• 한국강구조학회 논문집
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• 제16권1호통권68호
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• pp.81-89
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• 2004

구조물과 같은 아치의 진동해석은 많은 산업분야에서 다양하게 적용되기 때문에 공학적 문제에 중요한 주제이다. 특히 변화하는 단면형상을 가지는 아치는 질량이나 강도를 최적화 하거나 특별한 구조물이나 요구조건들을 만족하기 위해서 폭넓게 사용되어 진다. 최근에는 일반화 미분구적법(GDQM)이나 미분변환법(DTM)은 각각 Shu와 Zou에 의해서 제안이 되었다. 연구에서는 변화하는 단면형상을 가지는 아치의 진동해석이 일반화 미분구적법과 미분변환법을 적용하였다. 변화하는 단면형상을 가지는 아치에 대하여 지배방정식이 유도되어졌으며, 미분변환과 일반화 미분구적법의 개념이 간단히 소개되었다. 변화하는 단면형상을 가지는 아치의 무차원화된 고유진동수가 다양한 경계조건에 대해서 구해졌으며, 이러한 방법들에 의해서 얻어지는 결과들은 선행연구와 비교 되어졌다. 일반화 미분구적법과 미분변환법은 변화하는 단면형상을 가지는 아치의 진동문제를 해석함에 있어서 빠른 수렴, 정확도, 효율성, 유효성을 보인다.

• Structural Engineering and Mechanics
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• 제68권6호
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• pp.713-720
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• 2018

In this paper a new numerical method to determine the elastic curve of the simply supported beams of variable cross-section is demonstrated. In general case it needs to solve linear or small nonlinear second order differential equations with prescribed boundary conditions. For numerical solution the initial values of the slope and the deflection of the end cross-section of the beam is necessary. For obtaining the initial values a lively procedure is developed: it is a special application of the shooting method because boundary value problems can be transformed into initial value problems. As a result of these transformations the initial values of the differential equations are obtained with high accuracy. Procedure is applied for calculating of elastic curve of a simply supported beam of variable cross-section. Results of these numerical procedures, analytical solution of the linearized version and finite element method are compared. It is proved that the suggested procedure yields technically accurate results.

• Structural Engineering and Mechanics
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• 제75권6호
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• pp.737-746
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• 2020

This paper attempts to investigate the free vibration of functionally graded material beams with nonuniform width based on the nonlocal elasticity theory. The theoretical formulations are established following the Euler-Bernoulli beam theory, and the governing equations of motion of the system are derived from the minimum total potential energy principle using the nonlocal elasticity theory. In addition, the Differential Quadrature Method (DQM) is applied, along with the Chebyshev-Gauss-Lobatto polynomials, in order to determine the weighting coefficient matrices. Furthermore, the effects of the nonlocal parameter, cross-section area of the functionally graded material (FGM) beam and various boundary conditions on the natural frequencies are examined. It is observed that the nonlocal parameter and boundary conditions significantly influence the natural frequencies of the functionally graded material beam cross-section. The results obtained, using the Differential Quadrature Method (DQM) under various boundary conditions, are found in good agreement with analytical and numerical results available in the literature.

• 소음진동
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• 제9권6호
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• pp.1193-1199
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• 1999

This paper deals with the free vibrations of circular curved beams with thin-walled cross-section. The differential equation for the coupled flexural-torsional vibrations of such beams with warping is solved numerically to obtain natural frequencies and mode shapes. The Runge-Kutta and determinant search methods, respectively, are used to solve the governing differential equation and to compute the eigenvalues. The lowest three natural frequencies and corresponding mode shapes are calculated for the thin-walled horizontally curved beams with hinged-hinged, hinged-clamped, and clamped-clamped end constraints. A wide range of opening angle of beam, warping parameter, and two different values of slenderness ratios are considered. Numerical results are compared with existing exact and numerical solutions by other methods.

• 한국소음진동공학회:학술대회논문집
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• 한국소음진동공학회 2003년도 춘계학술대회논문집
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• pp.858-863
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• 2003

In the practical engineering fields, the horizontally curved beams are frequently erected as the major/minor structural components. The effects of both variable curvature and variable cross-section on structural behavior are very important and therefore these effects should be included in structural analyses. From this viewpoint, this paper deals with the free vibrations of horizontally curved beams with variable curvature and variable cross-section. In this study, the parabola as the curvilinear shape and stepped beam as the variable cross-section are considered. The ordinary differential equation governing free vibrations of such beams are derived. For calculating the natural frequencies, the governing equations are solved by numerical methods. The Runge-Kutta and Determinant search Methods are used for integrating the differential equations and for calculating the natural frequencies, respectively. With regard to numerical results, the relationships between frequency parameters and various beam parameters are presented in the forms of Table and Figures.

• Structural Engineering and Mechanics
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• 제2권4호
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• pp.345-357
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• 1994

The differential equations governing free, in-plane vibrations of linearly elastic circular arches with variable cross-sections are derived and solve numerically for quadratic arches with three types of rectangular cross sections. Frequencies, mode shapes, cross-sectional load distributions, and the effects of rotatory inertia on frequencies are reported. Experimental measurements of frequencies and their corresponding mode shapes agree closely with those predicted by theory. The numerical methods presented here for computing frequencies and mode shapes are efficient and reliable.

• 대한토목학회논문집
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• 제29권1A호
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• pp.53-60
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• 2009

이 논문은 양단회전 후좌굴 변단면 기둥의 기하 비선형 해석에 관한 연구이다. 기둥의 변단면은 변화폭, 변화깊이, 정방형 변단면으로 채택하였다. Bernoulli-Euler 보 이론을 이용하여 후좌굴 기둥의 정확탄성곡선을 지배하는 미분방정식을 유도하였다. 이 미분방정식은 두 개의 미지수를 가지며 이러한 미분방정식을 풀 수 있는 수치해석 방법을 개발하였다. 후좌굴 기둥의 수치해석 결과로 평형경로, 정확탄성곡선 및 합응력을 산정하였다. 실험을 통하여 후좌굴 거동의 이론을 검증하였다.

• 한국전기전자재료학회:학술대회논문집
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• 한국전기전자재료학회 2002년도 춘계학술대회 논문집 유기절연재료 전자세라믹 방전플라즈마 일렉트렛트 및 응용기술
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• pp.11-14
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• 2002

Accurate sets of electron collision cross sections for atoms and molecules are necessary for quantitative understanding and modeling of plasma phenomena. So, in this study, we explains the concept of electron collision cross sections for gases, and the principle of determination of the electron collision cross sections for atoms and molecules by using the present electron swarm method.

• Steel and Composite Structures
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• 제11권6호
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• pp.489-504
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• 2011

This paper presents a theoretical investigation in free vibration of sigmoid functionally graded beams with variable cross-section by using Bernoulli-Euler beam theory. The mechanical properties are assumed to vary continuously through the thickness of the beam, and obey a two power law of the volume fraction of the constituents. Governing equation is reduced to an ordinary differential equation in spatial coordinate for a family of cross-section geometries with exponentially varying width. Analytical solutions of the vibration of the S-FGM beam are obtained for three different types of boundary conditions associated with simply supported, clamped and free ends. Results show that, all other parameters remaining the same, the natural frequencies of S-FGM beams are always proportional to those of homogeneous isotropic beams. Therefore, one can predict the behaviour of S-FGM beams knowing that of similar homogeneous beams.

• 한국소음진동공학회:학술대회논문집
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• 한국소음진동공학회 2002년도 춘계학술대회논문집
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• pp.417-422
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• 2002

The main purpose of this paper is to determine the dynamic optimal shapes of tapered column with constant volume. The linear, parabolic and sinusoidal tapers with the regular polygon cross-section are considered, whose material volume and span length are always held constant. The ordinary differential equation including the effect of axial load is applied to calculate the natural frequencies. The Runge-Kutta method and Regula-Falsi methods are used to integrate the differential equation and compute the frequencies, respectively. Then the dynamic optimal shape whose lowest natural frequency is highest is determined by reading the critical value of the frequency versus section ratio curve plotted by the frequency data. In the numerical examples, the tapered columns are analysed and the numerical result of this study are shown in table and figures.