• Title/Summary/Keyword: algebraic solution

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A Comparison Study of Real-Time Solution to All- Attitude Angles of an Aircraft

  • Shin Sung-Sik;Lee Jung-Hoon;Yoon Sug-Joon
    • Journal of Mechanical Science and Technology
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    • v.20 no.3
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    • pp.376-381
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    • 2006
  • In this paper, the quaternion, the dual Euler, and the direction cosine methods are numerically compared using a non-aerodynamic 6 degree-of-freedom rigid model at all-attitude angles of an aircraft. The dual Euler method turns out to be superior to the others in the applications because it shows better numerical accuracy, stability, and robustness in integration step sizes. The dual Euler method is affordably less efficient than the quaternion method in terms of computational cost. Numerical accuracy and stability, which allow larger integration step sizes, are more critical in modern real-time applications than computational efficiency because of today's increased computational power. If the quaternion method is required because of constraints in computation time, then a suppression mechanism should be provided for algebraic constraint errors which will eventually add computational burden.

Analysis of Dynamic Contact and Stress of a Valve in Internal Combustion Engine (내연기관 밸브의 동적 접촉 및 응력 해석)

  • 이기수;김동우;박상호;조성호;김방원
    • Transactions of the Korean Society of Automotive Engineers
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    • v.10 no.2
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    • pp.159-165
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    • 2002
  • Numerical analysis of dynamic contact and stress developing in the high-speed driven valve of an internal combustion engine is presented. The valve is modeled by finite element techniques, and the dynamic contact between the valve and the valve seat is analyzed by the solution strategies of differential algebraic equations. Also an iterative scheme similar to the augmented Lagrange multiplier method is employed to enforce the contact constraints. It is shown that the contact and separation between the valve and the valve seat can be computed by the finite element techniques without assuming the artificial springs, and the efficiency and accuracy of the solution are demonstrated by the numerical examples.

Numerical Analysis for Valve Train Dynamics of an Internal Combustion Engine (내연기관 밸브 트레인 동역학의 수치해석)

  • 이기수;김동우
    • Transactions of the Korean Society of Automotive Engineers
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    • v.11 no.2
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    • pp.31-39
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    • 2003
  • Numerical analysis for valve train dynamics of an internal combustion engine is presented. The components of the valve train are modeled by finite element techniques, and the dynamic contacts between the components are analyzed by the solution strategies of differential algebraic equations. Also an iterative scheme similar to the augmented Lagrange multiplier method is employed to enforce the contact constraints. It is shown that the contact and separation between the components of the valve train can be computed by the finite element techniques, and the numerical examples are presented to demonstrate the efficiency of the solution.

Maximum Output Power using the Doubly Fed Induction Generator (회전자 여자제어를 이용한 권선형 유도발전기의 최대출력)

  • Lee, Woo-Suk;Seo, Young-Taek;Oh, Chul-Soo
    • Proceedings of the KIEE Conference
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    • 1998.07a
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    • pp.6-8
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    • 1998
  • This paper deals with the maximum output power generation using the Dounly Fed Induction Generator(DFIG) in the super-synchronous speed regions, by control of both magnitude and phase of the voltage fed to the rotor. Steady-state algebraic equations of the euivalent circuit are solved using numerical analysis. For the normal operating region, in which the generator ratings are not exceeded, rotor current is less than or equal to the rated value. By selecting the permisible rated current at rotor coil, there are the optimal solution existng which covers the magnitude and phase of the injected voltage to the rotor for the given slip. This optimal solution is pointing out how the maximum output power can be carried out.

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A Study on VLSI-Oriented 2-D Systolic Array Processor Design for APP (Algebraic Path Problem) (VLSI 지향적인 APP용 2-D SYSTOLIC ARRAY PROCESSOR 설계에 관한 연구)

  • 이현수;방정희
    • Journal of the Korean Institute of Telematics and Electronics B
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    • v.30B no.7
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    • pp.1-13
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    • 1993
  • In this paper, the problems of the conventional special-purpose array processor such as the deficiency of flexibility have been investigated. Then, a new modified methodology has been suggested and applied to obtain the common solution of the three typical App algorithms like SP(Shortest Path), TC(Transitive Closure), and MST(Minimun Spanning Tree) among the various APP algorithms using the similar method to obtain the solution. In the newly proposed APP parallel algorithm, real-time Processing is possible, without the structure enhancement and the functional restriction. In addition, we design 2-demensional bit-parallel low-triangular systolic array processor and the 1-PE in detail. For its evaluation, we consider its computational complexity according to bit-processing method and describe relationship of total chip size and execution time. Therefore, the proposed processor obtains, on which a large data inputs in real-time, 3n-4 execution time which is optimal o(n) time complexity, o(n$^{2}$) space complexity which is the number of total gate and pipeline period rate is one.

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Development of a General Analytical Model for Desiccant Wheels (로터리 제습기의 일반 해석 모델)

  • Kim, Dong-Seon;Lee, Dae-Young
    • Korean Journal of Air-Conditioning and Refrigeration Engineering
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    • v.25 no.2
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    • pp.109-118
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    • 2013
  • The absence of a simple and general analytical model has been a problem in the design and analysis of desiccant-assisted air-conditioning systems. In this study, such an analytical model has been developed based on the approximate integral solution of the coupled transient ordinary differential equations for the heat and mass transfer processes in a desiccant wheel. It turned out that the initial conditions should be determined by the solution of four linear algebraic equations including the heat and mass transfer equations for the air flow as well as the energy and mass conservation equations for the desiccant bed. It is also shown that time-averaged exit air temperature and humidity relations could be given in terms of the heat and mass transfer effectiveness.

Dynamic Analysis of the Pantograph of a High-speed Electrical Train Considering Contact and Separation (고속 전철 급전기의 접촉 분리를 고려한 동역학적 해석)

  • Lee, Ki-Su
    • Transactions of the Korean Society for Noise and Vibration Engineering
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    • v.16 no.6 s.111
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    • pp.634-642
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    • 2006
  • For the analysis of dynamic contact between a catenary and a pantograph of high-speed electrical train, the numerical solution of the equations of motion of the vehicle pantograph and the catenary system subjected to the contact condition is obtained. The whole equations of motion of the catenary and the pantograph are simultaneously time integrated with the strict application of the contact condition. For the stability of the numerical solution, with the cubic spline interpolation of the catenary displacement, the velocity and acceleration constraints as well as the displacement constraint are imposed on the contact point. Especially it is shown that the Coriolis and centripetal accelerations are critical for the accuracy and stability of the computation.

Automated initial process planning system for three-axis NC machining of sculptured surfaces (자유 곡면의 3축 NC 가공을 위한 초기 공정 계획 기능의 자동화)

  • Kang, Jae-Kwan
    • Journal of the Korean Society for Precision Engineering
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    • v.14 no.3
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    • pp.114-121
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    • 1997
  • In this paper, the automated initial process planning for 3-axis NC machining of sculptured surfaces is persented. The solution algorithms determining three process planning functions, i.e. machining feasibility, setup orientation and feasible machine selection are developed. The machining feasibility is determined by means of BSM(Binary Spherical Map) which derives its solution quickly in algebraic form, and the setup orientation is determined so that the cutting force is minimized. Finally, the feasible machine is determined by computing the minimum motion ranges of each control axisl. The developed algorithms are tested by numerical simulations, convincing they can by readily implemented on the CAD/CAM system as a process planner.

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Moving-load dynamic analysis of AFG beams under thermal effect

  • Akbas, S.D.
    • Steel and Composite Structures
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    • v.42 no.5
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    • pp.649-655
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    • 2022
  • In presented paper, moving load problem of simply supported axially functionally graded (AFG) beam is investigated under temperature rising based on the first shear beam theory. The material properties of beam vary along the axial direction. Material properties of the beam are considered as temperature-dependent. The governing equations of problem are derived by using the Lagrange procedure. In the solution of the problem the Ritz method is used and algebraic polynomials are used with the trivial functions for the Ritz method. In the solution of the moving load problem, the Newmark average acceleration method is used in the time history. In the numerical examples, the effects of material graduation, temperature rising and velocity of moving load on the dynamic responses ofAFG beam are presented and discussed.

Size dependent vibration of laminated micro beams under moving load

  • S.D. Akbas
    • Steel and Composite Structures
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    • v.46 no.2
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    • pp.253-261
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    • 2023
  • The goal of this paper is to investigate dynamic responses of simply-supported laminated micro beams under moving load. In the considered micro-scale problem, the modified coupled stress theory which includes the length scale parameter is used. The governing equations of problem are derived by using the Lagrange procedure. In the solution of the problem the Ritz method is used and algebraic polynomials are used with the trivial functions for the Ritz method. In the solution of the moving load problem, the Newmark average acceleration method is used in the time history. In the numerical examples, the effects of stacking sequence of laminas, fibre orientation angles and the length scale parameter on the dynamic responses of laminated micro beams are examined and discussed.