• 한국소음진동공학회논문집
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• 제13권7호
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• pp.555-561
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• 2003

An iterative modal analysis approach is developed to determine the effect of transverse open cracks on the dynamic behavior of simply supported Euler-Bernoulli beams with the moving masses. The influences of the velocities of moving masses, the distance between the moving masses and a crack have been studied on the dynamic behavior of a simply supported beam system by numerical method. The Presence of crack results In large deflection of beam. The crack section is represented by a local flexibility matrix connecting two undamaged beam segments i.e. the crack is modelled as a rotational spring. This flexibility matrix defines the relationship between the displacements and forces across the crack section and is derived by applying fundamental fracture mechanics theory. Totally, as the velocity of the moving masses and the distance between the moving masses are increased, the mid-span deflection of simply supported beam with the crack is decreased.

• Computers and Concrete
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• 제25권5호
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• pp.427-432
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• 2020

In this research, the buckling analysis of sandwich beam with composite reinforced by graphene platelets (GPLs) in two face sheets is investigated. Three type various porosity patterns including uniform, symmetric and asymmetric are considered through the thickness direction of the core. Also, the top and bottom face sheets layers are considered composite reinforced by GPLs/CNTs based on Halpin-Tsai micromechanics model and extended mixture rule, respectively. Based on various shear deformation theories such as Euler-Bernoulli, Timoshenko and Reddy beam theories, the governing equations of equilibrium using minimum total potential energy are obtained. It is seen that the critical buckling load decreases with an increase in the porous coefficient, because the stiffness of sandwich beam reduces. Also, it is shown that the critical buckling load for asymmetric distribution is lower than the other cases. It can see that the effect of graphene platelets on the critical buckling load is higher than carbon nanotubes. Moreover, it is seen that the difference between carbon nanotubes and graphene platelets for Reddy and Euler-Bernoulli beam theories is most and least, respectively.

• 한국소음진동공학회:학술대회논문집
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• 한국소음진동공학회 2003년도 춘계학술대회논문집
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• pp.1085-1090
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• 2003

An iterative modal analysis approach is developed to determine the effect of transverse open cracks on the dynamic behavior of simply supported Euler-Bernoulli beams with the moving masses. The influences of the velocities of moving masses, the distance between the moving masses and a crack have been studied on the dynamic behavior or a simply supported beam system by numerical method. no presence or crack results in large deflection of beam. The crack section is represented by a local flexibility matrix connecting two undamaged beam segments i.e. the crack is modelled as a rotational spring. This flexibility matrix defines the relationship between the displacements and forces across the crack section and is derived by applying fundamental fracture mechanics theory. Totally, as the velocity of the moving masses and the distance between the moving masses are increased, the mid-span deflection of simply supported beam with the crack is decreased.

• 한국음향학회지
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• 제16권1호
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• pp.16-23
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• 1997

강제진동에 의한 외팔보의 동적응답과 진동모드를 연구하였다. Bernoulli-Euler 이론과 유한요소법을 이용하여 외팔보의 고유진동수와 진동모드를 수치해석하고 실험으로 측정하여 비교하였다. 가진주파수를 1Hz에서 70Hz까지 변화시켜 외팔보의 1차, 2차 공진주파수를 구하고, 응답위치에 따른 진동 변위를 측정하여 진동모드를 살펴보았다. 실험결과에서 외팔보의 절점(node)이 1차모드에서는 0.2차모드에서는 0,0.786으로 측정되었다. 외팔보의 공진주파수와 진동모드에 대해 이론적으로 예상했던 결과와 실험으로 측정한 결과가 거의 일치하였다.

• Steel and Composite Structures
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• 제39권5호
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• pp.543-564
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• 2021

In this study free vibration analysis of a cracked Goland composite wing is investigated. The wing is modelled as a cantilevered beam based on Euler- Bernoulli equations. Also, composite material is modelled based on lamina fiber-reinforced. Edge crack is modelled by additional boundary conditions and local flexibility matrix in crack location, Castigliano's theorem and energy release rate formulation. Governing differential equations are extracted by Hamilton's principle. Using the separation of variables method, general solution in the normalized form for bending and torsion deflection is achieved then expressions for the cross-sectional rotation, the bending moment, the shear force and the torsional moment for the cantilevered beam are obtained. The cracked beam is modelled by separation of beam into two interconnected intact beams. Free vibration analysis of the beam is performed by applying boundary conditions at the fixed end, the free end, continuity conditions in the crack location of the beam and dynamic stiffness matrix determinant. Also, the effects of various parameters such as length and location of crack and fiber angle on natural frequencies and mode shapes are studied. Modal analysis results illustrate that natural frequencies and mode shapes are affected by depth and location of edge crack and coupling parameter.

• Journal of Mechanical Science and Technology
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• 제19권9호
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• pp.1731-1741
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• 2005

In this paper, we studied about the effect of the open crack and a tip mass on the dynamic behavior of a cantilever pipe conveying fluid with a moving mass. The equation of motion is derived by using Lagrange's equation and analyzed by numerical method. The cantilever pipe is modelled by the Euler-Bernoulli beam theory. The crack section is represented by a local flexibility matrix connecting two undamaged pipe segments. The influences of the crack, the moving mass, the tip mass and its moment of inertia, the velocity of fluid, and the coupling of these factors on the vibration mode, the frequency, and the tip-displacement of the cantilever pipe are analytically clarified.

• 대한토목학회논문집
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• 제10권1호
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• pp.1-7
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• 1990

이 논문은 자유단에 집중하중과 만재 등분포하중이 작용하는 캔틸레버 보의 과대처짐을 해석한 연구이다. 과대처짐을 해석하기 위하여 처짐곡선의 Bernoulli-Euler 미분방정식을 이용하였고, 이 미분방정식을 Runge Kutta method와 Regula Falsi method를 이용하여 수치해석할 수 있는 기법을 개발하였다. 수치해석의 결과로 하중과 자유단의 수평처짐, 수직처짐 및 회전각과의 관계를 무차원화하여 도시하였고 또한 몇 개의 전형적인 과대처짐곡선을 무차원화하여 도시하였다.

• Structural Engineering and Mechanics
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• 제63권2호
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• pp.137-146
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• 2017

The size-dependent behavior of single walled carbon nanotubes (SWCNT) embedded in the elastic medium and subjected to the initial axial force is investigated using the mixed finite element method. The SWCNT is assumed to be Euler-Bernoulli beam incorporating nonlocal theory developed by Eringen. The mixed finite element model shows its great advantage of dealing with nonlocal behavior of SWCNT subjected to a concentrated load owing to the existence of two coefficients ${\alpha}_1$ and ${\alpha}_2$. This is the first numerical approach to deal with a puzzling fact of nonlocal theory with concentrated load. Numerical examples are performed to show the accuracy and efficiency of the present method. In addition, parametric study is carefully carried out to point out the influences of nonlocal effect, the elastic medium, and the initial axial force on the behavior of the carbon nanotubes.

• Structural Engineering and Mechanics
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• 제65권3호
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• pp.335-342
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• 2018

The transverse free vibration of chiral double-walled carbon nanotube (DWCNTs) embedded in elastic medium is modeled by the non-local elasticity theory and Euler Bernoulli beam model. The governing equations are derived and the solutions of frequency are obtained. According to this study, the vibrational mode number, the small-scale coefficient, the Winkler parameter and chirality of double-walled carbon nanotube on the frequency ratio (xN) of the (DWCNTs) are studied and discussed. The new features of the vibration behavior of (DWCNTs) embedded in an elastic medium and the present solutions can be used for the static and dynamic analyses of double-walled carbon nanotubes.

• 대한기계학회논문집A
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• 제31권2호
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• pp.231-236
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• 2007

This paper presents the effect of the center of the series on convergence in solving vibration problems by Differential Transformation Method(DTM) to the transverse vibration of the Euler-Bernoulli beam under varying axial force. The governing differential equation of the transverse vibration of the Euler-Bernoulli beam under varying axial force is derived. The concepts of DTM were briefly introduced. Numerical calculations are carried out and compared with previously published results. The effect of the center of the series on convergence in solving the problem by DTM is discussed.