• Title, Summary, Keyword: Partial Velocity Matrix

### Computational Method for Dynamic Analysis of Constrained Mechanical Systems Using Partial Velocity Matrix Transformation

• Park, Jung-Hun;Yoo, Hong-Hee;Hwang, Yo-Ha
• Journal of Mechanical Science and Technology
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• v.14 no.2
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• pp.159-167
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• 2000
• A computational method for the dynamic analysis of a constrained mechanical system is presented in this paper. The partial velocity matrix, which is the null space of the Jacobian of the constraint equations, is used as the key ingredient for the derivation of reduced equations of motion. The acceleration constraint equations are solved simultaneously with the equations of motion. Thus, the total number of equations to be integrated is equivalent to that of the pseudo generalized coordinates, which denote all the variables employed to describe the configuration of the system of concern. Two well-known conventional methods are briefly introduced and compared with the present method. Three numerical examples are solved to demonstrate the solution accuracy, the computational efficiency, and the numerical stability of the present method.

### Dynamic Analysis of Multibody Systems Undertaking Impulsive Force using Kane's Method (충격하중을 받는 시스템의 케인 방법을 이용한 다물체 동역학 해석)

• 김상국;박정훈;유홍희
• Transactions of the Korean Society of Automotive Engineers
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• v.6 no.3
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• pp.169-176
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• 1998
• A method for the dynamic analysis of multibody systems undertaking impulsive force is introduced in this paper. A partial velocity matrix based on Kane's method is introduced to reduce the number of equations to be solved. Only minimum number of equations of motion can be obtained by using the partial velocity matrix. This reduces the computational effort significantly to obtain the dynamic response of the system. At the very moment of the impulse, instead of using the numerical integrator to solve the equations of motion, the impulse and momentum principle is used to obtain the dynamic response. The impulse as wall as the reaction force acting on the kinematic joints can easily calculated too.

### Partitioning method using kinematic uncoupling in train dynamics (열차 동역학에서 기구학적 비연성을 이용한 분할 해석 방법)

• Park, J.H.;Yoo, H.H.;Hwang, Y.H.;Kim, C.H.
• Journal of the Korean Society for Railway
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• v.2 no.1
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• pp.47-55
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• 1999
• In this paper, an efficient and accurate formulation for the transient analysis of constrained multibody systems is presented. The formulation employs Kane's method along with the null space method. Kane's method reduces the dimension of equations of motion by using partial velocity matrix: it can improve the efficiency of the formulation. Furthermore, the formulation partitions the coefficient matrix of linear and nonlinear equations into several sub-matrices using kinematic uncoupling. This can solve the equations more efficiently. The proposed formulation can be used to perform dynamic analysis of systems which can be partitioned into several sub-systems such as train systems. One numerical example is given to demonstrate the efficiency and accuracy of the formulation, and another numerical example is given to show its application to the train systems.

### Linearization Method and Vibration Analysis of a Constrained Multibody System Driven by Constant Generalized Speeds (일정 일반속력으로 구동되는 구속 다물체계의 선형화기법 및 진동해석)

• 최동환;박정훈;유홍희
• Proceedings of the Korean Society for Noise and Vibration Engineering Conference
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• pp.725-730
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• 2001
• This paper presents a vibration analysis method for constrained mechanical systems driven by constant generalized speeds. Equilibrium positions are obtained first and vibration analysis are performed around the positions. The method developed in this paper employs partial velocity matrix to obtain a minimum number of differential equations. To verify the accuracy of the proposed algorithm, linear vibration analyses of two numerical examples are performed and the results are compared with results from a commercial program or previous literature.

### Dynamic analysis of constrained multibody systems using Kane's method (케인방법을 이용한 구속 다물체계의 동역학 해석)

• Park, Jeong-Hun;Yu, Hong-Hui;Hwang, Yo-Ha;Bae, Dae-Seong
• Transactions of the Korean Society of Mechanical Engineers A
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• v.21 no.12
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• pp.2156-2164
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• 1997
• A new formulation for the dynamic analysis of constrained multibody systems is presented in this paper. The formulation employs Kane's method along with the null space method. Kane's method reduces the dimension of equations of motion by using partial velocity matrix introduced in this study : it can improve the efficiency of the formulation. Three numerical examples are given to demonstrate the accuracy and efficiency of the formulation.

### An Optimization Algorithm to Compute Pre-Loads of the Given Static Equilibrium State in Train Dynamics (열차동역학에서 주어진 정적평형상태의 초기하중을 계산하기 위한 최적화 알고리즘)

• 김종인;박정훈;유홍희;황요하
• Journal of the Korean Society for Railway
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• v.2 no.3
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• pp.9-17
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• 1999
• This paper presents a new algorithm to determine the pre-loads that sustain the static equilibrium state in a given position. The algorithm which uses a partial velocity matrix leads to an unconstrained optimization problem to compute the pre-loads of the suspensions. To demonstrate the validity of the proposed algorithm, the static analysis results that employ the pre-loads of three examples are presented using a reliable commercial program. Results of the analysis confirm the validity of the proposed algorithm.

### Static equilibrium and linear vibration analysis of a high speed electric train system (고속전철 시스템의 정적평형 및 선형진동 해석)

• 김종인;유홍희;황요하
• Journal of the Korean Society for Railway
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• v.2 no.4
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• pp.1-8
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• 1999
• A formulation to perform static equilibrium and linear vibration analysis is presented in this paper. The formulation employs minimum number of equations of motion which are derived by using a partial velocity matrix. The static equilibrium analysis is performed first, then the linear vibration analysis is performed at the static equilibrium position. By using the formulation presented in this paper, static equilibrium and linear vibration analysis of a high speed electric train system are performed. A single bogie system, a power car vehicle, and a train system which consists of five vehicles are analyzed, respectively. Natural frequencies and a few lowest mode shapes of the two are identified in this paper.

### Screening of Rayleigh Waves by Composite Barriers (복합방진벽에 의한 Rayleigh파의 차단)

• 이종세
• Proceedings of the Earthquake Engineering Society of Korea Conference
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• pp.133-140
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• 1997
• Based on the Green's function technique, an analytical approach is developed to examine the surface wave screening effectiveness of composite wave barriers. The composite barrier consists of a high velocity layer sandwiched between two thin layers of low shear velocity materials. The high velocity layer is represented by differential matrix operators which relate the wave fields on each side of the layer. The low velocity layers are modeled by non-rigid contact conditions which allow partial sliding at the interfaces. Screening ratio of barriers with various combination of material, geometric, and non-rigidness parameters are compared and discussed in some detail.

### A Study on Optimal Control of Heat Exchange of Thin Metal Moving at Constant Velocity Via the Paley Order of Walsh Functions (팰리배열 월쉬함수를 이용한 정속 이동 금속판의 열교환 최적제어에 관한 연구)

• Kim, Tai-Hoon;Lee, Myung-Kyu;Ahn, Doo-Soo
• The Transactions of the Korean Institute of Electrical Engineers D
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• v.50 no.11
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• pp.514-521
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• 2001
• This paper uses the distributed heating thin metal moving at constant velocity which are modeled as distributed parameter systems, and applies the Paley order of Walsh functions to high order partial differential equations and matrix partial differential equations. This thesis presents a new algorithm which usefully exercises the optimal control in the distributed parameter systems. In this paper, the excellent consequences are found without using the existing decentralized control or hierarchical control method.

### A Transfer Alignment Considering Measurement Time-Delay and Ship Body Flexure (측정치 시간지연과 선체의 유연성을 고려한 전달정렬 기법)

• Lim, You-Chol;Lyou, Joon
• Journal of the Korea Institute of Military Science and Technology
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• v.4 no.1
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• pp.225-233
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• 2001
• This paper deals with the transfer alignment problem of SDINS(StrapDown Inertial Navigation System) subjected to roll and pitch motions of the ship. Specifically, to reduce alignment errors induced by measurement time-delay and ship body flexure, an error compensation method is suggested based on delay state augmentation and DCM(Direction Cosine Matrix) partial matching. A linearized error model for the velocity and attitude matching transfer alignment system is first derived by linearizing the nonlinear measurement equation with respect to its time delay and augmenting the delay state into the conventional linear state equations. And then DCM partial matching is properly combined to reduce effects of a ship's Y axis flexure. The simulation results show that the suggested method is effective enough resulting in considerably less azimuth alignment errors.