• 한국정밀공학회지
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• 제13권2호
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• pp.176-184
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• 1996

The paper describes the vibration characteristics of the mechanical system consisting of a uniform Timoshenko beam with a guided mass and an elastic spring support. The free end of the beam does not rotate and the spring attatched to the guided mass is elastically restrained against translation. The guided mass is assumed to be a rigid body having a finite size, but not a mass point as it has been assumed so far. The effect of magnitudes, rotary inertia and the size of the guided mass on the vibration characteristics is fully investigated by the numerical simulation using FEM and experiment. In order to verify the eigenvalue sensitivity for considered system, comparison exact solutions with FEM is conducted, and a good agreement between two solutions is also highlighted.

• 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.

• Structural Engineering and Mechanics
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• 제91권2호
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• pp.197-209
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• 2024

The vibration of elastically supported bidirectional functionally graded (BDFG) sandwich beams on an elastic foundation is investigated. The sandwich structure is composed of upper and lower layers of BDFG material and the core layer of isotropic material. Material properties of upper and lower layers are assumed to vary continuously along the length and thickness of the beam with a power-law function. Hamilton's principle is used to deduce the vibration equations of motion of the sandwich Timoshenko beam. Then, the partial differential equation of motion is spatially discretized into a time-varying ordinary differential equation in terms of Chebyshev differential matrices. The eigenvalue equation associated with the free vibration is formulated to study the influence of various slenderness ratios, material gradient indexes, thickness ratios, foundation and support spring constants on the vibration frequency of BDFG sandwich beams. The present method can provide researchers with deep insight into the impact of various geometric, material, foundation and support parameters on the vibration behavior of BDFG sandwich beam structures.

• 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.

• 한국소음진동공학회:학술대회논문집
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• 한국소음진동공학회 2006년도 추계학술대회논문집
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• pp.815-818
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• 2006

This paper deals with the free, in-plane vibrations of curved members with the translational(radial and tangential directions) and rotational springs at the ends. The governing differential equations for the circular curved member are solved numerically using the corresponding boundary conditions. The lowest three natural frequencies and the corresponding mode shapes are obtained over a range of non-dimensional system parameters: the subtended angle, the slenderness ratio, the translational spring stiffness, and the rotational spring stiffness.

• 한국전산구조공학회:학술대회논문집
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• 한국전산구조공학회 2007년도 정기 학술대회 논문집
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• pp.105-110
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• 2007

The differential equations governing free, in-plane vibrations of circular curved beams with elastic springs at beth ends, including the effects of axial deformation, rotatory inertia and shear defamation. are solved numerically using the corresponding boundary conditions. The lowest three natural frequencies are calculated over a wide range of non-dimensional system parameters, the radial, tangential and rotational spring parameters, the subtended angle, the slenderness ratio and the shear parameter.

• 대한기계학회:학술대회논문집
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• 대한기계학회 2003년도 춘계학술대회
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• pp.868-873
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• 2003

This paper deals with the linear dynamic response of an elastically restrained beam under a moving mass, where the elastic support was modelled by translational springs of variable stiffness. Governing equations of motion taking into account of all inertia effects of the moving mass were derived by Galerkin's mode summation method, and Runge-Kutta integration method was applied to solve the differential equations. The effects of the speed, the magnitude of the moving mass, stiffness and the position of the support springs on the response of the beam have been studied. A variety of numerical results allows us to draw important conclusions for structural design purposes.

• 대한기계학회:학술대회논문집
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• 대한기계학회 2001년도 추계학술대회논문집A
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• pp.400-405
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• 2001

Nozzle of the double-plated grid plays the role of the spring to support a fuel rod as well as to provide the coolant path in grid. The nozzle was known to be necessary to reduce the spring stiffness for supporting performance. In this study the contact analysis between the fuel rod and the nozzle type spacer grid was performed by using ABAQUS standard to propose the preferable shape in tenn of spring performance. Two small cuts at the upper and lower part of the nozzle appeared to have a minor effect in decreasing the nozzle stiffness. A long slot at the center of the nozzle was turned out not only to decrease the spring constant as desired but also to increase the elastic displacement.

• 소음진동
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• 제4권4호
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• pp.469-478
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• 1994

This paper desfcribes the formulation for the analysis of the free vibration of a circular cylindrical shell with elastic supports by the transfer influence coefficient method. This method was developed on the base of the concept of the successive transmission of dynamic influence coefficients. The analysis algorithm for circular cylindrical shell elastically restrained by springs, which plays an important role in many industrial fields, is discussed. The supporting springs have the axial, circumferential, radial and rotational spring constants uniformly distributed along the circumference of the shell. The simple computational results on a personal computer demonstrate the validity of the present method, that is, the numerical high accuracy, the high speed analysis method and the flexibility for programming, compared with results of the transfer matrixmethod and reference. We also confirmed that the present algorithm could obtain the solutions of high accuracy for system with a number of intermediate rigid supports. And we could easily treat the intermediate support and all boundary conditions by adequately varying the values of spring constants.

• 한국방재학회 논문집
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• 제8권3호
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• pp.11-21
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• 2008

여러 가지 하중을 받는 임의의 탄성 경계 지지된 판과 쉘의 기하학적 선형 및 비선형해석을 수행하였다. 가정변형률 9절점 쉘 요소를 이용하였으며, 임의의 탄성 경계 지지를 표현하기 위해 6개의 자유도를 갖는 스프링 요소가 사용되었다. 탄성 경계지지 구조물 해석의 응용을 위하여, 여러 형태의 단부 지지를 받는 판과 쉘이 분석되었으며, 이들 단부 지지에 대한 휨 거동을 정확히 얻을 수 있었다. 6개의 스프링으로 표현된 탄성 경계 지지 조건에 대하여 적절한 결과를 얻을 수 있었다. 해석 결과로부터 본 연구의 해석 방법이 임의의 탄성 경계 조건을 갖는 판과 쉘의 거동을 해석하는데 폭넓게 사용될 수 있음을 알 수 있었다.