• 제목/요약/키워드: fourth-order equations

검색결과 109건 처리시간 0.022초

Joule-Thomson 효과를 고려한 천연가스 배관내의 온도 변화 (Temperature Variations in the Natural Gas Pipeline with the Joule-Thomson Effect)

  • 김윤제
    • 한국가스학회:학술대회논문집
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    • 한국가스학회 1997년도 추계학술발표회 논문집
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    • pp.14-19
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    • 1997
  • A numerical method for determining the temperature vartiation in a natural gas transmission line is presented. By considering an element of the gas pipeline and assuming radially lumped heat transfer at steady-state conditions, the energy equation is developed. The integration of the developed nonlinear differential equation is done numerically using the fourth order Runge-Kutta scheme. The results of the present study have been compared with the results of Coulter equations, and show a fairly good agreement.

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진동하는 원주 주위의 유체 유동에 관한 연구 (A Study on the Fluid Flow Around an Oscillating Circular Cylinder)

  • 서용권;문종춘
    • 한국해양공학회지
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    • 제4권2호
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    • pp.73-84
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    • 1990
  • A circular cylinder is oscillated in th otherwise quiescent viscous fluid. Numerical analysis performed for this problem by using the fourth-order Runge-kutta method for the unsteady Navier-stokes equations. For K(Kelegan-Carpenter's No.)=5, the flow developed symmetrically, while for K=10, it revealed random patterns. The coefficient of the rms force is overestimated by 20-30% compared with the experimental result.

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Asymptotic Results for a Class of Fourth Order Quasilinear Difference Equations

  • Thandapani, Ethiraju;Pandian, Subbiah;Dhanasekaran, Rajamannar
    • Kyungpook Mathematical Journal
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    • 제46권4호
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    • pp.477-488
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    • 2006
  • In this paper, the authors first classify all nonoscillatory solutions of equation (1) $${\Delta}^2|{\Delta}^2{_{y_n}}|^{{\alpha}-1}{\Delta}^2{_{y_n}}+q_n|y_{{\sigma}(n)}|^{{\beta}-1}y_{{\sigma}(n)}=o,\;n{\in}\mathbb{N}$$ into six disjoint classes according to their asymptotic behavior, and then they obtain necessary and sufficient conditions for the existence of solutions in these classes. Examples are inserted to illustrate the results.

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회전원판 근처에서 회전하는 유연디스크에 대한 실험 및 수치해석 (Experimental and Numerical Study on an Air-Stabilized Flexible Disk Rotating Close to a Rigid Rotating Disk)

  • 가드압델라솔;임윤철
    • 정보저장시스템학회논문집
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    • 제5권1호
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    • pp.19-35
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    • 2009
  • The present work is an experimental and analytical study on a flexible disk rotating close to a rigid rotating disk in open air. In the analytical study, the air flow in the gap between the flexible disk and the rigid disk is modeled using Navier-Stokes and continuity equations while the flexible disk is modeled using the linear plate theory. The flow equations are discretized using the cell centered finite volume method (FVM) and solved numerically with semi-implicit pressure-linked equations (SIMPLE algorithm). The spatial terms in the disk equation are discretized using the finite difference method (FDM) and the time integration is performed using fourth-order Runge-Kutta method. An experimental test-rig is designed to investigate the dynamics of the flexible disk when rotating close to a co-rotating, a counter-rotating and a fixed rigid disk, which works as a stabilizer. The effects of rotational speed, initial gap height and inlet-hole radius on the flexible disk displacement and its vibration amplitude are investigated experimentally for the different types of stabilizer. Finally, the analytical and experimental results are compared.

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Improved analytical method for adhesive stresses in plated beam: Effect of shear deformation

  • Guenaneche, B.;Benyoucef, S.;Tounsi, A.;Adda Bedia, E.A.
    • Advances in concrete construction
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    • 제7권3호
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    • pp.151-166
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    • 2019
  • This paper introduces a new efficient analytical method, based on shear deformations obtained with 2D elasticity theory approach, to perform an explicit closed-form solution for calculation the interfacial shear and normal stresses in plated RC beam. The materials of plate, necessary for the reinforcement of the beam, are in general made with fiber reinforced polymers (Carbon or Glass) or steel. The experimental tests showed that at the ends of the plate, high shear and normal stresses are developed, consequently a debonding phenomenon at this position produce a sudden failure of the soffit plate. The interfacial stresses play a significant role in understanding this premature debonding failure of such repaired structures. In order to efficiently model the calculation of the interfacial stresses we have integrated the effect of shear deformations using the equilibrium equations of the elasticity. The approach of this method includes stress-strain and strain-displacement relationships for the adhesive and adherends. The use of the stresses continuity conditions at interfaces between the adhesive and adherents, results pair of second-order and fourth-order coupled ordinary differential equations. The analytical solution for this coupled differential equations give new explicit closed-form solution including shear deformations effects. This new solution is indented for applications of all plated beam. Finally, numerical results obtained with this method are in agreement of the existing solutions and the experimental results.

상사해법을 이용한 쐐기형 물체 주위의 미세 극성유체 유동 특성에 관한 연구 (A Similarity Solution of the Characteristics of Micropolar Fluid Flow in the Vicinity of a Wedge)

  • 김윤제
    • 대한기계학회논문집B
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    • 제23권8호
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    • pp.969-977
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    • 1999
  • A similarity solution of a steady laminar flow of micropolar fluids past wedges has been studied. The similarity variables found by Falkner and Skan are employed to reduce the streamwise-dependence in the coupled nonlinear boundary layer equations. Numerical solutions of the equations are then obtained using the fourth-order Runge-Kutta method and the distribution of velocity, micro-rotation, shear and couple stress across the boundary layer are obtained. These results are compared with the corresponding flow problems for Newtonian fluid past wedges with various wedge angles. Numerical results show that, keeping ${\beta}$ constant, the skin friction coefficient is lower for a micropolar fluid, as compared to a Newtonian fluid. For the case of constant material parameter K, however, the velocity distribution for a micropolar fluid is higher than that of a Newtonian fluid.

효율적인 상세 반응 기구 해석을 위한 민감도 기반의 부분 음해법 (Partial Preconditioning Approach for the Solution of Detailed Kinetics Problems Based on Sensitivity Analysis)

  • 강기하;문성영;노진현;원수희;최정열
    • 한국연소학회지
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    • 제13권1호
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    • pp.17-22
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    • 2008
  • A partly implicit/quasi-explicit method is introduced for the solution of detailed chemical kinetics with stiff source terms based on the standard fourth-order Runge-Kutta scheme. Present method solves implicitly only the stiff reaction rate equations, whereas the others explicitly. The stiff equations are selected based on the survey of the chemical Jaconian matrix and its Eigenvalues. As an application of the present method constant pressure combustion was analyzed by a detailed mechanism of hydrogen-air combustion with NOx chemistry. The sensitivity analysis reveals that only the 4 species in NOx chemistry has strong stiffness and should be solved implicitly among the 13 species. The implicit solution of the 4 species successfully predicts the entire process with same accuracy and efficiency at half the price.

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경사 종동력과 끝질량을 갖는 크랙 보의 안정성 해석 (Stability Analysis of Cracked Beams with Subtangential Follower Force and Tip Mass)

  • 손인수;윤한익;노태우
    • 대한기계학회논문집A
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    • 제33권12호
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    • pp.1410-1416
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    • 2009
  • In this paper, the purpose is to investigate the stability and variation of natural frequency of a cracked cantilever beams subjected to follower force and tip mass. In addition, an analysis of the flutter instability(flutter critical follower force) of a cracked cantilever beam as slenderness ratio and crack severity is investigated. The governing differential equations of a Timoshenko beam subjected to an end tangential follower force is derived via Hamilton's principle. The two coupled governing differential equations are reduced to one fourth order ordinary differential equation in terms of the flexural displacement. Finally, the influence of the slenderness ratio and crack severity on the critical follower force, stability and the natural frequency of a beam are investigated.

종동력을 받는 외팔보의 진동특성에 미치는 세장비의 영향 (Effects of Slenderness ratio on Dynamic Behavior of Cantilever Beam Subjected to Follower Force)

  • 손인수;윤한익;안태수
    • 한국소음진동공학회:학술대회논문집
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    • 한국소음진동공학회 2008년도 춘계학술대회논문집
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    • pp.575-578
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    • 2008
  • In this paper, the purpose is to investigate the stability and variation of natural frequency of a Timoshenko cantilever beam subjected to follower force and tip mass. In addition, an analysis of the flutter instability(flutter critical follower force) of a cantilever beam as slenderness ratio is investigated. The governing differential equations of a Timoshenko beam subjected to an end tangential follower force is derived via Hamilton;s principle. The two coupled governing differential equations are reduced to one fourth order ordinary differential equation in terms of the flexural displacement. Finally, the influence of the slenderness ratio and tip mass on the critical follower force and the natural frequency of a Timoshenko beam are investigated.

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GENERALIZED EULER PROCESS FOR SYSTEMS OF NONLINEAR DIFFERENTIAL EQUATIONS

  • Yu, Dong-Won
    • Journal of applied mathematics & informatics
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    • 제7권3호
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    • pp.941-958
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    • 2000
  • Euler method is generalized to solve the system of nonlinear differential equations. The generalization is carried out by taking a special constant matrix S so that exp(tS) can be exactly computed. Such a matrix S is extracted from the Jacobian matrix of the given problem. Stability of the generalized Euler process is discussed. It is shown that the generalized Euler process is comparable to the fourth order Runge-Kutta method. We also exemplify that the important qualitative and geometric features of the underlying dynamical system can be recovered by the generalized Euler process.