• Journal of applied mathematics & informatics
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• 제7권1호
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• pp.41-60
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• 2000

In this paper we consider a series of algorithms for calculating radicals of matrix polynomial equations. A particular aspect of this problem arise in author's work. concerning parameter identification of linear dynamic stochastic system. Special attention is given of searching the solution of an equation in a neighbourhood of some initial approximation. The offered approaches and algorithms allow us to receive fast and quite exact solution. We give some recommendations for application of given algorithms.

• Structural Engineering and Mechanics
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• 제19권1호
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• pp.73-96
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• 2005

For the spatially coupled free vibration analysis of shear deformable thin-walled non-symmetric curved beam subjected to initial axial force, an exact dynamic element stiffness matrix of curved beam is evaluated. Firstly equations of motion and force-deformation relations are rigorously derived from the total potential energy for a curved beam element. Next a system of linear algebraic equations are constructed by introducing 14 displacement parameters and transforming the second order simultaneous differential equations into the first order simultaneous differential equations. And then explicit expressions for displacement parameters are numerically evaluated via eigensolutions and the exact $14{\times}14$ dynamic element stiffness matrix is determined using force-deformation relations. To demonstrate the accuracy and the reliability of this study, the spatially coupled natural frequencies of shear deformable thin-walled non-symmetric curved beams subjected to initial axial forces are evaluated and compared with analytical and FE solutions using isoparametric and Hermitian curved beam elements and results by ABAQUS's shell elements.

• 대한전기학회논문지:전력기술부문A
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• 제54권2호
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• pp.67-72
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• 2005

In conventional small signal stability analysis, system is assumed to be invariant and the state space equations are used to calculate the eigenvalues of state matrix. However, when a system contains switching elements such as FACTS devices, it becomes non-continuous system. In this case, a mathematically rigorous approach to system small signal stability analysis is by means of eigenvalue analysis of the system periodic transition matrix based on discrete system analysis method. In this paper, RCF(Resistive Companion Form) method is used to analyse small signal stability of a non-continuous system including switching elements. Applying the RCF method to the differential and integral equations of power system, generator, controllers and FACTS devices including switching elements should be modeled in the form of state transition equations. From this state transition matrix eigenvalues which are mapped to unit circle can be calculated.

• KIEE International Transactions on Power Engineering
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• 제5A권4호
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• pp.344-349
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• 2005

In conventional small signal stability analysis, the system is assumed to be invariant and the state space equations are used to calculate the eigenvalues of the state matrix. However, when a system contains switching elements such as FACTS equipments, it becomes a non-continuous system. In this case, a mathematically rigorous approach to system small signal stability analysis is performed by means of eigenvalue analysis of the system's periodic transition matrix based on the discrete system analysis method. In this paper, the RCF (Resistive Companion Form) method is used to analyze the small signal stability of a non-continuous system including switching elements. Applying the RCF method to the differential and integral equations of the power system, generator, controllers and FACTS equipments including switching devices should be modeled in the form of state transition equations. From this state transition matrix, eigenvalues that are mapped into unit circles can be computed precisely.

• 대한인간공학회지
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• 제26권3호
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• pp.111-115
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• 2007

Design equations for anthropometric product design are developed by considering the geometrical relationships of design dimensions and anthropometric dimensions. The present study applied the design structure matrix (DSM) method to the development of design equations for a computer workstation, and compared design values from the design equations with corresponding design values of ergonomic recommendations and existing products. The relationships between design dimensions (e.g., legroom and worktable) were analyzed by a DSM, and then the application order of design equations (e.g., seatpan, backrest, armrest, legroom, and worktable in descending order) was determined. Next, design equations were developed by analyzing the geometric relationships between computer workstation design dimensions and anthropometric dimensions. Finally, design values for a computer workstation were determined by considering a standard posture defined and representative human models (5th, 50th, 95th %ile). The design values calculated using the design equations were similar with those of ergonomic recommendations found in literature and two commercial products measured in the study; however, some design values (e.g., seatpan height) were different due to discrepancy in standard posture. The DSM method would be utilized to systematically analyze the relationships between design dimensions for anthropometric product design.

• 대한기계학회논문집
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• 제18권7호
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• pp.1730-1737
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• 1994

Theoretical equations for an influence of fiber breaks on the frictional heating phenomenon in a uniaxially fiber-reinforced ceramic matrix composite are formulated. The microslip and gross slip phases are considered for deriving the equations. During a complete loading/unloading cycle, the work done against friction is derived. In order to estimate interfacial shear in a unidirectionally reinforced ceramic matrix composite which has fiber fractures as well as matrix cracks, parametric studies using the derived equations are done. In a case of less than 10% fiber fractures, additional frictional work due to fiber breaks can be neglected compared to the rest.

• 제어로봇시스템학회논문지
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• 제14권12호
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• pp.1270-1277
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• 2008

A Haar wavelet based numerical method for solving singularly perturbed linear time invariant system is presented in this paper. The reduced pure slow and pure fast subsystems are obtained by decoupling the singularly perturbed system and differential matrix equations are converted into algebraic Sylvester matrix equations via Haar wavelet technique. The operational matrix of integration and its inverse matrix are utilized to reduce the computational time to the solution of algebraic matrix equations. Finally a numerical example is given to demonstrate the validity and applicability of the proposed method.

• 한국공작기계학회논문집
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• 제17권3호
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• pp.101-107
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• 2008

A composite mechanics for discontinuous fiber reinforced polymer matrix composites(PMC) is analysed in order to predict fiber axial stresses. In continuum approach. frictional slip which usually takes place between fibers and polymers is accounted to derive PMC equations. The interfacial friction stress is treated by the product of the coefficient of friction and the compressive stress norma1 to the fiber/matrix interface. The residual stress and the Poisson's contraction implemented by the rule of mixture(ROM) are considered for the compressive stress normal to the fiber/matrix interface. In addition. the effects of fiber aspect ratio and fiber volume fraction on fiber axial stresses are evaluated using the derived equations. Results are illustrated numerically using the present equations with reasonable materials data. It is found that the fiber axial stress in the center region shows no great discrepancy for different fiber aspect ratios and fiber volume fractions while some discrepancies are shown in the fiber end region.

• Structural Engineering and Mechanics
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• 제54권6호
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• pp.1153-1174
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• 2015

Deployable structures have gained more and more applications in space and civil structures, while it takes a large amount of computational resources to analyze this kind of multibody systems using common analysis methods. This paper presents a new approach for dynamic analysis of multibody systems consisting of both rigid bars and arbitrarily shaped rigid bodies. The bars and rigid bodies are connected through their nodes by ideal pin joints, which are usually fundamental components of deployable structures. Utilizing the Moore-Penrose generalized inverse matrix, equations of motion and constraint equations of the bars and rigid bodies are formulated with nodal Cartesian coordinates as unknowns. Based on the constraint equations, the nodal displacements are expressed as linear combination of the independent modes of the rigid body displacements, i.e., the null space orthogonal basis of the constraint matrix. The proposed method has less unknowns and a simple formulation compared with common multibody dynamic methods. An analysis program for the proposed method is developed, and its validity and efficiency are investigated by analyses of several representative numerical examples, where good accuracy and efficiency are demonstrated through comparison with commercial software package ADAMS.

• 전자공학회논문지 IE
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• 제44권4호
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• pp.26-29
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• 2007

본 논문에서는 섭동 시스템 행렬을 가지는 선형 시스템에 대하여 Lyapunov 방정식과 함수를 고려하여 섭동 유계를 유도한다. 그리고 Lyapunov 함수의 도함수가 음의 정의로 보장되는 가장 큰 섭동 구간을 허락하는 Lyapunov 함수의 선택에 대하여 고려한다. 행렬 계수를 가지는 행렬 리카티 방정식의 해 존재에 대하여 살펴보며, 예를 통하여 검증한다.