• Title/Summary/Keyword: Differential equation

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Field Experiments and Analysis of Drift Characteristics of Small Vessels in the Coastal Region off Busan Port (부산항 연안해역에서의 소형선박 표류 거동특성 관측 및 분석)

  • Kang, Sin-Young;Lee, Mun-Jin
    • Journal of Navigation and Port Research
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    • v.26 no.2
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    • pp.221-226
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    • 2002
  • To provide reliable data for drift prediction models, field experiments were carried out in the coastal region off Busan port. Four different size of vessels(10, 30, 50, 90G/T ton) were deployed for the experiment. Among them G/T 50ton class vessel was equipped with instruments measuring the currents, winds, headings and trajectory data. In the rest of vessels only the position data were recorded for the purpose of target divergence study. The trajectories of each vessel were measured by DGPS(Differential Global Positioning System) and collected by APRS(Automatic Position Reporting System). The experiment was done in wind of 2~10m/s and current of 0.5~1.5m/s. The leeway was derived by subtracting surface current velocity from target drifting velocity. The leeway rate of G/T 50ton vessel was found to be about 3.6% and the computed leeway speed equation was $U_L$=0.042 W - 0.034. The processed leeway angle data were deflected by $-30^{\circ}$~$40^{\circ}$ from the direction of ship drift.

Analysis of Carbon Dioxide Separation with Countercurrent Flow in Hollow Fiber Membrane by Numerical Analysis (수치해석에 의한 향류 흐름 중공사 분리막의 이산화탄소 분리 성능 해석)

  • Lee, Yong-Taek;Song, In-Ho;Ahn, Hyo-Seong;Lee, Young-Jin;Jeon, Hyun-Soo;Kim, Jeong-Hoon;Lee, Soo-Bok
    • Membrane Journal
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    • v.16 no.4
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    • pp.252-258
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    • 2006
  • A numerical analysis was performed for a separation process of carbon dioxide from a flue gas stream using polyethersulfone hollow fiber membranes. Countercurrent flow governing equations were regarded to be two point boundary-value problem and the nonlinear ordinary differential equation were simultaneously solved using the finite- difference method. A computer program was developed using the Compaq Visual Fortran 6.6 software. The carbon dioxide permeate driving force and the fred gas residence time at the inside of membrane were found to be very important factors affecting the permeation characteristics of carbon dioxide. The carbon dioxide concentration in the permeate and the flow rate of the permeate were found to be slightly larger by a few percent with a countercurrent flow analysis than those with a cocurrent flow analysis.

An analytic solution for the stirling engines with saw-toothed piston motions in adiabatic cylinders (단열실린더내에서 톱날파형 피스톤운동을 하는 스터링기관에 대한 해석적인 해)

  • 유호선
    • Transactions of the Korean Society of Mechanical Engineers
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    • v.12 no.5
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    • pp.1197-1205
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    • 1988
  • An analytical method to predict qualitative performance characteristics of the Stirling Engines in the preliminary design stages is investigated. Both the expansion and the compression cylinder are treated as adiabatic and piston motions are approximated as saw-toothed waves. Basic equations which were originally proposed by Finkelstein consist of mass conservation and energy balances for each adiabatic cylinder. The approximation on piston motions and physical conditions make it possible to divide an engine cycle into four fundamental processes. In each process, first, pressure can be expressed as a function of the crank angle by solving a nonlinear first order ordinary differential equation and other thermodynamic variables are determined in turn. Application of the cyclic steady condition to the whole processes can complete a cycle. Also, further analysis results in analytic expressions for cyclic work and heat transfer in terms of the engine parameters and thermodynamic variables at boundary points. The results are expected useful as a quick reference for the engine performances. Finally, the present method can be applied to the other adiabatic analyses on the Stirling Engines with piece wise linear piston motions, if mass variations are predictable.

An Investigation of the Performance of the Colored Gauss-Seidel Solver on CPU and GPU (Coloring이 적용된 Gauss-Seidel 해법을 통한 CPU와 GPU의 연산 효율에 관한 연구)

  • Yoon, Jong Seon;Jeon, Byoung Jin;Choi, Hyoung Gwon
    • Transactions of the Korean Society of Mechanical Engineers B
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    • v.41 no.2
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    • pp.117-124
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    • 2017
  • The performance of the colored Gauss-Seidel solver on CPU and GPU was investigated for the two- and three-dimensional heat conduction problems by using different mesh sizes. The heat conduction equation was discretized by the finite difference method and finite element method. The CPU yielded good performance for small problems but deteriorated when the total memory required for computing was larger than the cache memory for large problems. In contrast, the GPU performed better as the mesh size increased because of the latency hiding technique. Further, GPU computation by the colored Gauss-Siedel solver was approximately 7 times that by the single CPU. Furthermore, the colored Gauss-Seidel solver was found to be approximately twice that of the Jacobi solver when parallel computing was conducted on the GPU.

A Derivation of Sensitivity Equations of the Error Components to Analyze Performance in the Direct Fire Control System (직사화기 성능분석을 위한 오차요소별 민감도 식 유도)

  • Kim, Jaehun;Kim, Euiwhan;Lee, Jeongyeob;Kim, Gunkook
    • KIPS Transactions on Computer and Communication Systems
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    • v.4 no.12
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    • pp.399-408
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    • 2015
  • In the direct Gun Fire Control System(GFCS), it is essential to analyze the impact of the specific error components on the hit probability to optimize the system design. For this purpose the sensitivity equations of these error components are conveniently used, but it is too difficult to get those equations for the complex system with too many system elements. Normally sensitivity analysis is performed using numerical and statistical methods for the ground combat system. This method requires much computation, and makes us difficult to estimate the sensitivity change of specific error component intuitionally for the changing operating conditions. In this paper we propose a set of sensitivity equations deriving from closed form solution of the ballistic differential equation for the bullet. They are handy equations with very little computations, easy to understand the physical meaning of the related system variables. Some simulation results are shown to demonstrate usefulness of our algorithm for the 30mm projectile.

Development of Cable Excitation System for Evaluating Dynamic Characteristics of Stay Cables (사장교 케이블 동특성 평가를 위한 케이블 가진시스템 개발)

  • Kim, Nam-Sik;Jeong, Woon;Seo, Ju-Won;Ahn, Sang-Sup
    • Journal of the Earthquake Engineering Society of Korea
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    • v.7 no.4
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    • pp.71-79
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    • 2003
  • As a critical member of cable-stayed bridges, stay cables play on important role of supporting the entire structure. Traffic, wind or rain-wind induced vibrations of stay cables would be a major cause of degrading both safety and serviceability of the bridge. One of the effective alternatives to solve this problem is to employ the cable dampers. In order to design the cable damper optimally, it is necessary to exactly estimate the dynamic characteristics of the existing cables. To achieve more reliable dynamic properties of stay cables, precise excitations inducing forced vibration are needed. Therefore, in this study, a cable excitation system(exciter) controlled digitally was developed. And to evaluate the performance of the cable exciter developed, a solution of the differential equation of cable motion considering the exciter was derived, Using the cable exciter, sine sweeping and resonance tests on a cable model were carried out to obtain the dynamic characteristics effectively.

Modeling of the friction in the tool-workpiece system in diamond burnishing process

  • Maximov, J.T.;Anchev, A.P.;Duncheva, G.V.
    • Coupled systems mechanics
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    • v.4 no.4
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    • pp.279-295
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    • 2015
  • The article presents a theoretical-experimental approach developed for modeling the coefficient of sliding friction in the dynamic system tool-workpiece in slide diamond burnishing of low-alloy unhardened steels. The experimental setup, implemented on conventional lathe, includes a specially designed device, with a straight cantilever beam as body. The beam is simultaneously loaded by bending (from transverse slide friction force) and compression (from longitudinal burnishing force), which is a reason for geometrical nonlinearity. A method, based on the idea of separation of the variables (time and metric) before establishing the differential equation of motion, has been applied for dynamic modeling of the beam elastic curve. Between the longitudinal (burnishing force) and transverse (slide friction force) forces exists a correlation defined by Coulomb's law of sliding friction. On this basis, an analytical relationship between the beam deflection and the sought friction coefficient has been obtained. In order to measure the deflection of the beam, strain gauges connected in a "full bridge" type of circuit are used. A flexible adhesive is selected, which provides an opportunity for dynamic measurements through the constructed measuring system. The signal is proportional to the beam deflection and is fed to the analog input of USB DAQ board, from where the signal enters in a purposely created virtual instrument which is developed by means of Labview. The basic characteristic of the virtual instrument is the ability to record and visualize in a real time the measured deflection. The signal sampling frequency is chosen in accordance with Nyquist-Shannon sampling theorem. In order to obtain a regression model of the friction coefficient with the participation of the diamond burnishing process parameters, an experimental design with 55 experimental points is synthesized. A regression analysis and analysis of variance have been carried out. The influence of the factors on the friction coefficient is established using sections of the hyper-surface of the friction coefficient model with the hyper-planes.

Thermal, electrical and mechanical buckling loads of sandwich nano-beams made of FG-CNTRC resting on Pasternak's foundation based on higher order shear deformation theory

  • Arani, Ali Ghorbanpour;Pourjamshidian, Mahmoud;Arefi, Mohammad;Arani, M.R. Ghorbanpour
    • Structural Engineering and Mechanics
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    • v.69 no.4
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    • pp.439-455
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    • 2019
  • This research deals with thermo-electro-mechanical buckling analysis of the sandwich nano-beams with face-sheets made of functionally graded carbon nano-tubes reinforcement composite (FG-CNTRC) based on the nonlocal strain gradient elasticity theory (NSGET) considering various higher-order shear deformation beam theories (HSDBT). The sandwich nano-beam with FG-CNTRC face-sheets is subjected to thermal and electrical loads while is resting on Pasternak's foundation. It is assumed that the material properties of the face-sheets change continuously along the thickness direction according to different patterns for CNTs distribution. In order to include coupling of strain and electrical field in equation of motion, the nonlocal non-classical nano-beam model contains piezoelectric effect. The governing equations of motion are derived using Hamilton principle based on HSDBTs and NSGET. The differential quadrature method (DQM) is used to calculate the mechanical buckling loads of sandwich nano-beam as well as critical voltage and temperature rising. After verification with validated reference, comprehensive numerical results are presented to investigate the influence of important parameters such as various HSDBTs, length scale parameter (strain gradient parameter), the nonlocal parameter, the CNTs volume fraction, Pasternak's foundation coefficients, various boundary conditions, the CNTs efficiency parameter and geometric dimensions on the buckling behaviors of FG sandwich nano-beam. The numerical results indicate that, the amounts of the mechanical critical load calculated by PSDBT and TSDBT approximately have same values as well as ESDBT and ASDBT. Also, it is worthy noted that buckling load calculated by aforementioned theories is nearly smaller than buckling load estimated by FSDBT. Also, similar aforementioned structure is used to building the nano/micro oscillators.

Crystallization Behavior and Kinetics of Cu-Zr-Al-Be Bulk Metallic Glass (Cu-Zr-Al-Be 비정질합금의 결정화거동 및 속도론)

  • Kim, Yu-Chan;Fleury, Eric;Seok, Hyun-Kwang;Cha, Pil-Ryung;Lee, Jin-Kyu;Lee, Jae-Chul
    • Korean Journal of Metals and Materials
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    • v.46 no.6
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    • pp.338-344
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    • 2008
  • The crystallization kinetics of the $Cu_{43}Zr_{43}Al_7Be_7$ bulk metallic glass were studied by differential scanning calorimetry(DSC) in the continuous heating and isothermal annealing modes. Only one major peak could be detected on the DSC traces of $Cu_{43}Zr_{43}Al_7Be_7$ bulk amorphous alloy, and the activation energy for crystallization corresponding to the peak determined by the Kissinger method was resulted of 239 kJ/mol. The isothermal kinetic, analyzed by the Johnson-Mehl-Avrami equation yielded values for the Avrami exponents in the range 1.69 to 2.37, which implied a crystallization governed by a three-dimensioned growth. Primary phases were essentially the cubic structure CuZr together with the $Cu_{10}Zr_7$ phase. At higher temperature, the CuZr disappeared while the $Cu_{10}Zr_7$ became predominant. After long term annealing at 731 K, the phases were $Cu_{10}Zr_7$, $Cu_2ZrAl$ and $Al_3Zr_5$.

Theoretical simulation on evolution of suspended sodium combustion aerosols characteristics in a closed chamber

  • Narayanam, Sujatha Pavan;Kumar, Amit;Pujala, Usha;Subramanian, V.;Srinivas, C.V.;Venkatesan, R.;Athmalingam, S.;Venkatraman, B.
    • Nuclear Engineering and Technology
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    • v.54 no.6
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    • pp.2077-2083
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    • 2022
  • In the unlikely event of core disruptive accident in sodium cooled fast reactors, the reactor containment building would be bottled up with sodium and fission product aerosols. The behavior of these aerosols is crucial to estimate the in-containment source term as a part of nuclear reactor safety analysis. In this work, the evolution of sodium aerosol characteristics (mass concentration and size) is simulated using HAARM-S code. The code is based on the method of moments to solve the integro-differential equation. The code is updated to FORTRAN-77 and run in Microsoft FORTRAN PowerStation 4.0 (on Desktop). The sodium aerosol characteristics simulated by HAARM-S code are compared with the measured values at Aerosol Test Facility. The maximum deviation between measured and simulated mass concentrations is 30% at initial period (up to 60 min) and around 50% in the later period. In addition, the influence of humidity on aerosol size growth for two different aerosol mass concentrations is studied. The measured and simulated growth factors of aerosol size (ratio of saturated size to initial size) are found to be matched at reasonable extent. Since sodium is highly reactive with atmospheric constituents, the aerosol growth factor depends on the hygroscopic growth, chemical transformation and density variations besides coagulation. Further, there is a scope for the improvement of the code to estimate the aerosol dynamics in confined environment.