• Structural Engineering and Mechanics
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• 제62권5호
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• pp.607-618
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• 2017

In this paper, an analytical procedure based on the perturbation technique is presented to study the free vibrations of annular viscoelastic plates by considering the first order shear deformation theory as the displacement field. The viscoelastic properties obey the standard linear solid model. The equations of motion are extracted for small deflection assumption using the Hamilton's principle. These equations which are a system of partial differential equations with variable coefficients are solved analytically with the perturbation technique. By using a new variable change, the governing equations are converted to equations with constant coefficients which have the analytical solution and they are appropriate especially to study the sensitivity analysis. Also the natural frequencies are calculated using the classical plate theory and finite elements method. A parametric study is performed and the effects of geometry, material and boundary conditions are investigated on the vibrational behavior of the plate. The results show that the first order shear deformation theory results is more closer than to the finite elements with respect to the classical plate theory for viscoelastic plate. The more results are summarized in conclusion section.

• 전자공학회논문지C
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• 제36C권10호
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• pp.66-74
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• 1999

이 논문에서는 잘 알려진 N-P complete 문제인 TSP를 풀수 있는 통계적 홉필드 신경망의 일반화된 모델을 제안한다. 정규화를 통한 형태의 목적함수를 가진 반 덴 바우트의 방법은 필요한 외란 효과를 다 고려하지 않은 심각한 단점이 있다. 제안된 모델에서는 향상된 목적함수가 사용되었고 반 덴 바우트가 고려한 2가지와 박찬익이 더 고려한 1가지를 포함하는 5가지의 외란 효과와 외란 효과들의 비를 이용하는 방법을 제안한다. 임의로 만든 10개 도시의 시뮬레이션을 통해 제안한 모델이 100가지의 경우에서 90가지가 최적이나 거의 최적에 도달함을 보여준다. (오차 5% 이내로) 30개와 50개 도시의 큰 규모의 TSP에 대해 좋은 결과를 얻었다.

• Structural Engineering and Mechanics
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• 제52권5호
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• pp.997-1017
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• 2014

According to the structure characteristics of the non-uniform beam bridge, a practical model for calculating the vibration equation of the non-uniform beam bridge is given and the application scope of the model includes not only the beam bridge structure but also the non-uniform beam with added masses and elastic supports. Based on the Bernoulli-Euler beam theory, extending the application of the modal perturbation method and establishment of a semi-analytical method for solving the vibration equation of the non-uniform beam with added masses and elastic supports based is able to be made. In the modal subspace of the uniform beam with the elastic supports, the variable coefficient differential equation that describes the dynamic behavior of the non-uniform beam is converted to nonlinear algebraic equations. Extending the application of the modal perturbation method is suitable for solving the vibration equation of the simply supported and continuous non-uniform beam with its arbitrary added masses and elastic supports. The examples, that are analyzed, demonstrate the high precision and fast convergence speed of the method. Further study of the timesaving method for the dynamic characteristics of symmetrical beam and the symmetry of mode shape should be developed. Eventually, the effects of elastic supports and added masses on dynamic characteristics of the three-span non-uniform beam bridge are reported.

• 한국항공우주학회지
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• 제46권11호
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• pp.902-910
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• 2018

본 논문은 지구의 J2 섭동을 고려한 비공면 타원궤도에서의 우주비행체의 요격 문제를 다룬다. J2에 의한 영향은 지구를 돌고 있는 우주비행체 궤도를 변화시키는 주된 요인이 되며, 이를 해결하기 위해 실시간 요격 방법을 제안한다. 구형의 지구와 순간추력을 고려한 운동방정식을 기반으로 최적화 문제를 구성하고 수치적으로 얻어진 최적해를 인터셉터의 추진방향으로 설정한다. 위치 오차는 최적화 문제를 반복적으로 해결하고 인터셉터의 추진방향을 수정하는 방식으로 해결한다. 다양한 궤도를 상황을 고려하여 제안하는 방법을 검증한다.

• 한국기계가공학회지
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• 제13권6호
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• pp.88-98
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• 2014

A moving mass on a skewed linear guideway model to analyze the friction-induced stick-slip behavior of ball-screw-driven slides is proposed. To describe the friction force, a friction coefficient function is modelled as a third-order polynomial of the relative velocity between the slide mass and a guideway. A nonlinear differential equation of motion is derived and an approximate solution is obtained using a perturbation method for the amplitudes and base frequencies of both pure-slip and stick-slip oscillations. The results are presented with time responses, phase plots, and amplitude plots, which are compared adequately with those obtained by Runge Kutta 4th-order numerical integration, as long as the difference between the static and kinematic friction coefficients is small. However, errors in the results by the approximate solution increase and are not negligible if the difference between the friction coefficients exceeds approximately 40% of the static friction coefficient.

• Structural Engineering and Mechanics
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• 제61권5호
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• pp.657-661
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• 2017

In this paper, it has been tried to propose a new semi analytical approach for solving nonlinear vibration of conservative systems. Hamiltonian approach is presented and applied to high nonlinear vibration systems. Hamiltonian approach leads us to high accurate solution using only one iteration. The method doesn't need any small perturbation and sufficiently accurate to both linear and nonlinear problems in engineering. The results are compared with numerical solution using Runge-Kutta-algorithm. The procedure of numerical solution are presented in detail. Hamiltonian approach could be simply apply to other powerfully non-natural oscillations and it could be found widely feasible in engineering and science.

• Journal of applied mathematics & informatics
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• 제31권1_2호
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• pp.131-145
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• 2013

In this paper, we present an initial value technique for solving singularly perturbed differential difference equations with a boundary layer at one end point. Taylor's series is used to tackle the terms containing shift provided the shift is of small order of singular perturbation parameter and obtained a singularly perturbed boundary value problem. This singularly perturbed boundary value problem is replaced by a pair of initial value problems. Classical fourth order Runge-Kutta method is used to solve these initial value problems. The effect of small shift on the boundary layer solution in both the cases, i.e., the boundary layer on the left side as well as the right side is discussed by considering numerical experiments. Several numerical examples are solved to demonstate the applicability of the method.

• Journal of applied mathematics & informatics
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• 제28권1_2호
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• pp.411-423
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• 2010

In this paper, a numerical method for singular perturbation problems arising in chemical reactor theory for general singularly perturbed two point boundary value problems with boundary layer at one end(left or right) of the underlying interval is presented. The original second order differential equation is replaced by an approximate first order differential equation with a small deviating argument. By using the trapezoidal formula we obtain a three term recurrence relation, which is solved using Thomas Algorithm. To demonstrate the applicability of the method, we have solved four linear (two left and two right end boundary layer) and one nonlinear problems. From the results, it is observed that the present method approximates the exact or the asymptotic expansion solution very well.

• KSTLE International Journal
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• 제2권1호
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• pp.46-54
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• 2001

The herringbone groove journal bearing (HGJB) has chevron type grooves on stationary or rotating member of the bearing so that they pump the lubricant inward the grooves when journal rotates. As a result, the pressure is generated around the journal so that the radial stiffness and dynamic stability are improved comparing to the plain journal bearing (PJB) when the bearing operates near the concentric condition. The narrow groove theory, conventionally adopted to simulate the concentric operation of HGJB, is limited to the infinite number of grooves. A numerical study of air-lubricated HGJB is presented for the finite number of grooves. The compressible isothermal Reynolds equation is solved by using Finite Element Method together with the Newton-Raphson iterative procedure and perturbation method. The solutions render the static and dynamic performances of HGJB. Comparison of present results with a PJB validates previously published finite difference solution. The HGJB's geometric parameters influence its static and dynamic characteristics. The optimum geometric parameters are presented for the air-lubricated HGJB in particular conditions.

• Structural Engineering and Mechanics
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• 제50권6호
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• pp.853-862
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• 2014

In this paper, two approximate analytical methods have been applied to forced nonlinear vibration problems to assess a high accurate analytical solution. Variational Iteration Method (VIM) and Perturbation Method (PM) are proposed and their applications are presented. The main objective of this paper is to introduce an alternative method, which do not require small parameters and avoid linearization and physically unrealistic assumptions. Some patterns are illustrated and compared with numerical solutions to show their accuracy. The results show the proposed methods are very efficient and simple and also very accurate for solving nonlinear vibration equations.