• Industrial Engineering and Management Systems
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• 제12권1호
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• pp.2-8
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• 2013

Uncertainty theory is a branch of mathematics based on normolity, duality, subadditivity and product axioms. Uncertain process is a sequence of uncertain variables indexed by time. Canonical Liu process is an uncertain process with stationary and independent increments. And the increments follow normal uncertainty distributions. Uncertain differential equation is a type of differential equation driven by the canonical Liu process. Stability analysis on uncertain differential equation is to investigate the qualitative properties, which is significant both in theory and application for uncertain differential equations. This paper aims to study stability properties of linear uncertain differential equations. First, the stability concepts are introduced. And then, several sufficient and necessary conditions of stability for linear uncertain differential equations are proposed. Besides, some examples are discussed.

• 조명전기설비학회논문지
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• 제27권7호
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• pp.76-81
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• 2013

This paper presents an effective pedagogical method for nodal analysis in linear circuit. In the proposed method, basic equations are built only for passive elements and independent current sources. And then, the basic equations are modified by considering other sources such as voltage sources and dependent current sources. In the proposed method, the equations are presented in form of a matrix and a vector of which elements are built systematically by considering every element in a circuit one by one. This make the proposed method easy to apply to intricately composed circuit and easy to solve the final simultaneous equations and easy to realize as computer program for nodal analysis and easy to memorize compared to the conventional method.

• 한국전산유체공학회지
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• 제5권1호
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• pp.14-21
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• 2000

A method of two and three dimensional orthogonal grid generation with control of spacing by using the covariant Laplace equation is presented. An important feature of the methodology is its ability to control effectively the grid spacing especially near the boundaries still maintaining good orthogonality in whole field. The method is based on the concept of decomposition of the global transformation into consecutive transformation of an approximate conformal mapping and an auxiliary orthogonal mapping to have linear and uncoupled equations. Control of cell spacing is based on the concept of reference arc length, and orthogonal correction is peformed in the auxiliary domain. It is concluded that the methodology can successfully generate well controlled orthogonal grids around bodies of 2 and 3 dimensional configurations.

• 소음진동
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• 제10권5호
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• pp.838-842
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• 2000

The vibration of an axially moving string is studied when the string has geometric non-linearity and translating acceleration. Based upon the von karman strain theory, the equations of motion are derived considering the longitudinal and transverse deflection. The equation for the longitudinal vibration is linear and uncoupled, while the equation for the transverse vibration is non-linear and coupled between the longitudinal and transverse deflections. These equations are discretized by using the Galerkin approximation after they are transformed into the variational equations, i.e. the weak forms so that the admissible and comparison functions can be used for the bases of the longitudinal and transverse deflections respectively. With the discretized nonlinear equations, the time responses are investigated by using the generalized-$\alpha$ method.

• 대한기계학회논문집A
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• 제27권9호
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• pp.1579-1588
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• 2003

In this paper, the finite element equations for the transient linear viscoelastic stress analysis are presented in time domain, whose variational formulation is derived by using the Galerkin's method based on the equations of motion in time integral. Since the inertia terms are not included in the variational formulation, the time integration schemes such as the Newmark's method widely used in the classical dynamic analysis based on the equations of motion in time differential are not required in the development of that formulation, resulting in a computationally simple and stable numerical algorithm. The viscoelastic material is assumed to behave as a standard linear solid in shear and an elastic solid in dilatation. To show the validity of the presented method, two numerical examples are solved nuder plane strain and plane stress conditions and good results are obtained.

• 대한수학교육학회지:수학교육학연구
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• 제19권3호
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• pp.461-477
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• 2009

본 연구에서는 조작적 수학활동의 관점에서 일차방정식 해결과정에 관한 이론적 분석을 시도하였다. 연구방법으로 TEP(Teaching Experiment Methodology)를 사용하였다. 이 분석은 학생들의 자연수학습과 분수학습에 관해 기존에 연구 되어왔던 이차적 모델들과 연구자 자신들의 수학적 지식을 근거로 한 일차적 분석이 조합되어 이루어 졌으며, 학생들의 Explicitly Nested number Sequence (ENS)로부터 시작하여 일차방정식을 풀기 위해 필요한 그 이상의 수학적 지식에 이르기까지 고찰되었다. 연구 결과, 같은 형태의 일차방정식이라 하더라도, 일차방정식을 구성하고 있는 계수와 상수의 종류에 따라 필요한 수학적 지식이 달라질 수 있음을 보여주고 있으며, 따라서 교수학적 시사점으로서 교사들은 요구되는 수학적 지식에 따라 다양한 일차방정식 문제들을 구분할 수 있어야 하고, 또한 구분된 문제들을 상응하는 수준의 학생들에게 적절히 제시하여야 할 것이다.

• 한국소음진동공학회:학술대회논문집
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• 한국소음진동공학회 2003년도 춘계학술대회논문집
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• pp.677-682
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• 2003

The non-linear dynamic characteristics of a semi-circular pipe conveying fluid are investigated when the pipe is clamped at both ends. To consider the geometric non-linearity for the radial and circumferential displacements, this study adopts the Lagrange strain theory for large deformation and the extensible dynamics based on the Euler-Bernoulli beam theory for slenderness assumption. By using the Hamilton principle, the non-linear partial differential equations are derived for the in-plane motions of the pipe, considering the fluid inertia forces as a kind of non-conservative forces. The linear and non-linear terms in the governing equations are compared with those in the previous study, and some significant differences are discussed. To investigate the dynamic characteristics of the system, the discretized equations of motion are derived form the Galerkin method. The natural frequencies varying with the flow velocity are computed fen the two cases, which one is the linear problem and the other is the linearized problem in the neighborhood of the equilibrium position. Finally, the time responses at various flow velocities are directly computed by using the generalized- method. From these results, we should to describe the non-linear behavior to analyze dynamics of a semi-circular pipe conveying fluid more precisely.

• Steel and Composite Structures
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• 제41권6호
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• pp.821-829
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• 2021

Nonlinear dynamic response of a sandwich beam considering porous core and nano-composite face sheet on nonlinear viscoelastic foundation with temperature-variable material properties is investigated in this research. The Hamilton's principle and beam theory are used to drive the equations of motion. The nonlinear differential equations of sandwich beam respect to time are obtained to solve nonlinear differential equations by Homotopy perturbation method (HPM). The effects of various parameters such as linear and nonlinear damping coefficient, linear and nonlinear spring constant, shear constant of Pasternak type for elastic foundation, temperature variation, volume fraction of carbon nanotube, porosity distribution and porosity coefficient on nonlinear dynamic response of sandwich beam are presented. The results of this paper could be used to analysis of dynamic modeling for a flexible structure in many industries such as automobiles, Shipbuilding, aircrafts and spacecraft with solar easured at current time step and the velocity and displacement were estimated through linear integration.

• Steel and Composite Structures
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• 제42권5호
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• pp.711-722
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• 2022

In this paper, hyperbolic shear deformation plate theory is developed for thermal buckling of functionally graded plates with porosity by dividing transverse displacement into bending and shear parts. The present theory is variationally consistent, and accounts for a quadratic variation of the transverse shearstrains across the thickness and satisfies the zero traction boundary conditions on the top and bottom surfaces of the plate without using shear correction factors. Three different patterns of porosity distributions (including even and uneven distribution patterns, and the logarithmic-uneven pattern) are considered. The logarithmic-uneven porosities for first time is mentioned. Equilibrium and stability equations are derived based on the present theory. The non-linear governing equations are solved for plates subjected to simply supported boundary conditions. The thermal loads are assumed to be uniform, linear and non-linear distribution through-the-thickness. A comprehensive parametric study is carried out to assess the effects of volume fraction index, porosity fraction index, aspect ratio and side-to-thickness ratio on the buckling temperature difference of imperfect FG plates.

• Journal of applied mathematics & informatics
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• 제29권1_2호
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• pp.145-159
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• 2011

The numerical solution to the linear and nonlinear and linear system of Fredholm and Volterra integral equations of the second kind are investigated. We have used crooked lines which includ the nodes specified by modified rationalized Haar functions. This method differs from using nominal Haar or Walsh wavelets. The accuracy of the solution is improved and the simplicity of the method of using nominal Haar functions is preserved. In this paper, the crooked lines with unknown coefficients under the specified conditions change the system of integral equations to a system of equations. By solving this system the unknowns are obtained and the crooked lines are determined. Finally, error analysis of the procedure are considered and this procedure is applied to the numerical examples, which illustrate the accuracy and simplicity of this method in comparison with the methods proposed by these authors.