• Title/Summary/Keyword: Sommerfeld Method

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Aerial image analysis of replicated linewidths patterned by synchrontron X-ray proximity lithography (싱크로트론 X선 근접 리소그래피에 의하여 전사되어진 라인의 폭에 대한 에어리얼 이미지 시뮬레이션)

  • 이재웅;서용덕;김오윤;최보경;김희상
    • Journal of the Korean Institute of Telematics and Electronics D
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    • v.35D no.2
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    • pp.70-77
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    • 1998
  • An aerial image simulator for the synchroton X-ray proximity lithography system has been developed. The modal expansion method and Rayleigh-Sommerfeld diffraction theory are used in calculating the aerial image which is formed by diffracting of the partially coherent X-ray, Experimental results of PALC(POSTECH Advanced Lithography Center) lighography system and simulated results are compared. The experimental and theoretical values of the width of replicated lines are consisted with the relative error less than ~5%. The method to determine the divergent angle of X-ray from the analysis of the width of replicated lines is given.

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Integral equation formulation for electromagnetic coupling through an arbitrarily shaped aperture into a parallel-plate waveguide (임의 형태의 개구에 의한 평행평판 도파관으로의 전자기적 결합 문제 해석을 위한 적분 방정식 방법)

  • Lee, Young-Soon;Lee, Chang-Won;Cho, Young-Ki;Son, Hyon
    • Journal of the Korean Institute of Telematics and Electronics A
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    • v.32A no.12
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    • pp.25-35
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    • 1995
  • An analysis method of electromagnetic coupling through an arbitrarily shaped aperture on the upper wall of parallel-plate waveguide, when excited by an electromagnetic plane wave from outside, is considered. The mixed-potential integral equation, in which Green's functions are expressed in a computationally efficient closed form by using the Prony's method and the Sommerfeld identity, is formulated. Expanding the unknown equivalent magnetic surface current in terms of two-dimensional rooftop-type basis functions and choosing razor testing, the integral equation is reduced to a linear algebraic equation, which is solved. The results are compared with the previous results. Fairly good agreements between them are observed.

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Estimation and Measurement of Forward Propagated Ultrasonic Fields in Layered Fluid Media

  • Ha, Kang-Lyeol;Kim, Moo-Joon;Hyun, Byung-Gook
    • The Journal of the Acoustical Society of Korea
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    • v.19 no.2E
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    • pp.14-19
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    • 2000
  • The forward propagated ultrasonic fields resulting from a circular plane or a concave transducer in layered fluid media as well as in homogeneous water are theoretically estimated by the angular spectrum method(ASMJ) combined with Rayleigh-Sommerfeld diffraction theory(RSDT), and measured by a precision 3-D scanning system with a needle-point hydrophone. To make the aliasing error negligible on the 2-D FFT in the theoretical estimation, the spatial discretization in the ASM are carefully considered for optimal selection of spatial sampling intervals and the size of discretization area. It is shown that the estimated fields agree reasonably with the measured ones.

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Finite Element Analysis of a Coupled Hydrodynamic Journal and Thrust Bearing in a Computer Hard Disk Drive (컴퓨터 하드디스크 드라이브에 사용되는 저널과 스러스트가 연성된 유체 동압 베어링의 유한 요소 해석)

  • Kim, Hakwoon;Lee, Sanghoon;Jang, Gunhee
    • Transactions of the Korean Society for Noise and Vibration Engineering
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    • v.15 no.1 s.94
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    • pp.87-95
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    • 2005
  • This paper proposes a method to calculate the characteristics of a coupled hydrodynamic journal and thrust bearing of a HDD spindle motor. The governing equations for the journal and thrust bearings are the two dimensional Reynolds equations in $\theta z$ and $ r\theta$ planes, respectively. Finite element method is appropriately applied to analyze the coupled journal and thrust bearing by satisfying the continuity of mass and pressure at the interface between the journal and thrust bearings. The pressure in a coupled bearing is calculated by applying the Reynolds boundary condition and compared with that by using the Half-Sommerfeld boundary condition. The static characteristics are obtained by integrating the pressure along the fluid film. The flying height of spindle motor is measured to verify the proposed analytical result. This research shows that the proposed method can describe HDB in a HDD system more accurately and realistically than the separate analysis of a journal or thrust bearing.

Two-Dimensional Sub-diffraction-limited Imaging by an Optimized Multilayer Superlens

  • Ahmadi, Marzieh;Forooraghi, Keyvan;Faraji-Dana, Reza;Ghaffari-Miab, Mohsen
    • Journal of the Optical Society of Korea
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    • v.20 no.6
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    • pp.653-662
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    • 2016
  • An optimized multilayer superlens is designed, using a rigorous and efficient approach based on the method of moments (MoM) in conjunction with a simulated annealing (SA) algorithm. For the MoM solution, fast evaluation of closed-form Green's functions (GFs) in the spatial domain is performed by applying the complex-image (CI) technique, which obviates the time-consuming numerical evaluation of Sommerfeld integrals. The imaging capability of the superlens is examined with the correlation coefficient; results show that using circular polarization for the incident wave can improve this coefficient. To validate the proposed method, finite-element-based simulations are exploited, which reveal the method's accuracy and computational efficiency. Simulation results indicate that the designed structure is capable of producing two-dimensional sub-diffraction-limited images in the visible range, which may make it more versatile for practical applications. Finally, as a considerable finding, it is demonstrated for the proposed design that using circularly polarized illumination provides improved super-resolving performance, compared to linearly polarized illumination.

Finite Element Analysis of a Coupled Hydrodynamic Journal and Thrust Bearing in a Computer Hard Disk Drive (컴퓨터 하드디스크 드라이브에 사용되는 저널과 스러스트가 연성된 유체 동압 베어링의 유한 요소 해석)

  • Kim, Hak-Woon;Lee, Sang-Hoon;Jang, Gun-Hee
    • Proceedings of the Korean Society for Noise and Vibration Engineering Conference
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    • 2004.11a
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    • pp.846-852
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    • 2004
  • This paper proposes a method to calculate the characteristics of a coupled hydrodynamic journal and thrust bearing of a HDD spindle motor. The governing equations for the journal and thrust bearings are the two dimensional Reynolds equations in ${\theta}z$ and $r\theta$ planes, respectively. Finite element method is appropriately applied to analyze the coupled journal and thrust bearing by satisfying the continuity of mass and pressure at the interface between the journal and thrust bearings. The pressure in a coupled bearing is calculated by applying the Reynolds boundary condition and compared with that by using the Half-Sommerfeld boundary condition. The static characteristics are obtained by integrating the pressure along the fluid film. The flying height of spindle motor is measured to verify the proposed analytical result. This research shows that the proposed method can describe HDB in a HDD system more accurately and realistically than the separate analysis of a journal or thrust bearing.

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LINEAR INSTABILITY ANALYSIS OF A WATER SHEET TRAILING FROM A WET SPACER GRID IN A ROD BUNDLE

  • Kang, Han-Ok;Cheung, Fan-Bill
    • Nuclear Engineering and Technology
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    • v.45 no.7
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    • pp.895-910
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    • 2013
  • The reflood test data from the rod bundle heat transfer (RBHT) test facility showed that the grids in the upper portion of the rod bundle could become wet well before the arrival of the quench front and that the sizes of liquid droplets downstream of a wet grid could not be predicted by the droplet breakup models for a dry grid. To investigate the water droplet generation from a wet grid spacer, a viscous linear temporal instability model of the water sheet issuing from the trailing edge of the grid with the surrounding steam up-flow is developed in this study. The Orr-Sommerfeld equations along with appropriate boundary conditions for the flow are solved using Chebyshev series expansions and the Tau-Galerkin projection method. The effects of several physical parameters on the water sheet oscillation are studied by determining the variation of the temporal growth rate with the wavenumber. It is found that a larger relative steam velocity to water velocity has a tendency to destabilize the water sheet with increased dynamic pressure. On the other hand, a larger ratio of steam boundary layer to the half water sheet thickness has a stabilizing effect on the water sheet oscillation. Droplet diameters downstream of the spacer grid predicted by the present model are found to compare reasonably well with the data obtained at the RBHT test facility as well as with other data recently reported in the literature.

A Method of Analysis to Predict Sound Transmission Loss of an Extruded Aluminum Panel for Use on Railway Vehicles (철도차량용 알루미늄 압출재의 음향 투과손실 예측에 관한 연구)

  • Kim, Kwanju;Lee, Jun-Heon;Kim, Dae-Yong;Kim, Seock-Hyun
    • Journal of the Korean Society for Railway
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    • v.16 no.1
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    • pp.20-25
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    • 2013
  • The frame elements of modern high speed trains are typically fabricated with extruded aluminum panels. However, the sound transmission loss (STL) of extruded aluminum panels is less satisfactory than flat panels with the same surface density. This study proposes a method for prediction of the sound transmission loss of extruded aluminum panels using finite element analysis. The panel is modeled by finite element analysis, and the STL is calculated using a measure of Sommerfeld radiation at the specimen surface, boundary conditions, and the internal loss factor of the material. In order to verify the validity of the predicted value, intensity transmission loss was measured on the aluminum specimen according to ASTM E2249-02. The proposed method of analysis will be utilized to predict the sound insulation performance of extruded aluminum panels for railway vehicles in the design stage, and to establish measures for their improvement.

Performance Analysis of Oil-lubricated Thrust Collars in Integrally Geared Compressors (증속 기어 압축기용 스러스트 칼라의 윤활 성능 해석)

  • Lee, Donghyun;Kim, Byungok;Sun, Kyungho
    • Tribology and Lubricants
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    • v.34 no.5
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    • pp.169-174
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    • 2018
  • A multi-stage compressor (MSC) is comprised of several impellers installed in the pinion gear shaft driven by a main bull gear. In the pinion shaft, a thrust collar (TC) is installed to support the thrust load. The TC makes the lubrication system simpler in the MSC; therefore, it is widely used in similar kinds of machinery. Typically, TCs are installed on both sides of the bull gear and pressure is developed in the lubricated area by creating a taper angle on the TC and bull gear surface. In the current study, we developed a numerical analysis model to evaluate the performance of the TC considering its design parameters. We sloved the Reynolds equation using the finite element method and applied the half Sommerfeld condition to consider cavitation. Based on the pressure calculated in the lubricated area, we calculated the power loss and minimum film thickness. In addition, we calculated stiffness and damping using perturbation method. We performed parametric studies using the developed model. The results of the analysis show that the maximum pressure presents in the center area of the TC and it increases with the taper angle. The area over which pressure is developed decreases with the taper angle. The results also show that there is an optimum taper angle providing minimum power loss and maximum film thickness. Additionally, the stiffness and damping decrease with the taper angle. As the applied load increases, the power loss increases and the minimum film thickness decreases. However, the stiffness and damping increase with the applied load.

Influence of initial stresses on the critical velocity of the moving load acting in the interior of the hollow cylinder surrounded by an infinite elastic medium

  • Akbarov, Surkay D.;Mehdiyev, Mahir A.
    • Structural Engineering and Mechanics
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    • v.66 no.1
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    • pp.45-59
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    • 2018
  • The bi-material elastic system consisting of the pre-stressed hollow cylinder and pre-stresses surrounding infinite elastic medium is considered and it is assumed that the mentioned initial stresses in this system are caused with the compressing or stretching uniformly distributed normal forces acting at infinity in the direction which is parallel to the cylinder's axis. Moreover, it is assumed that on the internal surface of the cylinder the ring load which moves with constant velocity acts and within these frameworks it is required to determine the influence of the aforementioned initial stresses on the critical velocity of the moving load. The corresponding investigations are carried out within the framework of the so-called three-dimensional linearized theory of elastic waves in initially stresses bodies and the axisymmetric stress-strain state case is considered. The "moving coordinate system" method is used and the Fourier transform is employed for solution to the formulated mathematical problem and Fourier transformation of the sought values are determined analytically. However, the originals of those are determined numerically with the use of the Sommerfeld contour method. The critical velocity is determined from the criterion, according to which, the magnitudes of the absolute values of the stresses and displacements caused with the moving load approaches an infinity. Numerical results on the influence of the initial stresses on the critical velocity and interface normal and shear stresses are presented and discussed. In particular, it is established that the initial stretching (compressing) of the constituents of the system under consideration causes a decrease (an increase) in the values of the critical velocity.