• Journal of Electrical Engineering and Technology
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• 제8권6호
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• pp.1530-1541
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• 2013

The coexistence and extinction of species are important concepts for biological systems and can be distinguished by an investigation of stability. When determining local stability of nonlinear systems, Lyapunov indirect method based on the Jacobian linearization has been widely employed due to its simplicity. Despite such popularity, it is not applicable to singular systems whose Jacobian has at least one eigenvalue that is equal to zero. In such singular cases, an appropriate Lyapunov function should be sought to determine the stability of systems, which is rather difficult and quite involved. In this paper, we seek for a simple criterion to determine stability of the equilibrium that is located at the boundary of the positive orthant, when one of eigenvalues of the Jacobian is zero. The goal of the paper is to present a generalized condition for the equilibrium to attract all trajectories that starting from initial condition in the positive orthant and near the equilibrium. Unlike the Lyapunov direct method, the proposed method requires just a simple algebraic computation for checking the stability of the critical point. Our approach is applied to various biological systems to show the effectiveness of the proposed method.

• 한국철도학회:학술대회논문집
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• 한국철도학회 2003년도 추계학술대회 논문집(II)
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• pp.397-402
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• 2003

Infiltration of rainfall causes railway embankment to be unstable and may result in failure. Basic relationship between the rainfall and stability of railway embankment are defined to analyze the stability of embankment by rainfall. An experimental study for defining of infiltration rate of rainfall into slope is conducted in the lab. The results of Rainfall infiltration show that rainfall infiltration is not equal to infiltration as like reservoir because rate of rainfall infiltration is controlled by slope angle. Based on these results, boundary condition of rainfall is altered and various numerical analysis are performed. The variation of shear strength, the degree of saturation and pore-water pressure for railway slope during rainfall can be predicted and the safety factor of railway slope can be expressed as the function of rainfall amount, namely rainfall index. Therefore, it is judged that this rainfall index can be a good tool for the rail-transport operation control.

• Korean Chemical Engineering Research
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• 제52권2호
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• pp.199-204
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• 2014

2성분 응고계에서 다공성 mush 층에서의 조성 대류는 생성되는 제품의 질에 영향을 준다. 본 연구에서는 일정한 속도로 응고되는 mush 층을 고려하였다. 선형 안정성 이론을 사용하여 mush 층에 대한 교란방정식을 유도하였고, 기본상태 온도장과 mush 층에서 기공률의 분포를 수치해법으로 조사하였다. 과열량이 클 때 mush 층의 두께는 열경계층의 두께에 비해 상대적으로 작았다. 과열량이 감소함에 따라 mush 층의 두께를 기준으로 한 Rayleigh 수는 증가하였고, mush 층은 조성 대류에 대해 안정해졌다. mush 층의 윗면에 등온조건을 적용한 경우보다 온도 및 열속의 연속조건을 액체-mush 계면에 적용한 경우에 임계 Rayleigh 수가 더 작게 얻어졌다.

• Geomechanics and Engineering
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• 제15권4호
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• pp.947-955
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• 2018

In this study, we propose a three-dimensional simplified slope stability analysis using a hybrid-type penalty method (HPM). In this method, a solid element obtained by the HPM is applied to a column that divides the slope into a lattice. Therefore, it can obtain a safety factor in the same way as simplified methods on the slip surface. Furthermore, it can obtain results (displacement and strain) that cannot be obtained by conventional limit equilibrium methods such as the Hovland method. The continuity condition of displacement between adjacent columns and between elements for each depth is considered to incorporate a penalty function and the relative displacement. For a slip surface between the bottom surface and the boundary condition to express the slip of slope, we introduce a penalty function based on the Mohr-Coulomb failure criterion. To compute the state of the slip surface, an r-min method is used in the load incremental method. Using the result of the simple three-dimensional slope stability analysis, we obtain a safety factor that is the same as the conventional method. Furthermore, the movement of the slope was calculated quantitatively and qualitatively because the displacement and strain of each element are obtained.

• 대한기계학회논문집
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• 제16권12호
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• pp.2205-2215
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• 1992

본 연구에서는 동 베어링에 대한 해석을 바탕으로 원주방행 급유홈 프로팅링 저널베어링으로 지지된 탄성 회전체의 안정성에 대한 이론을 전개함과 동시에 실험을 통해 동 베어링의 안정성을 조사하고자 한다.

• Smart Structures and Systems
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• 제18권2호
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• pp.267-291
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• 2016

In this research work, an exact analytical solution for thermal buckling analysis of functionally graded material (FGM) sandwich plates with clamped boundary condition subjected to uniform, linear, and non-linear temperature rises across the thickness direction is developed. Unlike any other theory, the number of unknown functions involved is only four, as against five in case of other shear deformation theories. The theory accounts for parabolic distribution of the transverse shear strains, and satisfies the zero traction boundary conditions on the surfaces of the plate without using shear correction factor. A power law distribution is used to describe the variation of volume fraction of material compositions. Equilibrium and stability equations are derived based on the present refined theory. The non-linear governing equations are solved for plates subjected to simply supported and clamped boundary conditions. The thermal loads are assumed to be uniform, linear and non-linear distribution through-the-thickness. The effects of aspect and thickness ratios, gradient index, on the critical buckling are all discussed.

• Nuclear Engineering and Technology
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• 제52권1호
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• pp.37-50
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• 2020

A passive containment cooling system (PCCS) has been developed as advanced safety feature for innovative power reactor (iPOWER). Passive systems are inherently less stable than active systems and the PCCS encountered the flashing-induced instability previously identified. The objective of this study is to develop stability maps for flashing-induced instability using MARS (Multi-dimensional Analysis of Reactor Safety) code. Firstly, we conducted a series of sensitivity analysis to see the effects of time step size, nodalization, and alternative MARS user options on the onset of flashing-induced instability. The riser nodalization strongly affects the prediction of flashing in a long riser of the PCCS, while time step size and alternative user options do not. Based on the sensitivity analysis, a standard input and an analysis methodology were set up to develop the stability maps of PCCS. We found out that the calculated equilibrium quality at the exit of the riser as a stability boundary above 5 kW/㎡ was approximately 1.2%, which was in good agreement with Furuya's results. However, in case of a very low heat flux condition, the onset of instability occurred at the lower equilibrium quality. In addition, it was confirmed that inlet throttling reduces the unstable region.

• Structural Engineering and Mechanics
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• 제66권5호
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• pp.649-663
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• 2018

The scaled boundary finite element method is extended to evaluate the dynamic stress intensity factors and T-stress with a numerical procedure based on the improved continued-fraction. The improved continued-fraction approach for the dynamic stiffness matrix is introduced to represent the inertial effect at high frequencies, which leads to numerically better conditioned matrices. After separating the singular stress term from other high order terms, the internal displacements can be obtained by numerical integration and no mesh refinement is needed around the crack tip. The condition numbers of coefficient matrix of the improved method are much smaller than that of the original method, which shows that the improved algorithm can obtain well-conditioned coefficient matrices, and the efficiency of the solution process and its stability can be significantly improved. Several numerical examples are presented to demonstrate the increased robustness and efficiency of the proposed method in both homogeneous and bimaterial crack problems.

• Kyungpook Mathematical Journal
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• 제64권2호
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• pp.353-369
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• 2024

In this study, we investigate the unknown time-dependent heat source function in inverse problems. We consider three general nonlocal conditions; two classical boundary conditions and one nonlocal over-determination, condition, these genereate six different cases. The finite integration method (FIM), based on numerical integration, has been adapted to solve PDEs, and we use it to discretize the spatial domain; we use backward differences for the time variable. Since the inverse problem is ill-posed with instability, we apply regularization to reduce the instability. We use the first-order Tikhonov's regularization together with the minimization process to solve the inverse source problem. Test examples in all six cases are presented in order to illustrate the accuracy and stability of the numerical solutions.

• 전기학회논문지
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• 제66권12호
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• pp.1759-1771
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• 2017

In this paper, an improved continuous integral variable structure systems(ICIVSS) with the prescribed control performance is designed for simple regulation controls of uncertain general linear systems. An integral sliding surface with an integral state having a special initial condition is adopted for removing the reaching phase and predetermining the ideal sliding trajectory from a given initial state to the origin in the state space. The ideal sliding dynamics of the integral sliding surface is analytically obtained and the solution of the ideal sliding dynamics can predetermine the ideal sliding trajectory(integral sliding surface) from the given initial state to the origin. Provided that the value of the integral sliding surface is bounded by certain value by means of the continuous input, the norm of the state error to the ideal sliding trajectory is analyzed and obtained in Theorem 1. A corresponding discontinuous control input with the exponential stability is proposed to generate the perfect sliding mode on the every point of the pre-selected sliding surface. For practical applications, the discontinuity of the VSS control input is approximated to be continuous based on the proposed modified fixed boundary layer method. The bounded stability by the continuous input is investigated in Theorem 3. With combining the results of Theorem 1 and Theorem 3, as the prescribed control performance, the pre specification on the error to the ideal sliding trajectory is possible by means of the boundary layer continuous input with the integral sliding surface. The suggested algorithm with the continuous input can provide the effective method to increase the control accuracy within the boundary layer by means of the increase of the $G_1$ gain. Through an illustrative design example and simulation study, the usefulness of the main results is verified.