• 소음진동
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• 제8권2호
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• pp.297-305
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• 1998

The finite element method is used for the study of the eigenvalue problems of partially fixed end beams with intermediate elastic supports. The elastic critical loads and natural frquencies of the beams are investigated by changing the numbers of elastic supports and their stiffness, and also by changing Kinney's fixity factor, $f_a$. The relationship between two eigenvalues is established by calculating the corresponding values of $(w/w_n)^2$ through changing $(P/P_{cr})$ values. The results of this study are as follows : (1) The elastic critical loads and natural frequencies of beams increase with increases in Kinney's fixity factor, $f_a$ and with the increased numbers of intermediate elastic supports. (2) The relationship between elastic critical loads and the natural frequencies of partially fixed end beams with intermediated elastic supports is $P/P_{cr} + (w/w_n)^2/ = 1$ without regard to Kinney's fixity factor, the stiffness of elastic supports, or the number of elastic supports.

• 한국철도학회:학술대회논문집
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• 한국철도학회 2002년도 추계학술대회 논문집(I)
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• pp.125-130
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• 2002

This paper investigates the dynamic characteristics of a beam axially moving over multiple elastic supports. The spectral element matrix is derived first for the axially moving beam element and then it is used to formulate the spectral element matrix for the moving beam element with an interim elastic support. The moving speed dependance of the eigenvalues is numerically investigated by varying the applied axial tension and the stiffness of the elastic supports. Numerical results show that the fundamental eigenvalue vanishes first at the critical moving speed to generate the static instability.

• Journal of Mechanical Science and Technology
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• 제18권5호
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• pp.733-741
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• 2004

Vibration behavior of an initially stressed beam on discretely spaced multiple elastic supports has been studied and a theoretical formulation of the system is derived using the variational principle. Unlike beams on an elastic foundation, discretely spaced supports can distort the beam mode shapes when the supports have rather large stiffness, i.e. usually expected beam modes cannot be obtained, but rather irregular mode shapes are observed. Conversely, irregular modes can be recovered by changing initial stress. Since support location is closely associated with the dynamic characteristics, this work also discusses eigenvalue sensitivity with respect to the support position and some numerical examples are investigated to illustrate the above findings.

• Structural Engineering and Mechanics
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• 제52권5호
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• pp.997-1017
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• 2014

According to the structure characteristics of the non-uniform beam bridge, a practical model for calculating the vibration equation of the non-uniform beam bridge is given and the application scope of the model includes not only the beam bridge structure but also the non-uniform beam with added masses and elastic supports. Based on the Bernoulli-Euler beam theory, extending the application of the modal perturbation method and establishment of a semi-analytical method for solving the vibration equation of the non-uniform beam with added masses and elastic supports based is able to be made. In the modal subspace of the uniform beam with the elastic supports, the variable coefficient differential equation that describes the dynamic behavior of the non-uniform beam is converted to nonlinear algebraic equations. Extending the application of the modal perturbation method is suitable for solving the vibration equation of the simply supported and continuous non-uniform beam with its arbitrary added masses and elastic supports. The examples, that are analyzed, demonstrate the high precision and fast convergence speed of the method. Further study of the timesaving method for the dynamic characteristics of symmetrical beam and the symmetry of mode shape should be developed. Eventually, the effects of elastic supports and added masses on dynamic characteristics of the three-span non-uniform beam bridge are reported.

• 한국소음진동공학회:학술대회논문집
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• 한국소음진동공학회 2001년도 추계학술대회논문집 II
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• pp.1202-1206
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• 2001

The paper presents the dynamic stability of a vertical cantilevered pipe conveying fluid and having translational linear spring supports. Real pipe systems may have some elastic hanger supports or other mechanical attached parts., which can be regarded as attached spring supports. Governing equations are derived by energy expressions, and numerical technique using Galerkin's method is applied to discretize the equations of small motion of the pipe. Effects of spring supports on the dynamic stability of a vertical cantilevered pipe conveying fluid are fully investigated for various locations and spring constants of elastic supports.

• 한국강구조학회 논문집
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• 제11권2호통권39호
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• pp.201-212
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• 1999

탄성 경계에 의해 지지된 보는 브레이스된 보나 철도 궤도와 같은 구조 부재로서 사용된다. 이러한 탄성 경계는 단면의 임의의 점에 위치할 수 있다. 본 논문은 탄성 경계를 가진 보의 탄성 좌굴에 미치는 경계의 편심과 강성의 효과를 고찰하였다. 유한 요소 정식화를 통해 탄성 경계를 가진 보-요소와 해석 프로그램을 개발하였다. 탄성 경계는 탄성 스프링 요소를 사용하였으며 탄성 경계의 편심을 고려하기 위하여 옵셋(offset) 기법을 사용하였다. 보-요소는 딤 자유도를 고려하여, 요소당 14개의 자유도를 갖는 직선 보-요소를 사용하였다. 많은 수치 해석을 통해, 본 연구에서 개발한 좌굴 해석 프로그램이 탄성 경계를 가진 보의 탄성 좌굴 하중과 모드를 정확하게 산출함을 알 수 있다.

• Structural Engineering and Mechanics
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• 제52권5호
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• pp.1033-1049
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• 2014

The free vibration of functionally graded material (FGM) beams on an elastic foundation and spring supports is investigated. Young's modulus, mass density and width of the beam are assumed to vary in thickness and axial directions respectively following the exponential law. The spring supports are also taken into account at both ends of the beam. An analytical formulation is suggested to obtain eigen solutions of the FGM beams. Numerical analyses, based on finite element method by using a beam finite element developed in this study, are performed in order to show the legitimacy of the analytical solutions. Some results for the natural frequencies of the FGM beams are given considering the effect of various structural parameters. It is also shown that the spring supports show the greatest effect on the natural frequencies of FGM beams.

• Steel and Composite Structures
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• 제33권3호
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• pp.403-432
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• 2019

Axially functionally graded (AFG) beams are a new class of composite structures that have continuous variations in material and/or geometrical parameters along the axial direction. In this study, the exact analytical solutions for the free vibration of AFG and uniform beams with general elastic supports are obtained by using Euler-Bernoulli beam theory. The elastic supports are modeled with linear rotational and lateral translational springs. Moreover, the material and/or geometrical properties of the AFG beams are assumed to vary continuously and together along the length of the beam according to the power-law forms. Accordingly, the accuracy, efficiency and capability of the proposed formulations are demonstrated by comparing the responses of the numerical examples with the available solutions. In the following, the effects of the elastic end restraints and AFG parameters, namely, gradient index and gradient coefficient, on the values of the first three natural frequencies of the AFG and uniform beams are investigated comprehensively. The analytical solutions are presented in tabular and graphical forms and can be used as the benchmark solutions. Furthermore, the results presented herein can be utilized for design of inhomogeneous beams with various supporting conditions.

• 한국철도학회논문집
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• 제6권2호
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• pp.129-134
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• 2003

This paper investigates the dynamic characteristics of a beam axially moving over multiple elastic supports. The spectral element matrix is derived first for the axially moving beam element and then it is used to formulate the spectral element matrix for the moving beam element with an interim elastic support. The moving speed dependance of the eigenvalues is numerically investigated by varying the applied axial tension and the stiffness of the elastic supports. Numerical results show that the fundamental eigenvalue vanishes first at the critical moving speed to generate the static instability.

• 한국강구조학회 논문집
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• 제24권5호
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• pp.595-603
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• 2012

본 연구에서는 재하시험에 의하여 얻어지는 측정데이터를 적극적으로 활용하고 다양한 방법을 통하여 내하력을 평가하기 위하여 탄성지점을 적용하였다. 스프링력에 의한 구조해석의 적정성을 확인하고 실험결과의 신뢰도를 향상시키기 위하여 내민보로 제작한 탄성빔을 대상으로 처짐시험을 실시하였으며 이를 토대로 공용중인 교량의 내하력 평가 방법의 개선을 위하여 실제 공용중인 교량에 대한 정밀안전진단을 통한 검증을 실시하였다. 휨시험 결과 기존방법에 의하여 계산된 처짐보다 탄성지점을 적용하여 구한 처짐이 실측한 처짐과 근접한 것으로 나타났다. 준공 직후 초기점검 대상인 3경간 연속 강박스형교에 대한 내하력을 평가한 결과 탄성지점에 의한 내하력이 기존의 방법에 의한 내하력보다 최대 9.7% 작게 평가되었다. 본 연구는 기존 방법에 따라 교량의 내하력을 평가할 경우 응력보정계수의 적용과 같이 지침에 명확하게 제시되지 않은 부분으로 인하여 공학자에 따라 내하력이 상이하게 평가되는 경우가 빈번하므로 이에 대한 연구가 더욱 활발해 져야 한다는 취지에서 수행하였다.