• 한국정밀공학회지
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• 제27권6호
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• pp.47-54
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• 2010

In this paper, the purpose is to study a method for detection of crack in clamped-clamped beams using the vibration characteristics. The natural frequency of beam is obtained by FEM and experiment. The governing differential equations of a Timoshenko beam are derived via Hamilton's principle. The two coupled governing differential equations are reduced to one fourth order ordinary differential equation in terms of the flexural displacement. The crack is assumed to be in the first mode of fracture and to be always opened during the vibrations. The differences between the actual and predicted crack positions and sizes are less than 9.8% and 28%, respectively.

• 동력기계공학회지
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• 제9권3호
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• pp.58-65
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• 2005

This paper deals with the free vibrations of truncated conical shell with uniform thickness by the transfer influence coefficient method. The classical thin shell theory based upon the $Fl\ddot{u}gge$ theory is assumed and the governing equations of a conical shell are written as a coupled set of first order differential equations using the transfer matrix. The Runge-Kutta-Gill integration and bisection method are used to solve the governing differential equations and to compute the eigenvalues respectively. The natural frequencies and corresponding mode shapes are calculated numerically for the truncated conical shell with any combination of boundary conditions at the edges. And all boundary conditions and the intermediate supports between conical shell and foundation could be treated only by adequately varying the values of the spring constants. Numerical results are compared with existing exact and numerical solutions of other methods.

• Kyungpook Mathematical Journal
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• 제60권4호
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• pp.853-867
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• 2020

The aim of this study was to analyze the momentum and heat transfer of a rotating nanofluid with conducting spherical dust particles. The fluid flows over a stretching surface under the influence of an external magnetic field. By applying similarity transformations, the governing partial differential equations were trans-formed into nonlinear coupled ordinary differential equations. These equations were solved with the built-in function bvp4c in MATLAB. Moreover, the effects of the rotation parameter ω, magnetic field parameter M, mass concentration of the dust particles α, and volume fraction of the nano particles 𝜙, on the velocity and temperature profiles of the fluid and dust particles were considered. The results agree well with those in published papers. According to the result the hikes in the rotation parameter ω decrease the local Nusselt number, and the increasing volume fraction of the nano particles 𝜙 increases the local Nusselt number. Moreover the friction factor along the x and y axes increases with increasing volume fraction of the nano particles 𝜙.

• Structural Engineering and Mechanics
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• 제73권3호
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• pp.319-330
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• 2020

This paper investigates the free vibrations of cylindrical shells made of time-dependent materials for different viscoelastic models under various boundary conditions. During the extraction of equations, the displacement field is estimated through the first-order shear deformation theory taking into account the transverse normal strain effect. The constitutive equations follow Hooke's Law, and the kinematic relations are linear. The assumption of axisymmetric is included in the problem. The governing equations of thick viscoelastic cylindrical shell are determined for Maxwell, Kelvin-Voigt and the first and second types of Zener's models based on Hamilton's principle. The motion equations involve four coupled partial differential equations and an analytical method based on the elementary theory of differential equations is used for its solution. Relying on the results, the natural frequencies and mode shapes of viscoelastic shells are identified. Conducting a parametric study, we examine the effects of geometric and mechanical properties and boundary conditions, as well as the effect of transverse normal strain on natural frequencies. The results in this paper are compared against the results obtained from the finite elements analysis. The results suggest that solutions achieved from the two methods are ideally consistent in a special range.

• 한국생산제조학회지
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• 제7권6호
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• pp.110-116
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• 1998

For the vibration analysis of 3-dimensional piping system containing fluid flow, a transfer matrix method is presented. The fluid velocity and pressure were considered, that coupled to longitudinal and flexural vibrations. Transfer matrices and point matrices were derived from direct solutions of the differential equations of motion of pipe conveying fluids, and the variations of natural frequency with flow velocity for 3-dimensional piping system were investigated.

• 한국지반공학회논문집
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• 제27권3호
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• pp.75-83
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• 2011

일반적인 불포화지반의 거동뿐만 아니라, 열과 관련된 분야, 지반환경 분야 등 다양한 분야에서 불포화 다공질 재료의 열적-수리적-역학적으로 결합된 문제들이 대두되면서 이러한 문제들을 해석하기 위한 수치도구 개발의 필요성이 대두되고 있다. 본 논문에서는 거시적 접근법(macroscopic approach)에 근거하여 불포화지반에 대한 열-수리-역학거동의 수식화를 하였다. 흙, 물, 공기에 대한 질량보존의 법칙, 에너지 보존법칙, 그리고 하중평형 조건식으로부터 결합된(coupled) 4개의 지배방정식을 유도하였다. Galerkin 간략화와 시간적분으로부터 주 변수인 변위(u), 가스압($P_g$), 유체압($P_1$), 온도(T)를 Newton의 반복과정을 이용하여 구하는 유한요소 프로그램(FEM)을 작성하였다. 개발된 프로그램을 이용하여 다공질재료에서 2상 흐름 문제 중 일차원 배수실험(u-$P_g-P_1$), 온도 압밀(u-$P_1$-T), 그리고 지표면 온도변화에 의한 말뚝의 주변지반에 대한 영향(u-$P_1$-T)에 대하여 수치해석을 수행하고 논의하였다.

• Structural Engineering and Mechanics
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• 제52권4호
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• pp.787-813
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• 2014

Starting with Hamilton's variational principle, the governing field equations for the steady state response of thin-walled beams under harmonic forces are derived. The formulation captures shear deformation effects due to bending and warping, translational and rotary inertia effects and as well as torsional flexural coupling effects due to the cross section mono-symmetry. The equations of motion consist of four coupled differential equations in the unknown displacement field variables. A general closed form solution is then developed for the coupled system of equations. The solution is subsequently used to develop a family of shape functions which exactly satisfy the homogeneous form of the governing field equations. A super-convergent finite element is then formulated based on the exact shape functions. Key features of the element developed include its ability to (a) isolate the steady state response component of the response to make the solution amenable to fatigue design, (b) capture coupling effects arising as a result of section mono-symmetry, (c) eliminate spatial discretization arising in commonly used finite elements, (d) avoiding shear locking phenomena, and (e) eliminate the need for time discretization. The results based on the present solution are found to be in excellent agreement with those based on finite element solutions at a small fraction of the computational and modelling cost involved.

• Structural Engineering and Mechanics
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• 제65권4호
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• pp.381-388
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• 2018

Dynamic behaviour of beam carrying masses has attracted attention of many researchers and engineers. Many studies on the analytical solution of beam with concentric tip mass have been published. However, there are limited works on vibration analysis of beam with an eccentric three dimensional object. In this case, bending and torsional deformations of beam are coupled due to the boundary conditions. Analytical solution of equations of motion of the system is complicated and lengthy. Therefore, in this study, Differential Transform Method (DTM) is applied to solve the relevant equations. First, the Timoshenko beam with 3D tip attachment whose centre of gravity is not coincident with beam end point is considered. The beam is assumed to undergo bending in two orthogonal planes and torsional deformation about beam axis. Using Hamilton's principle the equations of motion of the system along with the possible boundary conditions are derived. Later DTM is applied to obtain natural frequencies and mode shapes of the system. According to the relevant literature DTM has not been applied to such a system so far. Moreover, the problem is modelled by Ansys, the well-known finite element method, and impact test is applied to extract experimental modal data. Comparing DTM results with finite element and experimental results it is concluded that the proposed approach produces accurate results.

• Journal of applied mathematics & informatics
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• 제35권3_4호
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• pp.277-302
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• 2017

In this paper, we have proposed a numerical method for Singularly Perturbed Boundary Value Problems (SPBVPs) of reaction-diffusion type of third order Ordinary Differential Equations (ODEs). The SPBVP is reduced into a weakly coupled system of one first order and one second order ODEs, one without the parameter and the other with the parameter ${\varepsilon}$ multiplying the highest derivative subject to suitable initial and boundary conditions, respectively. The numerical method combines boundary value technique, asymptotic expansion approximation, shooting method and finite difference scheme. The weakly coupled system is decoupled by replacing one of the unknowns by its zero-order asymptotic expansion. Finally the present numerical method is applied to the decoupled system. In order to get a numerical solution for the derivative of the solution, the domain is divided into three regions namely two inner regions and one outer region. The Shooting method is applied to two inner regions whereas for the outer region, standard finite difference (FD) scheme is applied. Necessary error estimates are derived for the method. Computational efficiency and accuracy are verified through numerical examples. The method is easy to implement and suitable for parallel computing. The main advantage of this method is that due to decoupling the system, the computation time is very much reduced.

• 대한기계학회논문집
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• 제19권3호
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• pp.820-833
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• 1995

An analysis is performed to examine the equilibrium state and the stability of modeled Reynolds stress equations for homogeneous turbulent shear flows. The system of the governing equations consists of four coupled ordinary differential equations. The equilibrium states are found by the steady state solution of the governing equations. In order to investigate the stability of the system about its state in equilibrium, and eigenvalue problem is constructed. As a result, constraints for the coeffieients in the model equations are obtained by the stability condition of the equilibrium state as well as by their physically realizable bounds. It is observed that the models with pressure-strain rate correlation that are linear in the anisotropy tensor are stable and produce reasonable equilibrium tensor do not behave properly. Stability considerations about three most commonly used models are given in detail in the final section.