• Journal of the Korean Society for Aviation and Aeronautics
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• v.21 no.4
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• pp.47-52
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• 2013

In this paper, limit cycle flutter induced by Hopf bifurcation is studied with nonlinear system analysis approach and observed for the critical slowing down phenomenon. Considering an attractor of the dynamics of a system, when a small perturbation is applied to the system, the dynamics converge toward the attractor at some rate. The critical slowing down means that this recovery rate approaches zero as a parameter of the system varies and the size of the basin of attraction shrinks to nil. Consequently, in the pre-bifurcation regime, the recovery rates decrease as the system approaches the bifurcation. This phenomenon is one of the features used to forecast bifurcation before they actually occur. Therefore, studying the critical slowing down for limit cycle flutter behavior would have potential applicability for forecasting those types of flutter. Herein, modeling and nonlinear system analysis of the 2D airfoil with torsional nonlinearity have been discussed, followed by observation of the critical slowing down phenomenon.

• Journal of the Chungcheong Mathematical Society
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• v.16 no.1
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• pp.113-121
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• 2003

This paper is concerned with some properties of stable domains and limit functions. Using the relationship between cycles of periodic stable domains and orbits of critical points and using the Sullivan theorem [19], we prove that the value of a constant limit function in some stable domain for a rational function f of degree at least two lies in the closure of the set of critical orbits of f.

• Transactions of the Korean Society of Mechanical Engineers
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• v.12 no.2
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• pp.278-285
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• 1988

The Critical size of artificially induced micro-holes in 0.17%, 0.36% Carbon steel Specimens with Spheroidized Cementite and in 0.17% carbon steel specimens with martensite structure is compared with annealed pre-crack in order to discuss the physical meaning of the fatigue limit and evaluation of the tolerant micro flaw size at the stress level of the fatigue limit. Results obtained were summarized as follows; (1) In this study, non-propagating crack length of Smooth specimen and critical pre-crack length (lc) is coincide. (2) In the carbon steels with spheroidized cementite structure, critical pre-crack length (lc) and allowable micro-hole size (dc) is coincide each other at the fatigue limit level. (3) It has been published that there exists a particular size of micro-hole which has no effect on the fatigue limit. In this study, the micro-hole of critical size can be regarded as equivalent to a tolerant micro flaw which would not reduce the fatigue limit.

• Transactions of the Korean Society of Mechanical Engineers
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• v.8 no.2
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• pp.141-144
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• 1984

The fatigue limits of crack initiation and propagation on the edge elliptical notched semi-infinite plate under completely reversed fatigue stress are determined theoretically. Assuming that the crack initiation and propagation occur when stress intensity factors of notched plate reach the critical values obtained from critical micro-crack length under plain fatigue limit loading and the threshold stress intensity factory, respectively, the fatigue limits of crack initiation and propagation are obtained. The induced theoretical fatigue limit of crack initiation is expressed in terms of plain fatigue limit, critical micro-crack length and notch shape. The one of crack propagation is in terms of threshold stress intensity factor, plain fatigue limit and notch shape. These theoretical results are showed to be in good agreement of Frost's experimental data.

• Bulletin of the Korean Mathematical Society
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• v.46 no.2
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• pp.311-319
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• 2009

Let H be a Hilbert space which is the direct sum of five closed subspaces $X_0,\;X_1,\;X_2,\;X_3$ and $X_4$ with $X_1,\;X_2,\;X_3$ of finite dimension. Let J be a $C^{1,1}$ functional defined on H with J(0) = 0. We show the existence of at least four nontrivial critical points when the sublevels of J (the torus with three holes and sphere) link and the functional J satisfies sup-inf variational inequality on the linking subspaces, and the functional J satisfies $(P.S.)^*_c$ condition and $f|X_0{\otimes}X_4$ has no critical point with level c. For the proof of main theorem we use the nonsmooth version of the classical deformation lemma and the limit relative category theory.

• Korean Journal of Mathematics
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• v.22 no.3
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• pp.471-489
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• 2014

We investigate the number of the weak periodic solutions for the bifurcation problem of the Hamiltonian system with the superquadratic nonlinearity. We get one theorem which shows the existence of at least two weak periodic solutions for this system. We obtain this result by using variational method, critical point theory induced from the limit relative category theory.

• Proceedings of the Korean Society for Technology of Plasticity Conference
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• 2003.10a
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• pp.291-295
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• 2003

The occurrence of ductile fracture is the working limit of many metal forming processes. It is necessary to predict the criteria and to apply the condition in a process design. Over the years. the way for clarifying conditions have been studied and presented. However such a way needs lots of experiments and analysis. In this study, in order to determine the critical damage value of a used material Cu 4N, it was performed a tensile test and FEM analysis by using DEFORM 2D. For applying the obtained critical damage value it was also performed a upsetting test by using DEFORM 2D. The way of determining a critical damage value which is presented in this study will make possible to find easily it which is one of the working limit factor. And the way of determining a critical damage value will make possible to find in multi-pass drawing process.

• Journal of applied mathematics & informatics
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• v.29 no.5_6
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• pp.1229-1243
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• 2011

In this paper we consider a system of N-Laplacian elliptic equations with critical exponential growth. The existence and multiplicity results of solutions are obtained by a limit index method and Trudinger-Moser inequality.

• Journal of the korean Society of Automotive Engineers
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• v.11 no.1
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• pp.51-56
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• 1989

This study was performed to investigate the effect of defect on fatigue strength under the stress of rotary bending. The specimens were made of low carbon steel having artificial microholes, namely, single micro-hole and two adjacent micro-holes as natural defects, and the effects of the diameter of hole and the distance between the holes on fatigue strength have been investigated. The obtained result can be summarized as follows: 1, The critical defect means the largest size of defect that does not affect fatigue limit, and correspondes to the size of defect leading to final fracture under fatigue limit of smooth specimen. The size of defect which has an effect on fatigue limit is larger than that of critical defect. 2, The defect larger than the critical defect affects fatigue strength for as a kind of size effect, and the physical meaning of size effect of defect is considered same as the one of notch effect.

• Nuclear Engineering and Technology
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• v.54 no.3
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• pp.834-841
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• 2022

System thermal-hydraulic (STH) code is adopted for nuclear safety analysis. The critical flow model (CFM) is significant for the accuracy of STH simulation. To overcome the defects of current CFMs (low precision or long calculation time), a CFM based on a genetic neural network (GNN) has been developed in this work. To build a powerful model, besides the critical mass flux, the critical pressure and critical quality were also considered in this model, which was seldom considered before. Comparing with the traditional homogeneous equilibrium model (HEM) and the Moody model, the GNN model can predict the critical mass flux with a higher accuracy (approximately 80% of results are within the ±20% error limit); comparing with the Leung model and the Shannak model for critical pressure prediction, the GNN model achieved the best results (more than 80% prediction results within the ±20% error limit). For the critical quality, similar precision is achieved. The GNN-based CFM in this work is meaningful for the STH code CFM development.