• 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.

• 한국항공우주학회지
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• 제44권7호
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• pp.620-628
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• 2016

호모토피 알고리즘은 비선형성이 강하거나 다수의 최적해가 존재하는 비선형 최적제어 문제에서 점진적으로 비선형 항으로 고려하게 해줌으로써 강건하게 전역의 최적해를 구할 수 있는 방법이다. 본 논문에서는 초기 추정치에 둔감한 SBS 알고리즘과 호모토피 알고리즘을 결합한 비선형 최적제어 알고리즘을 제시하였다. 이러한 접근방식은 저추력 궤적최적화 문제와 같이 비선형성이 강한 문제의 최적해를 구하는데 효과적이다. 또한, 비선형성이 강한 문제들은 종종 다수 국소 해가 존재하게 되는데, 이러한 경우에 SBS-호모토피 방법은 점진적으로 전역해를 찾는 것을 가능하게 한다.

• Structural Engineering and Mechanics
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• 제48권6호
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• pp.823-831
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• 2013

In this paper, it has been attempted to present a powerful analytical approach called Homotopy Perturbation Method (HPM). Free vibration of an electrostatically actuated microbeam is considered to study analytically. The effect of important parameters on the response of the system is considered. Some comparisons are presented to verify the results with other researcher's results and numerical solutions. It has been indicated that HPM could be easily extend to any nonlinear equation. We try to provide an easy method to achieve high accurate solution which valid for whole domain.

• Structural Engineering and Mechanics
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• 제61권1호
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• pp.105-116
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• 2017

In this paper, the optimal extended homotopy analysis method (OEHAM) is introduced to deal with the damped Duffing resonator driven by a van der Pol oscillator, which can be described as a complex Multi-Degree-of-Freedom (MDOF) nonlinear coupling system. Ecumenically, the exact solutions of the MDOF nonlinear coupling systems are difficult to be obtained, thus the development of analytical approximation becomes an effective and meaningful approach to analyze these systems. Compared with traditional perturbation methods, HAM is more valid and available, and has been widely used for nonlinear problems in recent years. Hence, the method will be chosen to study the system in this article. In order to acquire more suitable solutions, we put forward HAM to the OEHAM. For the sake of verifying the accuracy of the above method, a series of comparisons are introduced between the results received by the OEHAM and the numerical integration method. The results in this article demonstrate that the OEHAM is an effective and robust technique for MDOF nonlinear coupling systems. Besides, the presented methods can also be broadly used for various strongly nonlinear MDOF dynamical systems.

• Journal of applied mathematics & informatics
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• 제41권4호
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• pp.861-868
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• 2023

Nonlinear network creates complex homotopy structural communication in wireless network medium because of complex distribution approach. Due to this multicast topological connection structure, the queuing probability was non regular principles to create routing structures. To resolve this problem, we propose a Co-cluster homotopy queuing model (Co-CHQT) for Nonlinear Algebraic Topological Structure (NLTS-) for improving poison distribution network communication. Initially this collects the routing propagation based on Nonlinear Distance Theory (NLDT) to estimate the nearest neighbor network nodes undernon linear at x_(a,b)→ax²+bx² = c. Then Quillen Network Decomposition Theorem (QNDT) was applied to sustain the non-regular routing propagation to create cluster path. Each cluster be form with co variance structure based on Two unicast 2(n+1)-Z2(n+1)-Z network. Based on the poison distribution theory X_(a,b) ≠ µ(C), at number of distribution routing strategies weights are estimated based on node response rate. Deriving shorte;'l/st path from behavioral of the node response, Hilbert -Krylov subspace clustering estimates the Cluster Head (CH) to the routing head. This solves the approximation routing strategy from the nonlinear communication depending on Max- equivalence theory (Max-T). This proposed system improves communication to construction topological cluster based on optimized level to produce better performance in distance theory, throughput latency in non-variation delay tolerant.

• 한국항공우주학회지
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• 제35권7호
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• pp.647-654
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• 2007

본 논문에서는 일정한 추력을 이용한 지구-달의 연료 최적 궤적해를 이용하여, 가변 추력기를 이용한 지구 탈출 궤적에서의 에너지 및 연료 최적 궤적을 설계하였다. 에너지 최적의 지구 탈출 궤적은 여러 차례 지구를 공전하게 되고, 궤도 천이 시간이 일반적인 궤도 천이 시간 보다 상대적으로 오래 소요되므로 최적화 문제를 해를 구하기가 쉽지 않다. 따라서 에너지 최적 해를 구하기 위하여, 초기 상태변수를 조정하면서 Discrete continuation의 기법을 적용하였다. 최적화 문제의 종말 조건은 일정한 추력기를 이용한 지구 탈출 궤적의 종말 조건을 이용하였고, 구속 시간은 일정한 추력기를 이용한 궤도 천이의 경우보다 큰 값으로 설정하였다. 한편, 연료 최적 궤적은 제어 입력의 형태가 불연속적이기 때문에 해를 구하기가 쉽지 않다. 따라서 연료 최적 궤적은 에너지 최적의 해와 호모토피(Homotopy) 기법을 적용시켜 그 해를 구하였다.

• Structural Engineering and Mechanics
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• 제44권3호
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• pp.405-416
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• 2012

In this study the investigation of large deflections subject in compliant mechanisms is presented using homotopy perturbation method (HPM). The main purpose is to propose a convenient method of solution for the large deflection problem in compliant mechanisms in order to overcome the difficulty and complexity of conventional methods, as well as for the purpose of mathematical modeling and optimization. For simplicity, a cantilever beam of linear elastic material under horizontal, vertical and bending moment end point load is considered. The results show that the applied method is very accurate and capable for cantilever beams and can be used for a large category of practical problems for the aim of optimization. Also the consequence of effective parameters on the large deflection is analyzed and presented.

• Journal of the Korean Society for Industrial and Applied Mathematics
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• 제4권2호
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• pp.99-110
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• 2000

This paper is devoted to the parallelism of a numerical matrix eigenvalue problem. The eigenproblem arises in a variety of applications, including engineering, statistics, and economics. Especially we try to approach the industrial techniques from mathematical modeling. This paper has developed a parallel algorithm to find all eigenvalues. It is contributed to solve a specific practical problem, a vibration problem in the industry. Also we compare the runtime between the serial algorithm and the parallel algorithm for the given problems.

• 호남수학학술지
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• 제27권1호
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• pp.115-129
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• 2005

In this paper, we give a digital graph-theoretical approach of the study of digital images with relation to a simplicial complex. Thus, a digital graph $G_k$ with some k-adjacency in ${\mathbb{Z}}^n$ can be recognized by the simplicial complex spanned by $G_k$. Moreover, we demonstrate that a graphically $(k_0,\;k_1)$-continuous map $f:G_{k_0}{\subset}{\mathbb{Z}}^{n_0}{\rightarrow}G_{k_1}{\subset}{\mathbb{Z}}^{n_1}$ can be converted into the simplicial map $S(f):S(G_{k_0}){\rightarrow}S(G_{k_1})$ with relation to combinatorial topology. Finally, if $G_{k_0}$ is not $(k_0,\;3^{n_0}-1)$-homotopy equivalent to $SC^{n_0,4}_{3^{n_0}-1}$, a graphically $(k_0,\;k_1)$-continuous map (respectively a graphically $(k_0,\;k_1)$-isomorphisim) $f:G_{k_0}{\subset}{\mathbb{Z}}^{n_0}{\rightarrow}G_{k_1}{\subset}{\mathbb{Z}^{n_1}$ induces the group homomorphism (respectively the group isomorphisim) $S(f)_*:{\pi}_1(S(G_{k_0}),\;v_0){\rightarrow}{\pi}_1(S(G_{k_1}),\;f(v_0))$ in algebraic topology.

• Advances in concrete construction
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• 제10권4호
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• pp.357-367
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• 2020

The impulse of this paper is to examine the influence of unsteady flow comprising of Eyring-Powell nanofluid over a stretched surface. This work aims to explore efficient transfer of heat in Eyring-Powell nanofluid with bio-convection. Nanofluids possess significant features that have aroused various investigators because of their utilization in industrial and nanotechnology. The influence of including motile microorganism is to stabilize the nanoparticle suspensions develop by the mixed influence of magnetic field and buoyancy force. This research paper reveals the detailed information about the linearly compressed Magnetohydrodynamics boundary layer flux of two dimensional Eyring-Powell nanofluid through disposed surface area due to the existence of microorganism with inclusion the influence of non- linear thermal radiation, energy activation and bio-convection. The liquid is likely to allow conduction and thickness of the liquid is supposed to show variation exponentially. By using appropriate similarity type transforms, the nonlinear PDE's are converted into dimensionless ODE's. The results of ODE's are finally concluded by employing (HAM) Homotopy Analysis approach. The influence of relevant parameters on concentration, temperature, velocity and motile microorganism density are studied by the use of graphs and tables. We acquire skin friction, local Nusselt and motil microorganism number for various parameters.