Two-dimensional Analytical Method Research Articles

Numerical extraction of three-dimensional acoustic polarizabilities for acoustically small scatterers

Polarizability is a convenient descriptor for scattering from low-ka inhomogeneities in both electromagnetism, where it originated, and in acoustics, where it is increasingly used in the design of metamaterial elements. In two or three dimensions, the polarizability is represented by a block matrix that couples the local pressure and particle velocity fields to the lowest-order components of the multipole expansion, usually truncated to dipole order. A fully dense acoustic polarizability matrix has components that couple spatially uniform pressure and velocity oscillations to dipole and monopole scattering, respectively. This unique coupling leads to acoustic bianisotropy, also known as Willis coupling, for a collection of scatterers. The design of Willis materials necessitates computationally efficient methods to extract all components of the polarizability matrix and, at present, only two-dimensional analytical extraction methods are found in the literature. In this work, we present an algorithm to extract all components of the three-dimensional polarizability matrix from a scatterer with arbitrary geometry and composition. The method presented here is numerically efficient and yields results that are in agreement with an analytically obtained benchmark polarizability, providing a useful tool for acoustic metamaterial design.

An Ultra-High-Performance Liquid Chromatography Coupled with Tandem Mass Spectrometry Method with Online Solid-Phase Extraction Sample Preparation for the High-Throughput and Sensitive Determination of Ostarine in Human Urine.

Ostarine is frequently misused as a selective androgen receptor modulator (SARM) in sports. Consequently, there is a pressing need for reliable and simple approaches to monitor its presence in biological systems. In this work, we developed a two-dimensional analytical method utilizing online solid-phase extraction (online-SPE) in conjunction with ultra-high-performance liquid chromatography and tandem mass spectrometry (triple quadrupole). This automated 2D separation approach is characterized by minimum manual steps in the sample preparation (only dilute-and-shoot), reflecting high sample throughput and the reliability of analytical data. It provides favorable performance parameters, including a limit of detection of 0.5 pg/mL, high accuracy (relative error = 1.6-7.5%), precision (relative standard deviation = 0.8-4.5%), and sensitivity. Additionally, it demonstrates excellent linearity (r2 = 0.9999) in the calibration range of 0.05 to 25 ng/mL and robustness, with no carryover effects observed. This comparative study revealed a two-decadic-order-lower LOD of the SPE-UHPLC-MS/MS method to the corresponding UHPLC-MS/MS method and the lowest one in the group of currently published LC-MS methods. The World Anti-Doping Agency screening and confirmation criteria were met through the analysis of spiked urine samples from ten healthy volunteers. Accordingly, the proposed method is suitable for routine use in antidoping laboratories.

ANALYSIS OF AN ASYMMETRIC TRUNCATED CONCAVE PARABOLIC FIN

An asymmetric truncated concave parabolic fin is analyzed using a two-dimensional analytical method. In this analysis, the variation in the ratio of the top surface temperature to the bottom surface temperature along the fin length is presented. Heat loss from each surface and that from the fin are shown as a function of the convection characteristic number and the fin base height. The ratios of heat loss from each surface to that from the fin are given as a function of the actual fin length. The relationship between the convection characteristic number and the fin base height, as well as that between the actual fin length and the fin base height, are presented for equal amounts of heat loss. One of the results shows that the effect of fin base height variation on heat loss from the fin bottom surface and on heat loss from the fin tip surface is negligible when the actual fin length is fixed.

Rich topological spin textures in single-phase and core-shell magnetic nanodisks

Magnetic skyrmions have potential applications in future high-density information storage devices due to their small size, topologically protected structure, and ultralow energy consumption. Here, we use a variational method to study rich topological spin textures in magnetic nanodisks, including skyrmions and skyrmionlike objects. The existence of skyrmions and $k\ensuremath{\pi}$-skyrmions in a single-phase nanodisk and a disk with a core-shell structure is investigated theoretically, where the phase diagrams of possible spin states are obtained for various Dzyaloshinskii-Moriya interaction (DMI) constants and disk dimeters. Our calculations suggest that skyrmions can be generated spontaneously in a core-shell nanodisk. We also study the transitions of spin textures in the nanodisk induced by spin currents. This paper may provide guidelines for experimental realization of different topological spin textures in nanodisks with certain DMIs. The simple two-dimensional analytical method used in this paper can be used to study the magnetic phase diagrams of thin films with interface-induced DMIs.

Magnetic Field Calculation for Flat Permanent-Magnet Linear Machines Using a Hybrid Analytical Model

This paper proposes an improved two-dimensional (2-D) hybrid analytical method (HAM) in Cartesian coordinates, based on the exact subdomain (SD) technique and the finite-difference method (FDM). It is applied to flat permanent-magnet (PM) linear machines with dual-rotor. The magnetic field solution is obtained by coupling an exact SD model, calculated in all regions having relative permeability equal to unity, with FDM in ferromagnetic regions. The analytical model and FDM are connected in both axes (x,y) of the (non-)periodicity direction (i.e., in the interface between the tooth regions and all its adjacent regions as slots and/or air-gap). To provide accuracy solutions, the current density distribution in slot regions is modeled by using Maxwell’s equations. It is found that, whatever the iron core magnetic parameters, the developed HAM gives accurate results for no- and on-load conditions. Finite-element analysis (FEA) demonstrates excellent results of the developed technique.

2‐D analytical on‐load electromagnetic model for double‐layer slotted interior permanent magnet synchronous machines

A fast hybrid analytical model is presented to predict the on-load performance of double-layer interior permanent-magnet synchronous machines (IPMSMs) considering both iron bridges saturation and slotting effects. The saturation of the iron bridges is defined by a constant flux in the magnetic equivalent circuit method. The slotting effect is defined by a flux path function and virtual surface currents (VSCs) in one-dimensional (1-D) and two-dimensional (2-D) analytical methods, respectively. For the no-load condition, double-layer IPMSMs are modelled via surface-mounted permanent magnet synchronous machines with two types of the permanent magnet model and the Magnetic Islands method are used to calculate the armature reaction. The effect of the stator slots is considered by using VSCs. To increase the computation speed in the 2-D analytical method, the amount of VSC is calculated by 1-D analysis. The 1-D and 2-D analytical results for a double-layer IPMSM are compared with those of finite element analysis and experimental set-up.

Analytical magnetic field calculation for flat permanent-magnet linear machines with dual-rotor by using improved two-dimensional hybrid analytical method

PurposeThis paper aims to propose an improved two-dimensional hybrid analytical method (HAM) in Cartesian coordinates, based on the exact subdomain technique and the magnetic equivalent circuit (MEC).Design/methodology/approachThe magnetic field solution is obtained by coupling an exact analytical model (AM), calculated in all regions having relative permeability equal to unity, with a MEC, using a nodal-mesh formulation (i.e. Kirchhoff’s current law) in ferromagnetic regions. The AM and MEC are connected in both axes (x, y) of the (non-)periodicity direction (i.e. in the interface between the tooth regions and all its adjacent regions as slots and/or air-gap). To provide accuracy solutions, the current density distribution in slot regions is modeled by using Maxwell’s equations instead of the MEC characterized by an equivalent magnetomotive force (MMF) located in slots, teeth and yokes.FindingsIt is found that whatever the iron core relative permeability, the developed HAM gives accurate results for no- and on-load conditions. The finite-element analysis demonstrates excellent results of the developed technique.Originality/valueThe main objective of this paper is to make a direct coupling between the AM and MEC in both directions (i.e. x- and y-edges). The current density distribution is modeled by using Maxwell’s equations instead of the MEC and characterized by an MMF.

Analysis of a concave parabolic fin with vertically cutting fin tip and variable fin base thickness

A concave parabolic fin with vertically cutting fin tip and variable fin base thickness is analyzed using a two-dimensional analytic method. Heat loss is presented as a function of the actual fin length, the ratio of the actual fin length to the imaginary fin length, the fin base height, and the convection characteristic number. Also, heat loss is shown as a function of the fin base thickness for both the fixed actual fin length and the fixed actual fin tip length. For equal amounts of heat loss, the relationships are presented between 1) the convection characteristic number and the fin base height, 2) the fin base thickness and the fin base height, and 3) the fin base thickness and the actual fin tip length. One of the results shows that the heat loss for the fixed actual fin tip length decreases more remarkably than that for the fixed actual fin length as the fin base thickness increases.

Acoustic analysis of a flute-like silence

The passive control of low-frequency duct noise remains a technical challenge. Herschel-Quincke (HQ) tube is effective in low frequency noise reflection. Previous studies showed that, when the bypass of the HQ tube is filled with a lighter gas and covered by tensioned membranes, the HQ tube becomes a flute-like silencer [L.Huang, Attenuation of low frequency duct noise by a flute-like silencer, Journal of Sound and Vibration 326 (2009) 161–176]. Another resonance occurs and the transmission loss spectrum can keep a desirable high level. In this paper, a two-dimensional analytical method for flute-like silencer is developed and this method offers an effective way in acoustic calculations with variable parameters. The details of the modal behavior are analyzed and a parametric study is conducted to obtain optimal design. It shows that the noise attenuation mechanism can be interpreted as destructive interference and the resonance of a single spring-mass system. The trends of the experimental results and theoretical calculations are in good agreement, however, significant deviations in absolute value are observed around the second peak of the transmission loss. Minimizing sound and gas leakage is still an issue that needs to be considered. The effects of cavity filling with different gases are also investigated and it is found that the use of hydrogen can bring performance improvement in low-frequency range. After the introduction of another stretched membrane, the optimal logarithmic bandwidth of the silencer can be further extended to about 5.2.

Analysis of Cooling Efficiency Using the Biot Number of a Rectangular Fin

The performance of a rectangular fin, the relative value of the performance for L=0.1, and the ratio of the heat transfer from the fin tip to the total heat transfer from the rectangular fin were investigated using a two-dimensional analytical method. The variables are the Biot number and non-dimensional fin length. The relative resistance, effect, and efficiency increase as the non-dimensional length increases for a small Biot number (Bi≤0.1). On the other hand, the relative resistance and effect decrease and the relative efficiency increases as the non-dimensional length increases for a large Biot number (Bi≥0.7).

Free Fluid-Structure Interaction Method for Accurate Nonlinear Dynamic Characteristics of the Plain Gas Journal Bearings

Comprehensive and deep understanding of the accurate nonlinear dynamic characteristics of the gas journal bearings plays an important role for reliable design of the rotor-bearing system. In this paper, the accurate nonlinear dynamics of a flexible rotor supported by two plain gas journal bearings (PGJB) are investigated by the free fluid-structure interaction method (FFSIM). The FFSIM does not make any simplifying assumptions, considers the interactions between the rotor shaft and the bearing sleeve at each transient time and uses the three-dimensional models for calculation. First, accuracy of the FFSIM is verified by the published experimental results. Then, bifurcation analysis, effects of rotating speed and rotor mass on shaft orbits, phase portraits and frequency response curves of the PGJB rotor system are performed, respectively. Results show that, under the same rotor system and boundary conditions, compared with the simplified two-dimensional analytical methods commonly seen in the open literature, the FFSIM could give more detailed and accurate nonlinear dynamic characteristics of the rotor-bearing system. The research of this paper is expected to further and deeply understand the accurate nonlinear dynamic characteristics of the PGJB rotor system.

Analytical Computation of Air-Gap Magnetic Field in a Viable Superconductive Magnetic Gear

The basic concept of superconductive magnetic gears (SMGs) is to maximize the benefits and impact of the magnetic gearing technology by highlighting the future perspective of SMGs to produce a more efficient and compact system. This paper deals with a new analytical method (AM) for the calculation of magnetic field distribution in an SMG. A 2-D AM based on Laplace's partial differential equations of magnetic scalar potential in the different subdomains of a magnetic gear is introduced and solved by considering the corresponding boundary conditions. The proposed method shows a significant reduction in the consumed calculation time compared with the finite-element method (FEM) and can be used as a basis for design optimizations. Two-dimensional AM results are compared against those obtained from 2-D FEM simulations, using an accurate, yet efficient, high-temperature superconductor (HTS) modeling, yielded by a detailed localized $E{-}J$ power law approach combining the different aspects of HTS in a numerical method, so as to find out the benefits and validity of the presented AM. Finally, the effects of PMs and pole pieces' dimensions on torque density are realized.

Comparative study and performance evaluation of analytical methods for surface mounted permanent magnet brushless motors

Analysis and determination of magnetic field distribution of surface mounted permanent magnet (SMPM) motors has always been a topic of research. Though a number of methods like two-dimensional numerical and analytical methods have been proposed to evaluate the magnetic field and parameters of radial flux SMPM motors, the methods developed for axial flux permanent magnet motors are mainly three dimensional. Numerical methods provide accurate results but are not suitable for initial design analysis. The analytical methods are known for their accuracy, convenience, as well as are less time consuming than numerical methods. The analytical methods like conventional design method, magnetic equivalent circuit, generalised machine theory and Fourier analysis present in the literature for SMPM motor have been investigated in this study and the results obtained are compared and evaluated for radial flux SMPM and axial flux SMPM. Experimental results are included to demonstrate the percentage error obtained from different methods and denote the accuracy. From the comparison of different results, it can be concluded that the Fourier transform method is more realistic approach and is capable of computing the performance as well as field distribution simultaneously.

Analytical Investigation of the Magnetic-Field Distribution in an Axial Magnetic-Field-Modulated Brushless Double-Rotor Machine

The axial magnetic-field-modulated brushless double-rotor machine (MFM-BDRM) is a novel possible alternative power-split device for hybrid electric vehicles (HEVs). This paper proposes a two-dimensional (2-D) analytical method to predict the performance of the axial MFM-BDRM to reduce computing time. The computation is based on the solution of Laplace’s or Poisson’s equation with boundary conditions for each elementary rectangular region. By taking account of the existence of modulating ring and the stator slotting effect, the proposed model is able to calculate magnetic-field distribution with high accuracy. In order to assess the proposed method, the 2-D analytical and three-dimensional (3-D) finite element analysis (FEA) results have been compared, and good agreements have been achieved. As the analytical computation is much faster and more flexible, the proposed method can be used in the preliminary design process of the axial MFM-BDRM.

A new analytical cone model for laterally-loaded vertical piles in cohesionless soil

ABSTRACTLaterally-loaded vertical piles are commonly designed by p-y curves or two-dimensional (2D) analytical methods. The former are vaguely correlated while the latter are oversimplified and conservative. Three-dimensional (3D) analysis can be used, but it is time consuming for practical applications. An improved analytical cone method is thus developed using spreadsheets. Subject to the lateral load under greenfield condition, the soil in front of a vertical pile is under constant volume plastic compression, heaving at the free boundary on top. Stress release occurs in the soil behind the pile. These mobilised soil masses are idealised as inclined right circular cones. The pile below the cone is subjected to the direct compression at the back and shear at the sides. Thus, the pile behaves as a simply-supported beam with one movable support at the loading point. This enables the rational prediction of the pile length required to satisfy the vertical tangent and the “zero-toe-kick” criteria. By plane of...

대칭 사다리꼴 핀과 비대칭 사다리꼴 핀의 성능 비교

Abstract : Heat loss and fin efficiency of symmetric and asymmetric trapezoidal fins with variable slope of fin's top surface are obtained by using a two-dimensional analytic method. Shapes of symmetric and asymmetric fins are changed from rectangular through trapezoidal to triangular by adjusting the fin shape factor. The ratio of symmetric trapezoidal fin length to asymmetric trapezoidal fin length is presented as a function of fin base height and convection characteristic number. The ratio of symmetric trapezoidal fin efficiency to asymmetric trapezoidal fin efficiency is presented as a function of the fin base height and fin shape factor. One of results shows that asymmetric trapezoidal fin length is shorter than symmetric trapezoidal fin length (i.e., asymmetric trapezoidal fin volume is smaller than symmetric trapezoidal fin volume) for the same heat loss when the fin base height and fin shape factor are the same. Key words : Symmetric trapezoidal fin(대칭 사다리꼴 핀), Asymmetric trapezoidal fin(비대칭 사다리꼴 핀), Convection characteristic number(대류특성계수), Fin shape factor(핀 형상계수), Fin efficiency(핀 효율)

Theoretical Study of Triple-Flame Temperature Distribution in Heat-Recirculated Microcombustor

AbstractThis paper presents a two-dimensional analytical method for investigating the triple-flame temperature profile in a microcombustor. For this purpose, the microcombustor chamber is divided into a preheat and a reaction zone and the role of heat recirculation from the flame zone into the preheat zone is taken into account in this research. It is indicated that the maximum temperature is strongly dependent on this phenomenon. This analysis is done by applying the energy conversion equation in each zone and then solving these equations along with required boundary and matching conditions by the use of partial differential equation method. The outcome of this research leads to the temperature profile in preheat and flame zone, and also the effects of combustor characteristics on the temperature distribution.

Two-dimensional analytical solution of elastic stresses for balanced single-lap joints—Variational method

A two-dimensional (2D) analytical method that is capable of providing an explicit closed-form solution is presented for the prediction of elastic stresses in balanced single-lap adhesive-bonded joints, assuming only a longitudinal normal stress linear distribution in the joint thickness direction. By selecting the four appropriate in-plane loading stress functions, the theory can predict the 2D stress distribution at any point, and the tensile force, shearing and bending moment at any cross section accurately, in both the adhesive and adherends. The method is based on 2D elasticity theory in conjunction with the variational theorem of complementary energy. Minimizing the energy functional leads to four coupled, fourth-order ordinary differential equations with constant coefficients for the determination of the stresses. All boundary conditions, including shear stress-free surfaces, are satisfied. The analytical method was verified by comparing with our previous 2D solutions, and the 2D geometrically nonlinear finite element analysis. It is indicated that the present solution can provide a good prediction for the stress and in-plane loading distributions in the adhesive and adherends.

Design Method of a Foldable Ventricular Assist Device for Minimally Invasive Implantation

To date, ventricular assist devices (VADs) have become accepted as a therapeutic solution for end-stage heart failure patients when a donor heart is not available. Newer generation VADs allow for a significant reduction in size and an improvement in reliability. However, the invasive implantation still limits this technology to critically ill patients. Recently, expandable/deployable devices have been investigated as a potential solution for minimally invasive insertion. Such a device can be inserted percutaneously via peripheral vessels in a collapsed form and operated in an expanded form at the desired location. A common structure of such foldable pumps comprises a memory alloy skeleton covered by flexible polyurethane material. The material properties allow elastic deformation to achieve the folded position and withstand the hydrodynamic forces during operation; however, determining the optimal geometry for such a structure is a complex challenge. The numerical finite element method (FEM) is widely used and provides accurate structural analysis, but computation time is considerably high during the initial design stage where various geometries need to be examined. This article details a simplified two-dimensional analytical method to estimate the mechanical stress and deformation of memory alloy skeletons. The method was applied in design examples including two popular types of blade skeletons of a foldable VAD. Furthermore, three force distributions were simulated to evaluate the strength of the structures under different loading conditions experienced during pump operation. The results were verified with FEM simulations. The proposed two-dimensional method gives a close stress and deformation estimation compared with three-dimensional FEM simulations. The results confirm the feasibility of such a simplified analytical approach to reveal priorities for structural optimization before time-consuming FEM simulations, providing an effective tool in the initial structural design stage of foldable minimally invasive VADs.

비대칭 사다리꼴 핀의 온도분포와 열손실 해석

변화되는 위 측면 기울기를 가진 비대칭 사다리꼴 핀의 온도분포가 2차원 해석적 방법을 사용하여 조사되어 진다. 이 비대칭 핀을 위해, 내부유체로부터 내벽까지의 대류, 내벽으로부터 핀 바닥까지의 전도, 그리고 핀 바닥을 통한 전도가 동시에 고려된다. 무차원 핀 길이와 높이좌표 변화에 따른 온도 형상이 보여진다. 또한 핀 아래 끝에서 온도 변화가 핀 형상계수의 함수로 나타내어진다. 핀 길이의 변화에 따라 핀 바닥을 통한 열손실과 각 면으로부터의 열손실들이 비교된다. 결과들 중 하나는 핀 형상계수가 증가함에 따라 핀 아래 끝에서 온도는 선형적으로 감소함을 보여준다.