• 한국소음진동공학회:학술대회논문집
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• 한국소음진동공학회 2002년도 추계학술대회논문집
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• pp.965-970
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• 2002

The purpose of this paper is to investigate the free vibration characteristics of tapered beams with general boundary condition(translational and rotational elastic support) at one end and carrying a tip mass with translational elastic support at the other end. The beam model is based on the classical Bernoulli-Euler beam theory which neglects the effects of rotatory inertia and shear deformation. The governing differential equation for the free vibrations of linearly tapered beams is solved numerically using the corresponding boundary conditions. Numerical results are compared with existing solutions by other methods for cases in which they are available. The lowest four natural frequencies are calculated over a wide range of section ratio, dimensionless spring constant and mass ratio.

• Structural Engineering and Mechanics
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• 제40권4호
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• pp.583-594
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• 2011

In the present study, free vibration of an axially functionally graded (AFG) pile embedded in Winkler-Pasternak elastic foundation is analyzed within the framework of the Euler-Bernoulli beam theory. The material properties of the pile vary continuously in the axial direction according to the power-law form. The frequency equation is obtained by using Lagrange's equations. The unknown functions denoting the transverse deflections of the AFG pile is expressed in modal form. In this study, the effects of material variations, the parameters of the elastic foundation on the fundamental frequencies are examined. It is believed that the tabulated results will be a reference with which other researchers can compare their results.

• Smart Structures and Systems
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• 제25권4호
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• pp.501-514
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• 2020

This article presents a comprehensive model to investigate a free vibration and resonance frequencies of nanostructure perforated beam element as nano-resonator. Nano-scale size dependency of regular square perforated beam is considered by using nonlocal differential form of Eringen constitutive equation. Equivalent mass, inertia, bending and shear rigidities of perforated beam structure are developed. Kinematic displacement assumptions of both Timoshenko and Euler-Bernoulli are assumed to consider thick and thin beams, respectively. So, this model considers the effect of shear on natural frequencies of perforated nanobeams. Equations of motion for local and nonlocal elastic beam are derived. After that, analytical solutions of frequency equations are deduced as function of nonlocal and perforation parameters. The proposed model is validated and verified with previous works. Parametric studies are performed to illustrate the influence of a long-range atomic interaction, hole perforation size, number of rows of holes and boundary conditions on fundamental frequencies of perforated nanobeams. The proposed model is supportive in designing and production of nanobeam resonator used in nanoelectromechanical systems NEMS.

• 한국추진공학회:학술대회논문집
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• 한국추진공학회 2006년도 제26회 춘계학술대회논문집
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• pp.371-375
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• 2006

Ballistic Range로부터 발사되는 발사체의 공기역학적 특성을 조사하기 위하여 축대칭 비정상 압축성 오일러 방정식에 이동경계법을 적용하여, 수치계산을 수행하였다. 그 결과, 발사체의 형상과 질량을 변화시켜 발사체의 순간속도, 가속도, 공기저항력을 조사한 결과, 발사 직후 발사체의 거동과 주위 유동장의 특성을 예측할 수 있었다.

• 한국농공학회지
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• 제42권1호
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• pp.105-112
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• 2000

This paper deals with the free vibrations of columns immersed in fluid. The column model is based on the classical Bernoulli-euler theory which neblects the effects of rotatory inerital and shear deformation. The eccentricity and rotatory inertial of the concentrated mass at the top are taken into accuont. In the governing equation for the free vibration of column, thedensity of immersed part was midified to account for theadded fluid mass. The govering differential equations are solved numerically using the corresponding boundary conditions. The lowest four natural frequencies and corresponding mode shapes are calculated over a range of non-dimensional system parameters ; the mas density ration of fluid to column, the ratio of fluid depth to span length, the ratio of tip mass to total column mass, the dimensionless mass moment of inertia, and the eccentricity.

• 대한수학회보
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• 제32권2호
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• pp.303-308
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• 1995

We consider a torus T, that is, a compact surface with genus 1 and $\Omega = D^2 \times S^1$ topologically with $\partial\Omega = T$, where $D^2$ is the open unit disk and $S^1$ is the unit circle. Let $\omega = (x,y)$ denote the generic point on T. For a smooth immersion $u : T \to R^3$, we define the Dirichlet functional by $$ E(u) = \frac{2}{1} \int_{T} $\mid$\nabla u$\mid$^2 d\omega $$ and the volume functional by $$ V(u) = \frac{3}{1} \int_{T} u \cdot u_x \Lambda u_y d\omege $$.

• 대한수학회보
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• 제32권2호
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• pp.211-214
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• 1995

Let M and N be compact Riemannian manifolds and $f : M \to N$ be a smooth map. Following J. Eells, f is exponentially harmonic if it represents a critical point of the exponential energy integral $$ E(f) = \int_{M} exp(\left\$\mid$ df \right\$\mid$^2) dM $$ where $(\left\ df $\mid$\right\$\mid$^2$ is the energy density defined as $\sum_{i=1}^{m} \left\$\mid$ df(e_i) \right\$\mid$^2$, m = dimM, for orthonormal frame $e_i$ of M. The Euler- Lagrange equation of the exponential energy functional E can be written $$ exp(\left\$\mid$ df \right\$\mid$^2)(\tau(f) + df(\nabla\left\$\mid$ df \right\$\mid$^2)) = 0 $$ where $\tau(f)$ is the tension field along f. Hence, if the energy density is constant, every harmonic map is exponentially harmonic and vice versa.

• 대한수학회보
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• 제51권3호
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• pp.717-737
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• 2014

We study the effect of numerical quadrature in space on semidiscrete and fully discrete piecewise linear finite element methods for parabolic interface problems. Optimal $L^2(L^2)$ and $L^2(H^1)$ error estimates are shown to hold for semidiscrete problem under suitable regularity of the true solution in whole domain. Further, fully discrete scheme based on backward Euler method has also analyzed and optimal $L^2(L^2)$ norm error estimate is established. The error estimates are obtained for fitted finite element discretization based on straight interface triangles.

• 한국철도학회논문집
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• 제3권4호
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• pp.229-236
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• 2000

In this study, the unsteady flow field induced by a high-speed train passing through a tunnel is numerically simulated by using an axi-symmetric Euler Equation. The modified patched grid scheme applied to a structured grid system was used to handle the relative motion of a train. The hybrid-dimensional approach which mixed 1D and axi-symmetric dimension was used to reduce the computation time and memory storage. By employing the hybrid-dimensional approach, a long tunnel as much as 5 km was able to be simulated efficiently. The results show that the maximum pressure rise in the tunnel by the entrance of the train is a function of both train speed and train-tunnel cross-sectional area ratio. The unsteady pressure fluctuation in the tunnel and around the train was also investigated in the real condition; Korean high-speed train on the Seoul-Pusan line.

• Interaction and multiscale mechanics
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• 제5권4호
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• pp.385-397
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• 2012

In this paper the dynamic stiffness matrix method was used for the free vibration analysis of axially moving micro beam with constant velocity. The extended Hamilton's principle was employed to derive the governing differential equation of the problem using the modified couple stress theory. The dynamic stiffness matrix of the moving micro beam was evaluated using appropriate expressions of the shear force and bending moment according to the Euler-Bernoulli beam theory. The effects of the beam size and axial velocity on the dynamic characteristic of the moving beam were investigated. The natural frequencies and critical velocity of the axially moving micro beam were also computed for two different end conditions.