• 한국전자통신학회논문지
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• 제5권5호
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• pp.541-546
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• 2010

유연한 로봇팔은 모터에 의해 관절 축을 회전할 때 진동이 발생한다. 유연한 팔이 원하는 각으로 회전하면서 동시에 팔 끝의 진동이 안정화되도록 제어하였다. 본 논문에서 유연한 로봇팔의 동력학은 bernoulli-Euler의 beam이론과 라그란지 방정식을 이용하여 구하였고, 섹터 내부에 연속입력함수를 가진 슬라이딩 섹터이론을 이용하여 히스테리시스 사구간을 가진 비선형 제어기를 제안한다.

• 한국농공학회지
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• 제42권2호
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• pp.108-114
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• 2000

This paper explores the non-linear behavior of tapered beam subjected to a floating concentration load. For applying the Bernoulli-Euler beam theory to this beam, the bending moment at any point of elastical is obtained from the final equilibrium stage. By using the bending moment equation and the Bernoulli-Euler beam theory, the differential equations governing the elastica of simple beam are derived , and solved numberically . Three kinds of tapered beam types are considered . The numerical results of the non-linear behavior obtained in this study are agreed quite well to the results obtained from the laboratory-scale experiments.

• Journal of the Korean Society for Industrial and Applied Mathematics
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• 제26권3호
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• pp.138-155
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• 2022

To solve the initial value problem we present a new single-step implicit method based on the Euler method. We prove that the proposed method has convergence order 2. In practice, numerical results of the proposed method for some selected examples show an error tendency similar to the second-order Taylor method. It can also be found that this method is useful for stiff initial value problems, even when a small number of nodes are used. In addition, we extend the proposed method by using weighted averages with a parameter and show that its convergence order becomes 2 for the parameter near $\frac{1}{2}$. Moreover, it can be seen that the extended method with properly selected values of the parameter improves the approximation error more significantly.

• 한국추진공학회지
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• 제23권6호
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• pp.1-10
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• 2019

노즐 내 파동은 노즐목을 빠져나가는 유동의 공력음향학적인 효과로 인해 연소불안정을 감쇠시키는 주요 요소 중 하나로 알려져 있다. 이와 같은 효과는 노즐 어드미턴스라는 지표를 통해 정량적으로 평가가 가능하다. 본 연구에서는 현재까지 로켓 연소불안정 억제에 가장 효과적인 노즐감쇠(nozzle damping)와 연계된 노즐 어드미턴스를 구하는 여러 기법을 소개한다. 이중, 가장 널리 알려진 1차원 선형 오일러 방정식을 도입하여 노즐의 주 설계 변수에 따른 노즐 어드미턴스의 경향을 분석하였다. 분석 결과, 노즐 수축부 길이가 짧아질수록 축방향 노즐 어드미턴스의 값이 낮게 나타나는 주파수 영역대가 확장되므로 짧은 노즐일수록 주파수 의존성을 줄인다는 기존 이론을 검증하였다. 또한, 짧은 노즐 이론을 통한 어드미턴스 예측은 1차 접선방향 압력 섭동에는 적합하지 않음을 알 수 있었다.

• Journal of the Korean Society for Industrial and Applied Mathematics
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• 제20권3호
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• pp.243-259
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• 2016

The Richards equation for water movement in unsaturated soil is highly nonlinear partial differential equations which are not solvable analytically unless unrealistic and oversimplifying assumptions are made regarding the attributes, dynamics, and properties of the physical systems. Therefore, conventionally, numerical solutions are the only feasible procedures to model flow in partially saturated porous media. The standard Finite element numerical technique is usually coupled with an Euler time discretizations scheme. Except for the fully explicit forward method, any other Euler time-marching algorithm generates nonlinear algebraic equations which should be solved using iterative procedures such as Newton and Picard iterations. In this study, lumped mass and distributed mass in the frame of Picard and Newton iterative techniques were evaluated to determine the most efficient method to solve the Richards equation with finite element model. The accuracy and computational efficiency of the scheme and of the Picard and Newton models are assessed for three test problems simulating one-dimensional flow processes in unsaturated porous media. Results demonstrated that, the conventional mass distributed finite element method suffers from numerical oscillations at the wetting front, especially for very dry initial conditions. Even though small mesh sizes are applied for all the test problems, it is shown that the traditional mass-distributed scheme can still generate an incorrect response due to the highly nonlinear properties of water flow in unsaturated soil and cause numerical oscillation. On the other hand, non oscillatory solutions are obtained and non-physics solutions for these problems are evaded by using the mass-lumped finite element method.

• Structural Engineering and Mechanics
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• 제44권5호
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• pp.681-704
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• 2012

The dynamic response of Euler-Bernoulli beams to resonant harmonic moving loads is analysed. The non-dimensional form of the motion equation of a beam crossed by a moving harmonic load is solved through a perturbation technique based on a two-scale temporal expansion, which permits a straightforward interpretation of the analytical solution. The dynamic response is expressed through a harmonic function slowly modulated in time, and the maximum dynamic response is identified with the maximum of the slow-varying amplitude. In case of ideal Euler-Bernoulli beams with elastic rotational springs at the support points, starting from analytical expressions for eigenfunctions, closed form solutions for the time-history of the dynamic response and for its maximum value are provided. Two dynamic factors are discussed: the Dynamic Amplification Factor, function of the non-dimensional speed parameter and of the structural damping ratio, and the Transition Deamplification Factor, function of the sole ratio between the two non-dimensional parameters. The influence of the involved parameters on the dynamic amplification is discussed within a general framework. The proposed procedure appears effective also in assessing the maximum response of real bridges characterized by numerically-estimated mode shapes, without requiring burdensome step-by-step dynamic analyses.

• 한국전산구조공학회논문집
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• 제21권5호
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• pp.475-482
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• 2008

본 논문은 로터 시스템의 디스크 회전운동을 표현하는데 있어 운동방정식을 통합하는 과정에서 기존 연구자들이 채택한 오일러 각 사용법이 일관성이 없음을 지적하였다. 기존 연구자들은 오일러 각 순서가 달라서 속도와 운동에너지도 달리 산정하였음은 물론, 운동방정식은 오직 선형 시스템만 취급해 왔다 이러한 오일러 각 사용법의 단점을 극복하기 위하여 회전운동을 더욱 단순하게 매개화할 수 있는 4원법(quaternion)과 구 좌표계를 적용하여 비선형 시스템을 도출하였다. 이를 바탕으로 수치해석을 통하여 기존 방법과 비교하여 제안한 방법의 신뢰성과 우수성을 보였다.

• Computers and Concrete
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• 제16권3호
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• pp.429-448
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• 2015

The dams are huge structures storing a large amount of water and failures of them cause especially irreparable loss of lives during the earthquakes. They are named as a group of structures subjected to fluid-structure interaction. So, the response of the fluid and its hydrodynamic pressures on the dam should be reflected more accurately in the structural analyses to determine the real behavior as soon as possible. Different mathematical and analytical modelling approaches can be used to calculate the water hydrodynamic pressure effect on the dam body. In this paper, it is aimed to determine the dynamic response of concrete gravity dams using different water modelling approaches such as Westergaard, Lagrange and Euler. For this purpose, Sariyar concrete gravity dam located on the Sakarya River, which is 120km to the northeast of Ankara, is selected as a case study. Firstly, the main principals and basic formulation of all approaches are given. After, the finite element models of the dam are constituted considering dam-reservoir-foundation interaction using ANSYS software. To determine the structural response of the dam, the linear transient analyses are performed using 1992 Erzincan earthquake ground motion record. In the analyses, element matrices are computed using the Gauss numerical integration technique. The Newmark method is used in the solution of the equation of motions. Rayleigh damping is considered. At the end of the analyses, dynamic characteristics, maximum displacements, maximum-minimum principal stresses and maximum-minimum principal strains are attained and compared with each other for Westergaard, Lagrange and Euler approaches.

• Journal of the Korean Society for Industrial and Applied Mathematics
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• 제13권4호
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• pp.315-321
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• 2009

In this paper, a level set based energy functional is proposed, the minimization of which results in simultaneous reference background image modeling and foreground segmentation. Due to the mutual constraint of the two processes, a good estimate of the background can be obtained with a small number of frames, and due to the use of the level set, an Euler-Lagrange equation that directly solves the problem can be derived.

• 대한수학회보
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• 제52권2호
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• pp.513-524
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• 2015

Here, we show that the title equation has no positive integer solutions (m, n), where ${\phi}$ is the Euler function.