Impedance Boundary Research Articles

Effect of Initial Stress and Impedance Boundary in Transversely Isotropic Materials

This paper aimed at studying the effect of initial stress and impedance boundary surface on the elastic waves propagation in transversely isotropic materials. The governing equations of transversely isotropic materials with initial stress are treated in the [Formula: see text]-plane to obtain the phase velocities of two waves, quasi-longitudinal ([Formula: see text]) and quasi-transverse ([Formula: see text]) waves. The normal mode operation is employed to obtain the expression of the displacement components and stress components. The problem of reflection of incident waves at the impedance boundary of transversely isotropic material is also investigated in the presence of initial stress to obtain the amplitude ratios of reflected waves. The variations of displacement and force stress are illustrated with respect to the axis of propagation by employing amplitude ratio expression. The effect of initial stress and impedance parameters on the expression of displacement and force stress as well as amplitude ratios of transversely isotropic materials are illustrated graphically for a particular model.

A metacontinuum model for phase gradient metasurfaces

Acoustic metamaterials and metasurfaces often present complex geometries and microstructures. The development of models of reduced complexity is fundamental to alleviate the computational cost of their analysis and derivation of optimal designs. The main objective of this paper is the derivation and validation of a metacontinuum model for phase gradient-based metasurfaces. The method is based on the transformation acoustics framework and defines the metasurface in terms of anisotropic inertia and bulk modulus. Thermal and viscous dissipation effects in the metacontinuum are accounted for by introducing a complex-valued speed of sound. The model is implemented in a commercial FEM code, and its predictions are compared with numerical simulations on the original geometry and also using an equivalent boundary impedance approach. The results are examined for an exterior acoustics benchmark and for an in-duct installation in terms of transmission coefficient with the four-pole matrix method. The metacontinuum model gives solid results for the prediction of the acoustic properties of the examined metasurface samples for all the analyzed configurations, as accurate as the equivalent impedance model on which it is based and outperforming it in some circumstances.

Acoustic impedance extraction method and acoustic characteristics analysis of perforated plates under grazing flow

As an important component of inlet and exhaust mufflers, the acoustic characteristics of perforated components are inevitably affected by the flow of air. Therefore, obtaining the acoustic impedance of the perforated element under airflow conditions is a prerequisite for accurate calculation of the muffler’s muffling performance. In this work, the frequency domain linear Navier–Stokes (L-NS) method is used to extract the acoustic impedance of perforated plates under grazing flow. The predicted perforated acoustic impedance is consistent with the calculation results of published acoustic impedance expression, and the impedance boundary condition is defined to calculate the transmission loss (TL) of the perforated muffler, which agrees well with the experimental results and verifies the accuracy of the method. The effect of perforation angles on the transmission loss of mufflers in different Mach numbers ( Ma) and aperture plate thickness ratio ( dh/ tp) is analyzed by the frequency domain L-NS method. The results show that when 1≤ dh/ tp<2 and Ma≤2, the effect of perforation angles on the muffler performance is obvious, and the angle tilted upstream shifts the resonant frequency to a lower frequency while its corresponding peak value is also increased. As an engineering application, it has certain significance for the prediction of muffler muffling performance and the regulation of the muffling frequency band.

Modeling impedance boundary conditions and acoustic barriers using the immersed boundary method: The three-dimensional case.

One of the main challenges in time domain wave-based acoustics is the accurate simulation of both boundary conditions and barriers capable of reflecting and transmitting energy. Such scattering structures are generally of irregular geometry and characterised in terms of frequency-dependent reflectances and transittances. Conditions for numerical stability can be difficult to obtain in either case. Immersed boundary methods, which are heavily used in computational fluid dynamics applications, replace boundaries by discrete driving terms, avoiding volumetric meshing and staircasing approaches altogether. The main contribution of this article is a unified numerical treatment of both impedance boundary conditions and barriers capable of transmitting energy and suitable for use in the setting of wave-based acoustics. It is framed in terms of the immersed boundary method within a finite difference time domain scheme, using a dual set of matched discrete driving terms in both the conservation of mass and momentum equations that can be tuned against a desired reflectance or transmittance. Numerical results in three dimensions are presented, illustrating non-porous barriers and impedance boundary conditions, and highlight important features such as spurious leakage through an immersed boundary. A brief demonstration of conditions for numerical stability of the immersed boundary method in this context is provided in an appendix.

Spectral-Domain Method of Moments for the Modal Analysis of Line Waveguides

A rigorous full-wave modal analysis based on the method of moments in the spectral domain is presented for line waveguides constituted by two-part impedance planes with arbitrary anisotropic surface impedances. An integral equation is formulated by introducing an auxiliary current sheet on one of the two half planes and extending the impedance boundary condition of the complementary half plane to hold on the entire plane. The equation is then discretized with the method of moments in the spectral domain, by employing exponentially weighted Laguerre polynomials as entire-domain basis functions and performing a Galerkin testing. Numerical results for both <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">bound</i> and <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">leaky</i> line waves are presented and validated against independent results, obtained for isotropic surface impedances with the analytical Sommerfeld–Maliuzhinets method and for the general anisotropic case with a commercial electromagnetic simulator. The proposed approach is computationally efficient, can accommodate the presence of spatial dispersion, and offers physical insight into the modal propagation regimes.

A Rough Estimation of Acoustics of the Cuboidal Room with Impedance Walls

The cuboidal room acoustics field is modelled with the Fourier method. A combination of uniform, impedance boundary conditions imposed on walls is assumed, and they are expressed by absorption coefficient values. The absorption coefficient, in the full range of its values in the discrete form, is considered. With above assumptions, the formula for a rough estimation of the cuboidal room acoustics is derived. This approximate formula expresses the mean sound pressure level as a function of the absorption coefficient, frequency, and volume of the room separately. It is derived based on the least-squares approximation theory and it is a novelty in the cuboidal room acoustics. Theoretical considerations are illustrated via numerical calculations performed for the 3D acoustic problem. Quantitative results received with the help of the approximate formula may be a point of reference to the numerical calculations.

Selected Aspects of Meshless Method Optimization in the Room Acoustics with Impedance Boundary Conditions

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.

Effect of rejuvenation heat treatment on the microstructure and stress relaxation behavior of nickel-based superalloy with excess hardness

The repair of R26 high-temperature alloy bolts with excessive hardness after ∼60,000 h of service using rejuvenation heat treatment was evaluated. Stress relaxation tests with different initial stresses were performed on R26 superalloy before and after rejuvenation heat treatment. The effect of rejuvenation heat treatment on the microstructure of the R26 superalloy was evaluated through a combination of scanning electron microscopy, transmission electron microscopy, and evaluation of the Brinell hardness and stress relaxation behavior. The results showed that the main precipitated phases in the R26 superalloy are the γ’ phase, Ni(Cr32Mo9Fe3), TiC, and Mo23C6. Rejuvenation heat treatment can effectively reduce the hardness of the alloy by dissolving intergranular carbides. In the stress relaxation test, the γ’ phase effectively impeded dislocation movement, whereas Ni(Cr32Mo9Fe3), TiC, and Mo23C6 impeded grain boundary slippage. The specimens without rejuvenation heat treatment showed normal stress relaxation, whereas the specimens subjected to rejuvenation heat treatment showed abnormal stress relaxation. This is attributed to the precipitation of solid-solution Mo from the γ matrix to form a precipitated phase, which induces lattice shrinkage of the γ matrix and size reduction (shrinkage) of the R26 superalloy. The γ’ phase spacing was smaller and dislocation movement was more difficult in the sample subjected to rejuvenation heat treatment than in the congener without rejuvenation heat treatment. The superalloy exhibited better resistance to stress relaxation, resulting in plastic strain during stress relaxation, which was less than the lattice shrinkage. In order to maintain a constant total strain, the external force needs to be increased; thus, the superalloy showed an abnormal stress relaxation phenomenon with increasing stress.

Weakly nonlocal Rayleigh waves with impedance boundary conditions

Weakly nonlocal Rayleigh waves with impedance boundary conditions

Advanced Numerical Methods for Graphene Simulation with Equivalent Boundary Conditions: A Review

Since the discovery of graphene, due to its excellent optical, thermal, mechanical and electrical properties, it has a broad application prospect in energy, materials, biomedicine, electromagnetism and other fields. A great quantity of researches on the physical mechanism of graphene has been applied to engineering in electromagnetism and optics. To study the properties of graphene, different kinds of numerical methods such as the mixed finite element method (Mixed FEM), the mixed spectral element method (Mixed SEM), Method of Auxiliary Sources (MAS), discontinuous Galerkin time-domain method (DGTD) and interior penalty discontinuous Galerkin time domain (IPDG) have been developed for simulating the electromagnetic field effects of graphene and equivalent boundary conditions such as impedance transmission boundary condition (ITBC), surface current boundary condition (SCBC), impedance matrix boundary condition (IMBC) and surface impedance boundary condition (SIBC) have been employed to replace graphene in the computational domain. In this work, the numerical methods with equivalent boundary conditions are reviewed, and some examples are provided to illustrate their applicability.

Impedance Sensitivity Analysis Based on Discontinuous Isogeometric Boundary Element Method in Automotive Acoustics

Abstract Acoustic sensitivity analysis is an essential technique to determine the direction of structural-acoustic optimization by evaluating the gradient of the objective functions with respect to the design variables. However, acoustic sensitivity analysis with respect to acoustic impedance, which is an important parameter representing the interior absorbent material in automotive acoustics, is lacking in the study. Moreover, acoustic sensitivity analysis implemented with conventional numerical methods is time and effort-consuming in automotive acoustics, due to the large-scale mesh generation. In this work, the impedance sensitivity analysis for automotive acoustics based on the discontinuous isogeometric boundary element method is presented. The regularized boundary integral equation with impedance boundary conditions is established, then the sensitivity is derived by differentiating the boundary integral equation. The efficiency of the proposed method is improved by employing the parallel technique and generalized minimal residual solver. A long duct example with an analytical solution validates the accuracy of the proposed method, and an automotive passenger compartment subjecting to impedance boundary conditions illustrates that the computing time of the proposed method is one order of magnitude less than the conventional method. This work presents an easily implementable and efficient tool to investigate acoustic sensitivity with respect to impedance, showing great potential in the application of automotive acoustics.

A data-driven approach to solving a 1D inverse scattering problem

In this paper, we extend a recently proposed approach for inverse scattering with Neumann boundary conditions [Druskin et al., Inverse Probl. 37, 075003 (2021)] to the 1D Schrödinger equation with impedance (Robin) boundary conditions. This method approaches inverse scattering in two steps: first, to extract a reduced order model (ROM) directly from the data and, subsequently, to extract the scattering potential from the ROM. We also propose a novel data-assimilation (DA) inversion method based on the ROM approach, thereby avoiding the need for a Lanczos-orthogonalization (LO) step. Furthermore, we present a detailed numerical study and A comparison of the accuracy and stability of the DA and LO methods.

Multiple Scattering Model for Beam Synthesis With Reconfigurable Intelligent Surfaces

This article presents a method of synthetic beamforming for reconfigurable intelligent surfaces (RIS). The method uses a <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">T</i> -matrix based multiple scattering model to compute the scattering from the RIS. We assume that the elements of the RIS are infinite circular cylinders. This allows us to make the model two-dimensional. Furthermore, we assume that the RIS elements satisfy the impedance boundary condition (IBC), the complex parameter of which adjusts the phase shift of the scattered field. We synthesize the beam both analytically and numerically. Both approaches rely on an approximation that assumes RIS elements that are small compared to the wavelength. We demonstrate the efficacy of the beam synthesis by applying it in a test case that features a linear array of RIS elements.

OCTRA as ultrasonically absorptive thermal protection material for hypersonic transition suppression

Previous investigations in the High Enthalpy Shock Tunnel Göttingen (HEG) of the German Aerospace Center (DLR) show that carbon fiber reinforced carbon ceramic (C/C) surfaces can be utilized to damp hypersonic boundary layer instabilities resulting in a delay of boundary layer transition onset. Numerical stability analyses confirmed these experimental results. However, C/C has some disadvantages, especially the limited oxidation resistance and its low mechanical strength, which could be critical during hypersonic flights. Thus, an ultrasonically absorptive fiber reinforced ceramic material based on a silicon carbide (C/C-SiC) was developed in the past years to fulfill this need. The present paper addresses the numerical rebuilding of the C/C-SiC absorber properties using impedance boundary conditions together with linear stability analysis. The focus of this paper is on the numerical comparison of the original C/C material and the improved C/C-SiC material, referred to as OCTRA in the literature. The influence on the second modes and the transition itself is investigated. The numerical results are compared with HEG wind tunnel tests. The wind tunnel model tested in HEG is a 7^circ half-angle blunted cone with an overall model length of about 1.1 ,textrm{m} and a nose tip radius of 2.5 mm. These experiments were performed at Mach 7.5 and at different freestream unit Reynolds numbers.

Linear stability analysis of second-mode attenuation via porous carbon-matrix ceramics

Effects of porous carbon-fiber-reinforced carbon-matrix ceramics (C/C) on the stability of second-mode waves on a 7°-half-angle cone were investigated for Reynolds numbers Rem=2.43×106–6.40×106 m−1 at the freestream Mach number of M∞=7.4, for both sharp and 2.5-mm-round nose tips. A broadband time-domain impedance boundary condition was used to model the effects of the C/C porosity on the flow dynamics leveraging direct ultrasonic benchtop experiments and homogenous absorber theory. A spectral linear stability solver based on orthogonal Laguerre functions, naturally vanishing in the free stream, was used to predict linear spatial growth rates, which are in agreement with independent pulsed axisymmetric direct-numerical simulations. The latter were carried out with the quasi-spectral viscosity closure—a dynamic quasi-spectral procedure capable of deactivating the sub-filter scale stresses in the absence of turbulent break down—verifying its suitability to carry out transitional calculations without affecting ultrasonic wave dynamics. The effectiveness of a porous C/C surface is shown to decrease drastically with static pressure and its presence is shown to decrease the second-mode growth rates in regions where it is unstable as well as increasing the attenuation rates in regions where it is stable.

Current Based Automated Design of Realizable Metasurface Antennas With Arbitrary Pattern Constraints

We present a 3-D method to numerically design a realizable metasurface, which transforms a given incident field into a radiated field that satisfies mask-type (inequality) constraints. The method is based on an integral equation formulation, with local impedance boundary condition (IBC) approximation. The procedure yields the spatial distribution of the impedance, yet the process involves the synthesis of the equivalent current only. This current is constrained to correspond to a realizable surface impedance, i.e., passive, lossless, and with reactance values bounded by practical realizability limits. The current-based design avoids any solution to the forward problem, and the impedance is obtained from the synthesized current only at the end of the process. The procedure is gradient-based, with the gradient expressed in closed form. This allows handling large metasurfaces, with full spatial variability of the impedance in two dimensions. The method requires no a priori information, and all relevant operations in the iterative process can be evaluated with <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$\boldsymbol { O}(N~\log~{N})$ </tex-math></inline-formula> complexity. Application examples concentrate on the case of on-surface excitation and far-field (FF) pattern specifications; they show designs of circular and rectangular metasurface antennas of 20 wavelengths in size, with pencil- and shaped-beam patterns, and for both circular and linear polarizations.

Effects of memory response and impedance barrier on reflection of plane waves in a nonlocal micropolar porous thermo-diffusive medium

This research problem is an investigation of reflection amplitude in a nonlocal porous-thermo-micropolar diffusion half-space under memory dependent derivative (MDD) thermo-elasticity subjected to impedance boundary reflecting surface. The governing equations for nonlocal porous-thermo-micropolar diffusion medium in MDD theory are formulated. This research challenge is solved analytically for a two-dimensional model in order to demonstrate the presence of four coupled longitudinal waves and two paired transverse waves denoted as coupled longitudinal displacement wave ( cLDW − I ), coupled longitudinal thermal wave ( cLDW − II ), coupled longitudinal mass diffusion wave ( cLDW − III ), coupled longitudinal void volume fraction wave ( cLDW − IV ), and coupled transverse displacement wave ( cTDW ) and coupled transverse micro-rotational wave ( cTMW ). When there is nonlocality, diffusion, and porous characteristics in the medium, it is discovered to have an impact on these coupled longitudinal waves, making them dispersive and attenuating. The transverse wave is non-attenuating but dispersive, it is unaffected by diffusion and porous characteristics. To find the expression for the reflection coefficients of reflected waves, the plane wave reflection from a thermally insulated surface subjected to an impedance boundary is explored. For a specific material, the reflection coefficients of the reflected waves are calculated, and graphic representations of the fluctuations of the reflection coefficients versus the incidence angle, nonlocality, diffusion and porous constants are provided. For further investigation, energy ratio can be studied in future.

Molecular coordination-doping engineering enables adjustable ion transport channel based on MOFs-derived UIOLiTF-LLZTO ionic conductor

The inferior ionic conductivity of composite polymer electrolytes (CPEs) caused by grain boundary impedance is one of the critical issues. Adjustable ion transport channels at the molecular level can improve ionic conductivity and lithium-ion transference number. Herein, UIO-66-NSO2CF3Li-Li6.4La3Zr1.4Ta0.6O12 (UIOLiTF-LLZTO) ionic conductor derived from metal-organic frameworks (MOFs) was designed by a covalent grafted strategy of trifluoromethylsulfonyl (TF) group on UIOLiTF and a doping process of LLZTO, showing two new lithium-ion transfer channels driven by molecular coordination-doping engineering. The first channel along UIOLiTF-UIOLiTF was constructed due to the existence of the TF group on UIOLiTF. The second channel along UIOLiTF-LLZTO was constructed due to the direct nanometer contact interface between the opened channel of UIOLiTF and LLZTO. Then TF group acts as “claws” to capture and transfer lithium-ion along the different channels, facilitating improving ionic conductivity and reducing grain boundary impedance. Benefiting from the molecular coordination-doping engineering, UIOLiTF-LLZTO exhibits high ionic conductivity of 9.86 × 10–4 S cm–1, a large lithium-ion transference number of 0.79, and a wide electrochemical window of 5.35 V. Meanwhile, all-solid-state Li|UIOLiTF-LLZTO|LiFePO4 batteries show a high specific capacity of 164.5 mAh g–1 and 155.6 mAh g–1 at 0.2 C and 0.5 C, respectively. Therefore, UIOLiTF-LLZTO demonstrates the way towards the development of MOFs-based CPEs for all-solid-state lithium batteries with high performance.

Halide‐based solid electrolytes: The history, progress, and challenges

AbstractLithium metal solid‐state batteries (LMSBs) have attracted extensive attention over the past decades, due to their fascinating advantages of safety and potential for high energy density. Solid‐state electrolytes (SEs) with fast ionic transport and excellent stability are indispensable components in LMSBs. Heretofore, a series of inorganic SEs have been extensively explored, such as sulfide‐ and oxide‐based electrolytes. Unfortunately, they both have difficulty in achieving a satisfactory balance of conductivity and stability, and oxides suffer from a high impedance of grain boundaries, while sulfides encounter poor stability. Halide‐based solid electrolytes are gradually emerging as one of the most promising candidates for LMSBs due to their advantages of decent room temperature ionic conductivity (&gt;10−3 S cm−1), good compatibility with oxide cathode materials, good chemical stability, and scalability. Herein, research and development of the widely studied metal halide SEs including fluorides, chlorides, bromides, and iodides are reviewed, mainly focusing on the structures and ionic conductivities as well as preparation methods and electrochemical/chemical stabilities. And then, based on typical metal halide solid electrolytes, we emphasize the interface issues (grain boundaries, cathode−electrolyte and electrolyte–anode interfaces) that exist in the corresponding LMSBs and summarize the related work on understanding and engineering these interfaces. Furthermore, the typical (or in situ) characterization tools widely used for solid‐state interfaces are reviewed. Finally, a perspective on the future direction for developing high‐performance LMSBs based on the halide electrolyte family is put out.

Subwavelength Broadband Perfect Absorption for Unidimensional Open‐Duct Problems

AbstractPassive metamaterials provide efficient solutions for sound absorption in the low‐frequency regime with deep subwavelength dimensions. They have been extensively applied in unidimensional reciprocal problems considering that an incident wave is either reflected or transmitted at the outlet boundary. However, the generalized problem with impedance boundary condition is not well understood yet. This work presents a general design methodology of metamaterial absorbers for open‐duct problems, which is a special case of impedance outlet boundary encountered in broad practical applications, for example, noise‐attenuation problems in heat ventilation and air conditioning systems. By properly using monopolar point scatterers made of arrays of Helmholtz resonators, the design process is significantly simplified; the transfer matrix modeling is sufficiently accurate to describe the acoustic response of the system. A single monopolar point scatterer is insufficient to attenuate both the reflected and radiated waves; a frequency‐dependent maximum absorption exists and is derived analytically. To go beyond this absorption bound and achieve perfect absorption, at least two point scatterers are necessary. Specific designs are provided and validated experimentally for maximum or perfect absorption, either at single frequencies or over specific frequency bands.