• Steel and Composite Structures
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• 제15권4호
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• pp.439-449
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• 2013

In this study simply supported nonlinear Euler-Bernoulli beams resting on linear elastic foundation and subjected to the axial loads is investigated. A new kind of analytical technique for a non-linear problem called He's Energy Balance Method (EBM) is used to obtain the analytical solution for non-linear vibration behavior of the problem. Analytical expressions for geometrically non-linear vibration of Euler-Bernoulli beams resting on linear elastic foundation and subjected to the axial loads are provided. The effect of vibration amplitude on the non-linear frequency and buckling load is discussed. The variation of different parameter to the nonlinear frequency is considered completely in this study. The nonlinear vibration equation is analyzed numerically using Runge-Kutta $4^{th}$ technique. Comparison of Energy Balance Method (EBM) with Runge-Kutta $4^{th}$ leads to highly accurate solutions.

• Geomechanics and Engineering
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• 제16권4호
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• pp.355-361
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• 2018

In this paper, nonlinear vibration of Euler-Bernoulli beams resting on linear elastic foundation is studied. It has been tried to prepare a semi-analytical solution for whole domain of vibration. Only one iteration lead us to high accurate solution. The effects of linear elastic foundation on the response of the beam vibration are considered and studied. The effects of important parameters on the ratio of nonlinear to linear frequency of the system are studied. The results are compared with numerical solution using Runge-Kutta $4^{th}$ technique. It has been shown that the Max-Min approach can be easily extended in nonlinear partial differential equations.

• 제어로봇시스템학회:학술대회논문집
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• 제어로봇시스템학회 2005년도 ICCAS
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• pp.906-909
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• 2005

In this study, the dynamic flying characteristics of the worn head sliders are investigated theoretically due to the change in head geometry caused by head and disk contact. The film shapes can be approximated as taper- truncated cycloidal-flat film. Two-dimensional time dependent modified Reynolds equation included molecular slip effect are formulated with neglected the roughness effect. The motion of head slider was assumed to have two degree of freedom in this work. Finite difference approximation with Newton Raphson iterative technique and the fourth order Runge-Kutta method were implemented to obtain the transient response of the slider head with various change in head geometry numerically and compared with the transient response of the IBM3380 type head slider. The simulation results show the film shape has affects significantly on the static and dynamic characteristic of slider head in magnetic storage systems.

• Journal of Advanced Marine Engineering and Technology
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• 제23권6호
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• pp.794-805
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• 1999

Pneumatic cushioning cylinders are commonly employed for vibration and shock control. A mathematical simulation model of a double acting pneumatic cushioning cylinder designed to absorb shock loads is presented which is based on the following assumptions; ideal equation of state isentropic flow through a port conservation of mass polytropic thermodynamics single degree of freedom piston dynamics and energy equivalent linear damping. These differential equation can be solved through numerical integration using the fourth order Runge-Kutta method. An experimental study was conducted to validate the results obtained by the numerical integra-tion technique. Simulated results show good agreement with experimental data. The computer simulation model presented here has been extremely useful not only in understanding the has been extremely useful not only in understanding the basic cushioning but also in evaluating different designs.

• 한국수자원학회논문집
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• 제39권7호
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• pp.593-603
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• 2006

강우로부터 유출현상은 고유적으로 비선형성이다. 더욱이 실제적으로 이와 같은 비선형성의 해석은 많은 어려움을 내포하고 있다. 또한, 부정류효과의 동적작용을 고려한 저류개념은 매개변수의 유역특성상 추정하기가 상당히 복잡하기 때문에 피해오고 있는 실정이다. 본 연구에서는 이와 같은 동적효과를 고려한 비선형의 저류함수에 대한 매개변수의 최적치를 얻고자 시도한다. 이를 위한 수치해법은 금강의 보청천유역의 관측치와 계산치의 오차를 최소로 하는 최소자승법에 의거 준선형화, Runge-Kutta 및 pattern-search 법들을 적용한다. 본 연구의 동적효과를 고려한 비선형 개념적모형의 적용성은 비선형성만을 고려한 저류함수모형 및 기존의 Nash 모형과 비교하여 검토하였다. 그 결과 2계모형이 l계모형보다 강우로부터 유출예측치를 보다 더 잘 재현하는 것을 알 수 있었으며, Nash 모형과는 대등함을 보여주었다. 여기서 획득된 매개변수들은 물리적 의미뿐만 아니라 본 모형의 국내 적용성도 제공한다.

• 대한토목학회논문집
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• 제4권1호
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• pp.69-77
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• 1984

본(本) 연구(硏究)에서는 아치의 미소요소(微小要素)에 대한 평형방정식(平衡方程式)과 D'Alembert의 원리(原理)를 이용(利用)하여 포물선(抛物線)아치의 자유진동(自由振動)에 관한 미분방정식(微分方程式)을 유도(誘導)하였고, 이 미분방정식(微分方程式)을 Runge-Kutta 적분기법(積分技法)에 적용(適用)하여 수치해석(數値解析)할 수 있는 알고리듬을 개발(開發)하였고 이를 콤퓨터 프로그램화(化) 하였다. 수치해석예제(數値解析例題)로는 아치의 지간(支間)길이가 10m인 양단(兩端)힌지 아치를 택(擇)하였으며 수치해석(數値解析)의 결과(結果)를 분석(分析)하여 아치의 높이, 회전반경(回轉半徑) 및 회전관성(回轉慣性)이 포물선(抛物線)아치의 자유진동(自由振動)에 미치는 영향(影響)에 대하여 고찰(考察)하였다.

• Structural Engineering and Mechanics
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• 제50권4호
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• pp.487-500
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• 2014

An analytical solution for the nonlinear in-plane free oscillations of the suspended cable which contains the quadratic and cubic nonlinearities is investigated via the homotopy analysis method (HAM). Different from the existing analytical technique, the HAM is indeed independent of the small parameter assumption in the nonlinear vibration equation. The nonlinear equation is established by using the extended Hamilton's principle, which takes into account the effects of the geometric nonlinearity and quasi-static stretching. A non-zero equilibrium position term is introduced due to the quadratic nonlinearity in order to guarantee the rule of the solution expression. Therefore, the mth-order analytic solutions of the corresponding equation are explicitly obtained via the HAM. Numerical results show that the approximate solutions obtained by using the HAM are in good agreement with the numerical integrations (i.e., Runge-Kutta method). Moreover, the HAM provides a simple way to adjust and control the convergent regions of the series solutions by means of an auxiliary parameter. Finally, the effects of initial conditions on the linear and nonlinear frequency ratio are investigated.

• 한국추진공학회:학술대회논문집
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• 한국추진공학회 2006년도 제26회 춘계학술대회논문집
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• pp.310-313
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• 2006

본 연구에서는 sub-cavity를 적용한 경우 얻어지는 압력진동의 제어효과를 수치계산 방법을 사용하여 조사하였으며, 삼각돌기와 블로잉제트를 사용하여 얻어진 결과들과 비교하여 그 효율성을 검토하였다. 사각형의 공동을 지나는 유동장은 3차원 비정상 압축성 Wavier-Stokes 방정식에 완전 내제적 유한체적법 및 다단계 Runge-Kutta 방법을 적용하여 수치모사하였으며, 공동유동의 난류상태량들을 적절히 예측하기 위하여 large eddy simulation(LES)을 수행하였다. 본 연구의 결과로부터, 공동후단 부근에서 발생하는 압력진동이 전체 공동유동의 비정상 거동을 지배하며, sub-cavity를 사용하여 압력진동의 폭을 감소시킬 수 있음을 알았다.

• Earthquakes and Structures
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• 제13권2호
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• pp.103-118
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• 2017

In vertical seismic isolation (VSI), a building is partitioned intentionally by vertical layers into two dynamically different substructures for seismic response reduction. Initially, a 1-story frame was partitioned into two substructures, interconnected by viscous and visco-elastic links, and seismic responses of the original and the vertically isolated structures (VIS) were obtained, considering a large number of stiffness and mass ratios of substructures with respect to the original structure. Color contour graphs were defined for presentation and investigation of large amounts of output results. Dynamic characteristics of the isolated structures were studied by considering the non-classical damping of the system, and then the effects of viscous and visco-elastic link parameters on the modal damping ratios were discussed. On this basis, three states of mass isolation, interactional state, and control mass were differentiated. Response history analyses were performed by Runge-Kutta numerical method. In these analyses, interaction of isolation ratios and link parameters, on response control of VIS was studied and the appropriate ranges for link parameters as well as the optimal ranges for isolation ratios were suggested. Results show that by using the VSI technique, seismic response reduction up to 50% in flexible substructure and even more in stiff substructure is achievable.

• Journal of the Korean Physical Society
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• 제73권9호
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• pp.1303-1309
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• 2018

In the present paper, we study the entropy analysis of boundary layer flow over a slender stretching sheet under the action of a non uniform magnetic field that is acting perpendicular to the flow direction. The effects of viscous dissipation and Joule heating are included in the energy equation. Using similarity transformation technique the momentum and thermal boundary layer equations to a system of nonlinear differential equations. Numerical solutions are obtained using the shooting and fourth-order Runge-Kutta method. The expressions for the entropy generation number and Bejan number are also obtained using a suggested similarity transformation. The main objective of this article is to investigate the effects of different governing parameters such as the magnetic parameter ($M^2$), Prandtl number (Pr), Eckert number (Ec), velocity index parameter (m), wall thickness parameter (${\alpha}$), temperature difference parameter (${\Omega}$), entropy generation number (Ns) and Bejan number (Be). All these effects are portrayed graphically and discussed in detail. The analysis reveals that entropy generation reduces with decreasing wall thickness parameter and increasing temperature difference between the stretching sheet and the fluid outside the boundary layer. The viscous and magnetic irreversibilities are dominant in the vicinity of the stretching surface.