• Title/Summary/Keyword: Differential algebraic equations

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High-speed simulation for fossil power plants uisng a parallel DSP system (병렬 DSP 시스템을 이용한 화력발전소 고속 시뮬레이션)

  • 박희준;김병국
    • Journal of the Korean Institute of Telematics and Electronics C
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    • v.35C no.4
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    • pp.38-49
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    • 1998
  • A fossil power plant can be modeled by a lot of algebraic equations and differential equations. When we simulate a large, complicated fossil power plant by a computer such as workstation or PC, it takes much time until overall equations are completely calculated. Therefore, new processing systems which have high computing speed is ultimately needed for real-time or high-speed(faster than real-time) simulators. This paper presents an enhanced strategy in which high computing power can be provided by parallel processing of DSP processors with communication links. DSP system is designed for general purpose. Parallel DSP system can be easily expanded by just connecting new DSP modules to the system. General urpose DSP modules and a VME interface module was developed. New model and techniques for the task allocation are also presented which take into account the special characteristics of parallel I/O and computation. As a realistic cost function of task allocation, we suggested 'simulation period' which represents the period of simulation output intervals. Based on the development of parallel DSP system and realistic task allocation techniques, we cound achieve good efficiency of parallel processing and faster simulation speed than real-time.

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Wave propagation in a microbeam based on the modified couple stress theory

  • Kocaturk, Turgut;Akbas, Seref Doguscan
    • Structural Engineering and Mechanics
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    • v.46 no.3
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    • pp.417-431
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    • 2013
  • This paper presents responses of the free end of a cantilever micro beam under the effect of an impact force based on the modified couple stress theory. The beam is excited by a transverse triangular force impulse modulated by a harmonic motion. The Kelvin-Voigt model for the material of the beam is used. The considered problem is investigated within the Bernoulli-Euler beam theory by using energy based finite element method. The system of equations of motion is derived by using Lagrange's equations. The obtained system of linear differential equations is reduced to a linear algebraic equation system and solved in the time domain by using Newmark average acceleration method. In the study, the difference of the modified couple stress theory and the classical beam theory is investigated for the wave propagation. A few of the obtained results are compared with the previously published results. The influences of the material length scale parameter on the wave propagation are investigated in detail. It is clearly seen from the results that the classical beam theory based on the modified couple stress theory must be used instead of the classical theory for small values of beam height.

A new and simple analytical approach to determining the natural frequencies of framed tube structures

  • Mohammadnejad, Mehrdad;Kazemi, Hasan Haji
    • Structural Engineering and Mechanics
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    • v.65 no.1
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    • pp.111-120
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    • 2018
  • This paper presents a new and simple solution for determining the natural frequencies of framed tube combined with shear-walls and tube-in-tube systems. The novelty of the presented approach is based on the bending moment function approximation instead of the mode shape function approximation. This novelty makes the presented solution very simpler and very shorter in the mathematical calculations process. The shear stiffness, flexural stiffness and mass per unit length of the structure are variable along the height. The effect of the structure weight on its natural frequencies is considered using a variable axial force. The effects of shear lag phenomena has been investigated on the natural frequencies of the structure. The whole structure is modeled by an equivalent non-prismatic shear-flexural cantilever beam under variable axial forces. The governing differential equation of motion is converted into a system of linear algebraic equations and the natural frequencies are calculated by determining a non-trivial solution for the system of equations. The accuracy of the proposed method is verified through several numerical examples and the results are compared with the literature.

The effect of in-plane deformations on the nonlinear dynamic response of laminated plates

  • Kazanci, Zafer;Turkmen, Halit S.
    • Structural Engineering and Mechanics
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    • v.42 no.4
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    • pp.589-608
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    • 2012
  • In this study, the effect of in-plane deformations on the dynamic behavior of laminated plates is investigated. For this purpose, the displacement-time and strain-time histories obtained from the large deflection analysis of laminated plates are compared for the cases with and without including in-plane deformations. For the first one, in-plane stiffness and inertia effects are considered when formulating the dynamic response of the laminated composite plate subjected to the blast loading. Then, the problem is solved without considering the in-plane deformations. The geometric nonlinearity effects are taken into account by using the von Karman large deflection theory of thin plates and transverse shear stresses are ignored for both cases. The equations of motion for the plate are derived by the use of the virtual work principle. Approximate solution functions are assumed for the space domain and substituted into the equations of motion. Then, the Galerkin method is used to obtain the nonlinear algebraic differential equations in the time domain. The effects of the magnitude of the blast load, the thickness of the plate and boundary conditions on the in-plane deformations are investigated.

Numerical simulation of single-phase two-components flow in naturally fractured oil reservoirs

  • Debossam, Joao Gabriel Souza;dos Santos Heringer, Juan Diego;de Souza, Grazione;Souto, Helio Pedro Amaral
    • Coupled systems mechanics
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    • v.8 no.2
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    • pp.129-146
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    • 2019
  • The main goal of this work is to develop a numerical simulator to study an isothermal single-phase two-component flow in a naturally fractured oil reservoir, taking into account advection and diffusion effects. We use the Peng-Robinson equation of state with a volume translation to evaluate the properties of the components, and the discretization of the governing partial differential equations is carried out using the Finite Difference Method, along with implicit and first-order upwind schemes. This process leads to a coupled non-linear algebraic system for the unknowns pressure and molar fractions. After a linearization and the use of an operator splitting, the Conjugate Gradient and Bi-conjugated Gradient Stabilized methods are then used to solve two algebraic subsystems, one for the pressure and another for the molar fraction. We studied the effects of fractures in both the flow field and mass transport, as well as in computing time, and the results show that the fractures affect, as expected, the flow creating a thin preferential path for the mass transport.

A Study on Stable Grasping Motion Control of Dual-Finger (듀얼-핑거의 안정적 파지 운동 제어에 관한 연구)

  • Um Hyuk;Choi Jong-Hwan;Kim Seung-Soo;Han Hyun-Yong;Yang Soon-Yong;Lee Jin-Gul
    • Transactions of the Korean Society of Machine Tool Engineers
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    • v.14 no.4
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    • pp.81-88
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    • 2005
  • This paper attempts to derive the dynamic model of handling tasks in finger robot which grasps stable and manipulates a rigid object with some dexterity. Firstly, a set of differential equation describing dynamics of the manipulators and object together with geometric constraint of tight area-contacts is formulated by Lagrange's equation. Secondly, the roblems of controlling both the forces of pressing object and the rotation angle of the object under the geometric constraints are discussed. The effect of geometric constraints of area-contacts between the link's end-effector and the object is analyzed and the model based on the differential-algebraic equations is presented. In this paper, the control method for dynamic stable grasping and enhancing dexterity in manipulating things is proposed. It is illustrated by computer simulation and the experiment that the control system gives the performance improvement in the dynamic stable grasping and nimble manipulating of the dual fingers robot with soft tips.

A Study on Stable Grasping Control of Dual-fingers with Soft-Tips (소프트-팁이 장착된 듀얼-핑거의 안정적 파지 제어에 관한 연구)

  • 심재군;한형용;양순용;이병룡;안경관;김성수
    • Proceedings of the Korean Society of Machine Tool Engineers Conference
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    • 2002.10a
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    • pp.219-224
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    • 2002
  • This paper aims to derive a mathematical model of the dynamics of handling tasks in robot finger which stable grasping and manipulates a rigid object with some dexterity. Firstly, a set of differential equation describing dynamics of the manipulators and object together with geometric constraint of tight area-contacts is formulated by Lagrange's equation. Secondly, problems of controlling both the internal force and the rotation angle of the grasped object under the constraints of area-contacts of tight area-contacts are discussed. The effect of geometric constraints of area-contacts on motion of the overall system is analyzed and a method of computer simulation for overall system of differential-algebraic equations is presented. Thirdly, simulation results are shown and the effects of geometric constraints of area-contact is discussed. Finally, it is shown that even in the simplest case of dual single D.O.F manipulators there exists a sensory feedback from sensing data of the rotational angle of the object to command inputs to joint actuators and this feedback connection from sensing to action eventually realizes secure grasping of the object, provided that the object is of rectangular shape and motion is confined to a horizontal plane.

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A Study on the Improvement of Numeric Integration Algorithm for the Dynamic Behavior Analysis of Flexible Machine Systems (탄성기계 시스템의 동적 거동 해석을 위한 수치 적분 알고리즘 개선에 관한 연구)

  • Kim, Oe-Jo;Kim, Hyun-chul
    • Journal of the Korean Society of Industry Convergence
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    • v.4 no.1
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    • pp.87-94
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    • 2001
  • In multibody dynamics, differential and algebraic equations which can satisfy both equation of motion and kinematic constraint equation should be solved. To solve this equation, coordinate partitioning method and constraint stabilization method are commonly used. The coordinate partitioning method divides the coordinate into independent and dependent coordinates. The most typical coordinate partitioning method arc LU decomposition, QR decomposition, projection method and SVD(sigular value decomposition).The objective of this research is to find a efficient coordinate partitioning method in flexible multibody systems and a hybrid decomposition algorithm which employs both LU and projection methods is proposed. The accuracy of the solution algorithm is checked with a slider-crank mechanism.

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A New Method of Collision Mode Evolution for Three-Dimensional Rigid Body Impact With Friction

  • Park, Jong-Hoon;Chung, Wan-Kyun;Youm, Young-Il
    • 제어로봇시스템학회:학술대회논문집
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    • 2004.08a
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    • pp.1769-1775
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    • 2004
  • In presence of collision between two rigid bodies, they exhibit impulsive behavior to generate physically feasible state. When the frictional impulse is involved, collision resolution can not be easily made based on a simple Newton's law or Poisson's law, mainly due to possible change of collision mode during collision, For example, sliding may change to sticking, and then sliding resumes. We first examine two conventional methods: the method of mode evolution by differential equation, and the other by linear complementarity programming. Then, we propose a new method for mode evolution by solving only algebraic equations defining mode changes. Further, our method attains the original nonlinear impulse cone constraint. The numerical simulation will elucidate the advantage of the proposed method as an alternative to conventional ones.

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A HYBRID SCHEME USING LU DECOMPOSITION AND PROJECTION MATRIX FOR DYNAMIC ANALYSIS OF CONSTRAINED MULTIBODY SYSTEMS

  • Yoo, W.S.;Kim, S.H.;Kim, O.J.
    • International Journal of Automotive Technology
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    • v.2 no.3
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    • pp.117-122
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    • 2001
  • For a dynamic analysis of a constrained multibody system, it is necessary to have a routine for satisfying kinematic constraints. LU decomposition scheme, which is used to divide coordinates into dependent and independent coordinates, is efficient but has great difficulty near the singular configuration. Other method such as the projection matrix, which is more stable near a singular configuration, takes longer simulation time due to the large amount of calculation for decomposition. In this paper, the row space and the null space of the Jacobian matrix are proposed by using the pseudo-inverse method and the projection matrix. The equations of the motion of a system are replaced with independent acceleration components using the null space of the Jacobian matrix. Also a new hybrid method is proposed, combining the LU decomposition and the projection matrix. The proposed hybrid method has following advantages. (1) The simulation efficiency is preserved by the LU method during the simulation. (2) The accuracy of the solution is also achieved by the projection method near the singular configuration.

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