• Title/Summary/Keyword: unstable equilibrium

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Geomechanical analysis of elastic parameters of the solid core of the Earth

  • Guliyev, Hatam H.
    • Geomechanics and Engineering
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    • v.14 no.1
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    • pp.19-27
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    • 2018
  • It follows from the basic principles of mechanics of deformable solids relating to the strength, stability and propagation of elastic waves that the Earth's inner core cannot exist in the form of a spherical structure in the assumed thermobaric conditions and calculation values of physico-mechanical parameters. Pressure level reaches a value that is significantly greater than the theoretical limit of medium strength in the model approximations at the surface of the sphere of the inner core. On the other hand, equilibrium state of the sphere is unstable on the geometric forming at much lower loads under the influence of the "dead" surface loads. In case of the action of "follower" loads, the assumed pressure value on the surface of the sphere is comparable with the value of the critical load of "internal" instability. In these cases, due to the instability of the equilibrium state, propagation of homogeneous deformations becomes uneven in the sphere. Moreover, the elastic waves with actual velocity cannot propagate in such conditions in solid medium. Violation of these fundamental conditions of mechanics required in determining the physical and mechanical properties of the medium should be taken into account in the integrated interpretations of seismic and laboratory (experimental) data. In this case, application of the linear theory of elasticity and elastic waves does not ensure the reliability of results on the structure and composition of the Earth's core despite compliance with the required integral conditions on the mass, moment of inertia and natural oscillations of the Earth.

Rock Slope Stability Analysis in Boeun Region Considering Properties of Discontinuities (불연속면의 특성은 고려한 보은지역 암반사면 안정성해석)

  • 이지수;박혁진;민경덕;구호본
    • Economic and Environmental Geology
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    • v.34 no.6
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    • pp.601-615
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    • 2001
  • The study area. Boeun-eup Boeun-kun, belongs to Ogchon metamorphic belt which is highly metamorphosed and consisted of complex geologic formations. Even though the geological structures and formations are complex and metamorphosed, the geological investigation and consideration are not enough and consequently the plane failure is occurred in the rock slope which was under construction on 1 : 0.5 gradient. This area is assessed as unstable and additional failure is possible by the discontinuity with same direction of failure surface. Therefore, the authors evaluate the slope stability using various analysis methods such as SMR, stereographic projection method, and the limit equilibrium analysis. In order to analyze stress redistribution and nonlinear displacement behavior caused by stress release, the authors conduct numerical analysis with UDEC and then the behavior of rock mass is analyzed after reinforcements are applied.

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Nature of Cold Injury and Resistance in Wheat and Barley (맥류의 한해와 내동성에 관하여)

  • 남윤일;연규복;구본철
    • KOREAN JOURNAL OF CROP SCIENCE
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    • v.34 no.s02
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    • pp.96-114
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    • 1989
  • There are several meterorolgical stresses in the winter cereal crops. Among these stresses, cold injury is one of the most important stresses for wheat and barley production in Korea. The reduction in grain yield of the wheat and barley due to cold injury has occurred almost every year in Korea. The objective of the study was to get the basic information in relation to the cold injury and to detect the method minimizing the damage of cold injury. When the air temperature was the ranges of -13$^{\circ}C$ to -15$^{\circ}C$, the soil temperature at the crown part of the plant was very stable, whereas in the ranges of -2$^{\circ}C$ to -3$^{\circ}C$ the soil surface temperature was more unstable and cold than air and subterranean temperatures. The different parts of the plant in wheat and barley possess the different levels of cold hardiness. In comparison to the cold hardiness of plant parts, the leaf and crown are the less sensitive to cold injury than root and vascular transitional zone. The type and extent of stress is determined by the redistribution pattern of water during freezing. These types from freezing processes were three types: a) Equilibrium freezing pattern b) Non -equilibrium freezing pattern, c) Non-equilibrium freezing pattern typical of tender tissues. Cold hardiness in wheat plants were more harder than barley plants at vegitative stage, but inverted at the reproductive stage. Injuries by low temperature during the seasons of barley cultivation in Korea were occured mainly in four stage; in the first and third stage, frost injury occurs, the second stage, freezing injury, and the fourth stage, chilling injury.

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Analysis of Talus Slope Stability using 2D FEM and 3D Limit Equilibrium Method (2차원 유한요소법과 3차원 한계평형법을 이용한 테일러스 사면안정성 해석)

  • Lee, Kyoung-Mi;Kim, Sung-Kwon;Seo, Yaung-Seok;Lee, Sun-Bok;Kim, Dong-Hyun;Kim, Do-Sik
    • The Journal of Engineering Geology
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    • v.17 no.3
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    • pp.381-391
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    • 2007
  • A series of talus slope stability analyses were carried out using 2D FEM and 3D limit equilibrium methods for this study. The FEM analyses on Phase 2 were performed to delineate failure depths based on stress distributions for each slope. The results revealed that the failure surface exist in the colluvium layer of about 3-10 m thickness. Three dimensional models, derived from the FEM analyses and geological field survey, were made for the use in a 3D limit equilibrium analysis. The result shows that all the talus slopes are stable under dry condition, but unstable under saturated condition due to heavy rain.

The mathematical model of temperature dependent growth of Scuticociliate Miamiensis avidus in vitro and in vivo conditions (In vitro와 in vivo에서의 온도에 따른 스쿠티카충 성장의 수리 모델)

  • Oh, Chun-Young
    • Journal of fish pathology
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    • v.26 no.2
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    • pp.65-75
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    • 2013
  • Population growth equation of scuticociliate Miamiensis avidus was obtained from the experimental results of in vitro culture condition to estimate the growth rate and carrying capacity from the growth equation. In addition, intraperitoneal infections into olive flounder Paralichthys olivaceus were carried out into 2 different conditions: different concentrations of M. avidus in same water temperature and same concentration of M. avidus in different water temperatures. Olive flounder mortality was threshold dependent with both the temperature and M. avidus density parameters. In this paper, we propose a mathematical model to study M. avidus growth in olive flounder based upon the interactions between parasite and host. The mathematical model was logistic growth differential equation (1.2). The parameters were found with Matlab program through the Levenberge-Marquardt method. In theorem, equilibrium values between the infected fish population and dead population could found. Our equilibrium points were a stable equilibrium and an unstable equilibrium. From the equation (1.6), it was possible to predict the amount of cumulative mortality of olive flounder along with the time after M. avidus infection.

A Study on In-Situ Slope Reinforcement Methods Using Nailed Geotextiles (네일 및 지오텍스타일을 이용한 원위치 사면보강공법에 관한 연구)

  • 김홍택
    • Geotechnical Engineering
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    • v.10 no.4
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    • pp.133-152
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    • 1994
  • In the present study, an economic design of Anchored Geosynthetic(AG) System applied mainly to reinforce unstable soil slopes is investigated. For this purpose methods of stability analysis are developed to determine the optimum installation angle, required minimum length and maximum spacing of nails. Anchorage of nails within the soil mass is achieved by frictional resistance to pull out along the effective length of the nails. Cases of infinite slope and finite slope are dealt with individually. Silce methods of stability analysis developed in the present study are limit-equilibrium-based. For the case of finite slope Spencer method which considers interslice force is modified to evalyate the overall stability. In addition, the effects of various design parameters on requried length and spacing of nails corresponding to the optimum orientation of nails are analyzed. Based on the analysis, a simplified equation is given for the optimum nail orientation. Also the importance of optimum nail orientation is illustrated throughout design example, and the appropriateness of judgment criterion are examined.

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A Study on the Stability Boundaries for Single Layer Latticed Domes under Combined Loads (조합하중을 받는 단층 래티스 돔의 안정경계에 관한 연구)

  • 한상을;이갑수
    • Proceedings of the Computational Structural Engineering Institute Conference
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    • 2000.04b
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    • pp.85-91
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    • 2000
  • The smallest value of the load when the equilibrium condition becomes to be unstable is defined as the buckling load. The primary objective of this paper is to analyse stability boundaries for star dome under combined loads and is to investigate the iteration diagram under the independent loading parameter In numerical procedure of the geometrically nonlinear problems, Arc Length Method and Newton-Raphson iteration method is used to find accurate critical point(bifurcation point and limit point). In this paper independent loading vector is combined as proportional value and star dome was used as numerical analysis model to find stability boundary among load parameters and many other models as multi-star dome and arches were studied. Through this study we can find the type of buckling mode and the value of buckling load.

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A Study the THMs Formation by Chloramination Disinfection (클로라민 소독에 의한 THMs 생성에 관한 연구)

  • 김평청;우달식;남상호
    • Journal of environmental and Sanitary engineering
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    • v.14 no.1
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    • pp.11-16
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    • 1999
  • This study was performed to investigate THMs formation by chloramination as a secondary disinfection in drinking water distribution system. As the $Cl_2/NH_3-N$ ratio increased from 1:1 to 4:1, the THMs concentration had actually no change in the breakpoint curve of pH 6, 7. At pH 8, THMs level was not augmented at between 1:1 and 5:1. In the $Cl_2/NH_3-N$ ratio of more than 5:1 and 6:1 respectively, THMs level was raised. Only the chloroform of THMs was insignificantly detected by both preformed chloramine and preammoniation applications, which was probably attributed to the stoichiometrically unstable equilibrium in the preparation of chloramine, whereas $CHCl_3$, $CHCl_2Br$ and $CHClBr_2$ of THMs were found in the application of free chlorine. However it turned out that the THMs levels by chloramine was incomparably inferior to that of free chlorine.

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Unstable Brake Pad Mode Due to Friction-velocity Slope (마찰 곡선에 의한 불안정 브레이크 패드 모드 해석)

  • Nam, Jaehyun;Kang, Jaeyoung
    • Transactions of the Korean Society for Noise and Vibration Engineering
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    • v.22 no.12
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    • pp.1206-1212
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    • 2012
  • The brake squeal propensity due to the friction-velocity curve is numerically investigated. The finite element models for the disc and pad are correlated with the modal test. In the friction-engaged system modeling, the friction function is linearized at the equilibrium. The damping term induced by friction-velocity slope is incorporated into the equations of motion. In the complex eigenvalue analysis, it is found that the pad shear mode is very sensitive to the friction curve. The results shows that the squeal propensity of the pad shear mode can be controlled by the design parameters such as pressure and stiffness.

Design of a Swing Up Controller for Inverted Pendulum System (도립진자의 스윙업 제어기 설계)

  • Kwon, Yo-Han;Choi, Won-Ho;Kim, Beom-Soo;Lim, Myo-Taeg
    • Proceedings of the KIEE Conference
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    • 1999.11c
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    • pp.643-645
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    • 1999
  • In experiment, a real inverted pendulum system has state constraints and limited amplitude of input. These problems make it difficult to design a swing-up controller. To overcome these problems, we design a sliding mode controller considering physical behaviour of the inverted pendulum system. This sliding mode controller uses a switching control action to converge along a specified path derived from energy equation from a state around the path to desired states(standing position). And optimal control method is used to guarantee stability at unstable equilibrium position. The designed controller can be applied to all inverted pendulum systems regardless of the values of their parameters. Compared with previous existing controllers, it is simple and easy to tune. Experimental results are given to show the effectiveness of this controller.

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