• 제목/요약/키워드: simultaneous differential equation

검색결과 18건 처리시간 0.035초

분포하중(分布荷重)을 받는 구형판(矩形板)의 탄성해석(彈性解析) (Analysis of Rectangular Plates under Distributed Loads of Various Intensity with Interior Supports at Arbitrary Positions)

  • 장석윤
    • 대한조선학회지
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    • 제13권1호
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    • pp.17-23
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    • 1976
  • Some methods of analysis of rectangular plates under distributed load of various intensity with interior supports are presented herein. Analysis of many structures such as bottom, side shell, and deck plate of ship hull and flat slab, with or without internal supports, Floor systems of bridges, included crthotropic bridges is a problem of plate with elastic supports or continuous edges. When the four edges of rectangular plate is simply supported, the double Fourier series solution developed by Navier can represent an exact result of this problem. If two opposite edges are simply supported, Levy's method is available to give an "exact" solution. When the loading condition and supporting condition of a plate does not fall into these cases, no simple analytic method seems to be feasible. Analysis of a simply supported rectangular plate under irregularly distributed loads of various intensity with internal supports is carried out by applying Navier solution well as the "Principle of Superposition." Finite difference technique is used to solve plates under irregularly distributed loads of various intensity with internal supports and with various boundary conditions. When finite difference technique is applied to the Lagrange's plate bending equation, any of fourth order derivative term in this equation produces at least five pivotal points leading to some troubles when the resulting linear algebraic equations are to be solved. This problem was solved by reducing the order of the derivatives to two: the fourth order partial differential equation with one dependent variable, namely deflection, is changed to an equivalent pair of second order partial differential equations with two dependent variables. Finite difference technique is then applied to transform these equations to a set of simultaneous linear algebraic equations. Principle of Superposition is then applied to handle the problems caused by concentrated loads and interior supports. This method can be used for the cases of plates under irregularly distributed loads of various intensity with arbitrary conditions such as elastic supports, or continuous edges with or without interior supports, and this method can also be solve the influence values of deflection, moment and etc. at arbitrary position of plates under the live load.

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System Representation for the Control System of the Follow-up Mechanism on the Marine Gyro Compass

  • Sang-Jib Lee
    • 한국항해학회지
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    • 제4권1호
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    • pp.31-50
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    • 1980
  • It does not seem necessarily practicable to keep the system always in optimal condition, athough the control system of the follow-up mechanism on the most marine gyro compasses is to be adjusted by the operator through the gain adjustment. Sometimes a sustained oscillation or an incorrect gyro reading occurs to the system. For such a system any systematical research or theoretical basis of the guide for the optimal gain adjustment has not been reported yet. As a basic investigation of the theoretical system analysis to solve the problems concerned, the author attempts in this paper to express the system in a mathematical model deduced from the results of the theoretical approach and the experimental observation of each element contained in the follow-up mechanism of Hokshin D-1 gyro compass, and to constitute an over-all closed loop transfer function. This funciton being reverted to a fourth orderlinear differential equation, the first order simultaneous differential equations are obtained by means of the state-variables. The latter equations are solved by the Runge-Kutta method with digital computer. By comparing the characteristic of the simulated over-all output with that of the experimental result, it is shown that both outputs are nearly consistent with each other. It is also expected that the system representation proposed by this paper is valid and will be a prospective means in a further study on the design and optimal adjustment of the system.

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복점시장에서 신상품의 동태적 최적가격설정에 관한 연구 (Dynamic Optimal Pricing for New Products in a Duopoly)

  • 전덕빈;최리군
    • 대한산업공학회지
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    • 제23권3호
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    • pp.545-557
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    • 1997
  • This paper deals with dynamic optimal pricing for new products by a firm which maximizes the discounted profit stream of it's own in a duopoly. The problem is constructed as differential games and dynamic optimization theory. Cost is assumed to decline as time goes on. A modified customer's choice model is formulated as a diffusion model and we solve a dynamic optimization problem by adopting the diffusion model. Since this paper focus on deriving real prices not showing a time trend, we formulate recursive form equations of costate variables(shadow price) and a simultaneous equation of price. Hence we derive a dynamic optimal pricing model for using in real market. In particular, we construct a dynamic optimal pricing model in the case that there are benefits from not only new subscribers but also previous subscribers. We analyze instant camera market in U.S.A(1976-1985) by utilizing the above model.

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Dynamic Adjustment of Noncooperative Games Where Informations are Given at Discrete Time Intervals

  • Oh, Hyungjae
    • 한국경영과학회지
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    • 제15권2호
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    • pp.71-83
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    • 1990
  • This paper concerns the analyses of dynamic adjustments in noncooperative games where the market informations are given at discrete time intervals. During the game period, the market informations are given at discrete time intervals. During the game period, the inventories initially stored by players are to be released one day based to the completely competitive market so as to maximize each player's revenue, where players' parameters are unknown one another. Game results have shown that the continuous dynamic adjustment does not necessarily assure the better revenue, and if a player thinks that his parameter is underestimated by hig opponent, then he is better overestimate his opponent's parameter.

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포물선 근사법에 의한 상태방정식의 새로운 수치해석적 접근법에 관한 연구 (A New Numerical Method for Solving Differential Equation by Quadratic Approximation)

  • 이종기;권용준;최병곤;문영현
    • 대한전기학회:학술대회논문집
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    • 대한전기학회 2003년도 하계학술대회 논문집 A
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    • pp.107-109
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    • 2003
  • 전력계통의 과도 안정도 해석의 접근방법에는 SI(Simultaneous Implicit)법과 PE(Partitioned Explicit)법 두 가지방법을 사용해오고 있다. SI법에는 Trapezoidal법 등이 있고, PE법에는 Runge-Kutta법, Euler법등이 사용되고 있다. SI법인 Trapezoidal법은 PE법의 Runge-Kutta법 또는 Euler법에 비해 시간간격을 크게 해서 계산속도를 줄일 수 있다는 장점이 있지만, 정화도면에서는 신뢰한 수 없는 단점이 있다. 이 논문에서는 포물선 사법을 이용하여 Trapezoidal법의 정확도를 개선학 수 있는 방법을 제시하고 명확한 수학적 증명을 통해 타당성을 보여준다. 연속함수와 불연속함수에 대해서 Runge-Kutta법과 Trapezoidal법과 제안한 방법을 적용시켜서 제안한 방법의 정화함을 보여준다.

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Symbolic computation and differential quadrature method - A boon to engineering analysis

  • Rajasekaran, S.
    • Structural Engineering and Mechanics
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    • 제27권6호
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    • pp.713-739
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    • 2007
  • Nowadays computers can perform symbolic computations in addition to mere number crunching operations for which they were originally designed. Symbolic computation opens up exciting possibilities in Structural Mechanics and engineering. Classical areas have been increasingly neglected due to the advent of computers as well as general purpose finite element software. But now, classical analysis has reemerged as an attractive computer option due to the capabilities of symbolic computation. The repetitive cycles of simultaneous - equation sets required by the finite element technique can be eliminated by solving a single set in symbolic form, thus generating a truly closed-form solution. This consequently saves in data preparation, storage and execution time. The power of Symbolic computation is demonstrated by six examples by applying symbolic computation 1) to solve coupled shear wall 2) to generate beam element matrices 3) to find the natural frequency of a shear frame using transfer matrix method 4) to find the stresses of a plate subjected to in-plane loading using Levy's approach 5) to draw the influence surface for deflection of an isotropic plate simply supported on all sides 6) to get dynamic equilibrium equations from Lagrange equation. This paper also presents yet another computationally efficient and accurate numerical method which is based on the concept of derivative of a function expressed as a weighted linear sum of the function values at all the mesh points. Again this method is applied to solve the problems of 1) coupled shear wall 2) lateral buckling of thin-walled beams due to moment gradient 3) buckling of a column and 4) static and buckling analysis of circular plates of uniform or non-uniform thickness. The numerical results obtained are compared with those available in existing literature in order to verify their accuracy.

열전도가 주도적인 삼차원 접촉융해에 대한 비정상 해석 (Unsteady Analysis of the Conduction-Dominated Three-Dimensional Close-Contact Melting)

  • 유호선
    • 대한기계학회논문집B
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    • 제23권8호
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    • pp.945-956
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    • 1999
  • This work reports a set of approximate analytical solutions describing the initial transient process of close-contact melting between a rectangular parallelepiped solid and a flat plate on which either constant temperature or constant heat flux is imposed. Not only relative motion of the solid block tangential to the heating plate, but also the density difference between the solid and liquid phase is incorporated in the model. The thin film approximation reduces the force balance between the solid weight and liquid pressure, and the energy balance at the melting front into a simultaneous ordinary differential equation system. The normalized model equations admit compactly expressed analytical solutions which include the already approved two-dimensional solutions as a subset. In particular, the normalized liquid film thickness is independent of all pertinent parameters, thereby facilitating to define the transition period of close-contact melting. A unique behavior of the solid descending velocity due to the density difference is also resolved by the present solution. A new geometric function which alone represents the three-dimensional effect is introduced, and its properties are clarified. One of the representative results is that heat transfer is at least enhanced at the expense of the increase in friction as the cross-sectional shape deviates from the square under the same contact area.

호텔기업의 조직문화와 세대 갈등, 조직몰입 간의 관계에 대한 연구 : M세대, Z세대 차이를 중심으로 (A study on the relationship between the organizational culture, generational conflict, and organizational commitment of Hotel companies : Focusing on M Generation and Z Generation Differences)

  • 김명용;심주리;강정구
    • 문화기술의 융합
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    • 제10권3호
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    • pp.643-650
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    • 2024
  • 현재 한국은 구인난과 구직난이 공존하는 모순된 상황을 겪고 있다. 이러한 환경 속에서 퇴직자들은 상사/동료와의 갈등과 조직문화 불만족을 가장 큰 퇴사원인으로 삼고 있으며, 이는 특히 MZ세대에게 더 큰 영향을 미치고 있다. 이에 학자들은 MZ세대의 조직문화와 다른 변수간 영향관계를 파악하는 선행연구들을 진행하여왔다. 하지만 대부분의 연구들은 MZ세대를 하나의 그룹으로 보는 MZ세대론을 바탕으로 진행되어 두 세대를 구분하여야 한다는 실무자들의 요구를 충족하지 못하고 있는 실정이다. 이에 본 연구에서는 호텔기업 종사원을 M세대와 Z세대로 구분하여 두 집단간 변수간 영향관계 차이를 파악하고자 한다. 이를 위해 M세대 170명, Z세대 110명을 대상으로 설문조사를 실시하고 이를 AMOS 구조방정식을 통해 분석하였다. 이를 통해 모든 세대에게 위계지향문화와 세대갈등이 유의한정의 관계에 있으며, 세대갈등은 조직몰입에 부정적인 영향을 미치는 것을 확인할 수 있었다. 또한, M세대는 관계지향문화가 세대갈등에 부정적 영향을 미치는 반면, Z세대에서는 영향관계가 없는 것과 같은 차이가 있음을 검증하였다. 본 연구를 통해 M세대와 Z세대간 영향관계 차이를 파악할 수 있었다.