. With a general shear flow, the Fredholm property is recovered for a weak enough shear and the dissipative radiation problem requires the introduction of extra conditions to be well-posed: enough dissipation, a large enough frequency, and nonintuitive conditions on the impedance value. [ABSTRACT FROM AUTHOR]

In this paper, we investigate two transmission eigenvalue problems associated with the scattering of a media with a coated boundary. In recent years, there has been a lot of interest in studying these eigenvalue problems. It can be shown that the eigenvalues can be recovered from the scattering data and hold information about the material properties of the media one wishes to determine. Motivated by recent works we will study the electromagnetic transmission eigenvalue problem and scalar 'zero-index' transmission eigenvalue problem for a media with a coated boundary. Existence of infinitely many real eigenvalues will be proven as well as showing that the eigenvalues depend monotonically on the refractive index and boundary parameter. Numerical examples in two spatial dimensions are presented for the scalar 'zero-index' transmission eigenvalue problem. Also, in our investigation we prove that as the boundary parameter tends to zero and infinity we recover the classical eigenvalue problems. [ABSTRACT FROM AUTHOR]

The influence of the non-uniformity of the external field to its distribution on the surface of the conducting half-space is investigated on the basis of exact analytical and approximate asymptotic calculation methods of an arbitrary three-dimensional electromagnetic field. The function that generalizes the impedance boundary condition for diffusion of non-uniform field into conducting body is proposed. On the basis of calculations results comparison by exact and approximate methods for concrete model of electromagnetic system the admissible value of the upper limit of the introduced small parameter is established. References 10, figures 5.

In this paper, we consider an acoustic wave transmission problem with mixed boundary conditions of Dirichlet, Neumann, and impedance type. We will derive a formulation as a direct, space-time retarded boundary integral equation, where both Cauchy data are kept as unknowns on the impedance part of the boundary. This requires the definition of single-trace spaces which incorporate homogeneous Dirichlet and Neumann conditions on the corresponding parts on the boundary. We prove the continuity and coercivity of the formulation by employing the technique of operational calculus in the Laplace domain. [ABSTRACT FROM AUTHOR]

We present a multifilament current method (MFCM) incorporated with generalized sheet transition condition (GSTC) to simulate 2-D cylindrical metasurfaces with arbitrary cross sections. The GSTC casts in the form of an impedance-type boundary condition to relate the tangential fields on two sides of a cylindrical metasurface. The MFCM is subsequently introduced and formulated by employing the GSTC. The doublet-current unit, including both electric and magnetic filamentary sources, is introduced in order to capture both co- and cross-polarized scattered and transmitted fields from the GSTC characterized cylindrical metasurfaces. Three illustrative examples are presented to validate the proposed simulation technique. The behaviors of filamentary sources in terms of scattered field singularities and the ill-conditioning issue of the constructed matrix are also discussed in detail. In comparison to existing numerical methods, the proposed technique has its merits on simplicity and conciseness. [ABSTRACT FROM AUTHOR]

It is proved that a convex polyhedral scatterer of impedance type can be uniquely determined by the electric far-field pattern of a nonvanishing incident field. The incoming wave is allowed to be an electromagnetic plane wave, a vector Herglotz wave function, or a point source wave incited by some magnetic dipole. Our proof relies on the refection principle for Maxwell's equations with the impedance (or Leontovich) boundary condition enforcing on a hyperplane. 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. [ABSTRACT FROM AUTHOR]

Two optimization aspects of the meshless method (MLM) based on nonsingular radial basis functions (RBFs) are considered in an acoustic indoor problem. The former is based on the minimization of the mean value of the relative error of the solution in the domain. The letter is based on the minimization of the relative error of the solution at the selected points in the domain. In both cases the optimization leads to the finding relations between physical parameters and the approximate solution parameters. The room acoustic field with uniform, impedance walls is considered. As results, the most effective Hardy's Radial Basis Function (H-RBF) is pointed out and the number of elements in the series solution as a function of frequency is indicated. Next, for H-RBF and fixed n, distributions of appropriate acoustic fields in the domain are compared. It is shown that both aspects of optimization improve the description of the acoustic field in the domain in a strictly defined sense. [ABSTRACT FROM AUTHOR]

This article extends the solution to an electromagnetic wave propagating along a thin wire parallel to the interface between two homogeneous half-spaces to wires coated with insulation. The solution presented in this article includes half-spaces with different magnetic permeability and wires with finite conductance. The solution agrees with earlier works after appropriate restrictions are applied. The effects of varying the parameters representing the half-spaces and conductor insulation on the system attenuation constant are investigated. Equivalent line parameters for the propagation are extracted from the full wave modal equation and analytical approximations of these parameters are provided for conductors located above or below the interface assuming the half-spaces are formed by the earth and air. The limitations of the approximations are investigated and compared with previous approximations that have been identified as used outside the range of their applicability. As well as reviewing some of the more fundamental works on the subject, this article contributes to understanding the limitations of existing theory and establishes an alternate process for further extensions in the field. [ABSTRACT FROM AUTHOR]

An efficiency of the nonsingular meshless method (MLM) was analyzed in an acoustic indoor problem. The solution was assumed in the form of the series of radial bases functions (RBFs). Three representative kinds of RBF were chosen: the Hardy's multiquadratic, inverse multiquadratic, Duchon's functions. The room acoustic field with uniform, impedance walls was considered. To achieve the goal, relationships among physical parameters of the problem and parameters of the approximate solution were first found. Physical parameters constitute the sound absorption coefficient of the boundary and the frequency of acoustic vibrations. In turn, parameters of the solution are the kind of RBFs, the number of elements in the series of the solution and the number and distribution of influence points. Next, it was shown that the approximate acoustic field can be calculated using MLM with a priori error assumed. All approximate results, averaged over representative rectangular section of the room, were calculated and then compared to the corresponding accurate results. This way, it was proved that the MLM, based on RBFs, is efficient method in description of acoustic boundary problems with impedance boundary conditions and in all acoustic frequencies. [ABSTRACT FROM AUTHOR]

In this paper, we consider an inverse rough surface scattering problem in near-field optical imaging. This problem is actually to reconstruct the scattering surface as well as its impedance coefficient from multifrequency near-field data, and can be reduced into an integral scheme by employing an integral representation. We solve this integral scheme by a non-linear integral equation method, and further develop a fast inversion algorithm for reconstructing both the rough surface and the impedance coefficient. Numerical experiments are presented to illustrate the effectiveness of the algorithm. [ABSTRACT FROM AUTHOR]

Graphene-based heterostructures provide a viable platform to implement optoelectronic devices that can operate in the terahertz (THz) band. In this study, the authors focus on multilayer (ML) graphene as the building block to implement high-frequency and low-energy plasmonic interconnects for on-chip signalling in next-generation systems. Two specific plasmonic interconnect geometries are analysed: single waveguide (SWG) and parallel-plate waveguide (PPWG). While SWG interconnects support propagating surface plasmons that are polarised in the transverse magnetic direction, in PPWG interconnects, nearly dispersion-less quasi-transverse electromagnetic modes are supported. The dispersion characteristics are derived by solving Maxwell's equations in the device setup in which ML graphene presents an impedance boundary condition. The effects of number of layers, electrostatic screening, and Fermi level are included in the model of intra-band dynamical surface conductivity of ML graphene. The authors also develop analytical models of energy-per-bit and bandwidth density for both SWG and PPWG interconnects. The energy dissipation includes the effect of plasmon generation, detection, and modulation circuitry within a thermal- and shot-noise-limited transmission of information. They quantify optimal interconnect length scales for which plasmonic interconnects provide lower energy and higher bandwidth when compared against their electrical (copper/low-κ) counterparts at the 2020 ITRS technology node.