• Steel and Composite Structures
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• 제17권1호
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• pp.123-131
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• 2014

In this paper we have considered the vibration of parametrically excited oscillator with strong cubic positive nonlinearity of complex variable in nonlinear dynamic systems with forcing based on Mathieu-Duffing equation. A new analytical approach called homotopy perturbation has been utilized to obtain the analytical solution for the problem. Runge-Kutta's algorithm is also presented as our numerical solution. Some comparisons between the results obtained by the homotopy perturbation method and Runge-Kutta algorithm are shown to show the accuracy of the proposed method. In has been indicated that the homotopy perturbation shows an excellent approximations comparing the numerical one.

• Earthquakes and Structures
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• 제11권1호
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• pp.129-140
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• 2016

This paper presents He's Energy Balance Method (EBM) for solving nonlinear oscillatory differential equations. Three strong nonlinear cases have been studied analytically. Analytical results of the EBM are compared with numerical solutions using Runge-Kutta's algorithm. The effects of different important parameters on the nonlinear response of the systems are studied. The results show the presented method is potentially to solve high nonlinear vibration equations.

• Structural Engineering and Mechanics
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• 제73권3호
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• pp.331-337
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• 2020

This paper proposes a new approximate analytical solution for highly nonlinear vibration of mechanical systems called Hamiltonian Approach (HA) that can be widely use for structural health monitoring systems. The complete procedure of the HA approach is studied, and the precise application of the presented approach is surveyed by two familiar nonlinear partial differential problems. The nonlinear frequency of the considered systems is obtained. The results of the HA are verified with the numerical solution using Runge-Kutta's [RK] algorithm. It is established the only one iteration of the HA leads us to the high accurateness of the solution.

• Earthquakes and Structures
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• 제7권1호
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• pp.1-15
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• 2014

In this paper we consider three different cases and we apply Variational Approach (VA) to solve the non-natural vibrations and oscillations. The method variational approach does not demand small perturbation and with only one iteration can lead to high accurate solution of the problem. Some patterns are presented for these three different cease to show the accuracy and effectiveness of the method. The results are compared with numerical solution using Runge-kutta's algorithm and another approximate method using energy balance method. It has been established that the variational approach can be an effective mathematical tool for solving conservative nonlinear dynamical equations.

• Steel and Composite Structures
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• 제17권5호
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• pp.721-734
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• 2014

In the current study, we consider a new class of analytical periodic solution for free nonlinear vibration of mechanical systems. Hamiltonian approach is applied to analyze nonlinear problems which occur in dynamics. The proposed method doesn't have the limitations of the classical methods and leads us to a high accurate solution by only one iteration. Two well known examples are studied to show the convenience and effectiveness of this approach. Runge-Kutta's algorithm is also applied and the results of it are compared with the Hamiltonian approach. High accuracy of the proposed approach reveals that the Hamiltonian approach can be very useful for other nonlinear practical problems in engineering.

• 전기의세계
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• 제21권3호
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• pp.48-52
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• 1972

The application of pontryagin's Maximum Principle to the optimal control eventually leads to the problem of solving the two point boundary value problem. Most of problems have been related to their own special factors, therfore it is very hard to recommend the best method of deriving their optimal solution among various methods, such as iterative Runge Kutta, analog computer, gradient method, finite difference and successive approximation by piece-wise linearization. The gradient method has been applied to the optimal control of two point boundary value problem in the power systems. The most important thing is to set up some objective function of which the initial value is the function of terminal point. The next procedure is to find out any global minimum value from the objective function which is approaching the zero by means of gradient projection. The algorithm required for this approach in the relevant differential equations by use of the Runge Kutta Method for the computation has been established. The usefulness of this approach is also verified by solving some examples in the paper.

• Journal of Astronomy and Space Sciences
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• 제17권1호
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• pp.107-116
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• 2000

본 연구는 지구 공전 궤도 근처의 Leonid의 출현 빈도와 속도 등을 예측하기 위한 연구의 초기 단계로서 meteoroid에 대한 기초 자료 조사와 더붙어 기존에 알려져 있는 meteoroid 입자의 분출 속도 모텔과 섭동 모델로부터 meteoroid의 운동 방향과 속도를 컴퓨터로 계산하기 위한 프로그램을 개발하고 이것을Leonid stream에 적용해 보았다. 입자의 초기 속도 모델로는Jones의 분출속도 분포모델을 사용하였으며, meteoroid의 궤도 운동 모델에는 태양과 달, 지구를 비롯한 각 행성들의 섭동 모델이 포함되었다. 태양계 천체들의 Ephemeris를 구하기 위해 JPL (Jet Propulsion L Laboratory)의 SSD (Solar System Dynamics) Laboratory에서 개발된 DE405 Solar System E Ephemeris 데이터 파일을 사용하였다. 이외에 중요한 섭동 요소로써 태양 복사압을 고려하였으며, 적분 알고리즘으로는 8차 Runge-Kutta 방법을 사용하였다.

• Nuclear Engineering and Technology
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• 제17권1호
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• pp.16-24
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• 1985

풀형 고속증식로에서의 과도 현상을 모사할 수 있는 전산 모델이 개발되었다. 이 전산 모델 SIM-FARP는 어떠한 펌프로의 전원 상실사고나 완전한 강제냉각 상실사고, 그리고 자연순환 과정 등을 모사할 수 있는 Fast Running Computer Code이다. 이에 따라 8개의 지배방정식이 유도되었으며, 이8개의 미분 방정식을 풀기 위해 Runge-Kutta의 수치해석방법이 사용되었다. 개발된 전산 프로그램은 두 가지 예제에 적용되었는데 이는 Super-Phenix-I에서의 펌프에의 전원상실사고 및 원자로가 정지되지 않는 상태에서의 외부전원 상실사고이다.

• Structural Engineering and Mechanics
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• 제65권4호
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• pp.409-413
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• 2018

In this paper, He's Variational Approach (VA) is used to solve high nonlinear vibration equations. The proposed approach leads us to high accurate solution compared with other numerical methods. It has been established that this method works very well for whole range of initial amplitudes. The method is sufficient for both linear and nonlinear engineering problems. The accuracy of this method is shown graphically and the results tabulated and results compared with numerical solutions.

• 전자공학회논문지SC
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• 제46권6호
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• pp.73-79
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• 2009

운동하는 물체를 제어하기 위한 제어이론은 디지털 컴퓨터(임베디드시스템)를 이용하여 복잡한 신경망 이론, 인공지능 이론, 비선형 모델 예측 제어 이론등이 제어기 설계 단계에서 구현되고 있다. 비행제어 시스템의 비선형 모델 예측 제어 예측기는 구현하는 컴퓨터의 성능과 각종 모듈의 응용프로그램을 하드실시간(Hard Real-Time)으로 처리할 수 있도록 응답 시간을 충족 하여야 한다. 이와 동시에 제어 시스템에의 성능을 충분히 발휘할 수 있는 정확성도 고려하여야 한다. 수학적 영역에서의 오류는 전체 알고리즘 구현에 영향을 준다. 그러나 이러한 수학적 오류 발생 요인은 예측기에서 생성되는 파라미터에서 최종 정확도 계산에 가끔 고려하지 않는다. 본 논문에서는 비행체 제어를 위한 디지털 제어 시스템에서 하드실시간 하중제어 모델 예측기를 구현하고, 알고리즘의 응답시간을 살펴본다. 또한 이에 따른 정밀도를 보장하는 고효율 예측기를 구현하는 알고리즘을 살펴본다. 예측기는 하중 제어 모델에서 오일러 방법, Heun 방법, Runge-kutta 방법, 테일러 방법의 수치적분 알고리즘을 사용하여 구현된다.