• 한국소음진동공학회:학술대회논문집
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• 한국소음진동공학회 2008년도 추계학술대회논문집
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• pp.348-353
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• 2008

A vibration analysis for a rotating cantilever beam with the tapered cross section is presented in this study. The stiffness changes due to the stretching caused by centrifugal inertia forces when a tapered cantilever beam rotates about the axis perpendicular to its longitudinal axis. When the cross section of cantilever beam are assumed to decrease constantly, the mass and stiffness also change according to the variation of the thickness and width ratio of a tapered cantilever beam. Such phenomena result in variations of natural frequencies and mode shapes. Therefore it is important to the equations of motion in order to be obtained accurate predictions of these variations. The equations of motion of a rotating tapered cantilever beam are derived by using hybrid deformation variable modeling method and numerical results are obtained along with the angular velocity and the thickness and width ratio.

• 한국소음진동공학회논문집
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• 제19권4호
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• pp.363-369
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• 2009

A vibration analysis for a rotating cantilever beam with the tapered cross section is presented in this study. The stiffness changes due to the stretching caused by centrifugal inertia forces when a tapered cantilever beam rotates about the axis perpendicular to its longitudinal axis. When the cross section of cantilever beam are assumed to decrease constantly, the mass and stiffness also change according to the variation of the thickness and width ratio of a tapered cantilever beam. Such phenomena result in variations of natural frequencies and mode shapes. Therefore it is important to the equations of motion in order to be obtained accurate predictions of these variations. The equations of motion of a rotating tapered cantilever beam are derived by using hybrid deformation variable modeling method and numerical results are obtained along with the angular velocity and the thickness and width ratio.

• 한국전산구조공학회논문집
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• 제27권5호
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• pp.361-368
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• 2014

본 연구에서는 테이퍼 보에 대한 미분방정식의 일반해에 캔틸레버 보의 경계조건을 적용하여 모드특성을 추정한다. 또한, 휨을 받는 테이퍼 원형강관 캔틸레버 보에 발생하는 관통균열을 모델링하기 위하여 에너지 방법을 이용하여 균열보에 대한 보 길이방향 휨강성을 구한 후 이를 이용하여 테이퍼 원형강관 캔틸레버 균열보에 대한 고유주파수와 모드형상을 추정한다. 보 길이에 따른 균열보의 휨강성 변화는 기존 연구에서 밝혀진 현상과 유사하게 합리적인 양상을 보였으며, 유도한 휨강성을 적용하여 산정한 균열보의 고유주파수는 균열 크기가 증가할수록 감소함을 확인하였고, 모드형상은 균열발생에 의해 변화함을 알 수 있었다. 연구결과는 향후 테이퍼 원형강관 캔틸레버 보 형태의 타워 구조물에 대한 진동기반 균열탐지에 활용될 수 있을 것으로 판단된다.

• Structural Engineering and Mechanics
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• 제59권1호
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• pp.1-14
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• 2016

In this paper, an alternative analytical method is presented to evaluate the nonlinear vibration behavior of single and double tapered cantilever beams. The admissible lateral displacement function satisfying the geometric boundary conditions of a single or double tapered cantilever beam is derived by using Rayleigh-Ritz method. Based on the Lagrange method and the Newton Harmonic Balance (NHB) method, analytical approximate solutions in closed and explicit form are obtained. These approximate solutions show excellent agreement with those of numeric method for small as well as large amplitude. Moreover, due to brevity of expressions, the present analytical approximate solutions are convenient to investigate effects of various parameters on the large amplitude vibration response of tapered beams.

• 한국소음진동공학회:학술대회논문집
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• 한국소음진동공학회 2002년도 추계학술대회논문초록집
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• pp.394.1-394
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• 2002

The purpose of this paper is to investigate the natural frequencies and mode shapes of tapered beams with general boundary condition(translational and rotational elastic support) at one end and carrying a tip mass of rotatory inertia 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. (omitted)

• Structural Engineering and Mechanics
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• 제61권5호
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• pp.685-691
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• 2017

The free transverse vibrations of axially functionally graded (AFG) cantilever beams with concentrated masses attached at different points are studied in this paper. The material properties of the AFG beam, consisting of metal and ceramic, vary continuously in the axial direction according to an established law form. Approximated solutions for the title problem are obtained by means of the Ritz Method. The influence of the material variation on the natural frequencies of vibration of the functionally graded beam is investigated and compared with the influence of the variation of the cross section. The phenomenon of dynamic stiffening of beams can be observed in various situations. The accuracy of the procedure is verified through results available in the literature that can be represented by the model under study.

• 대한기계학회:학술대회논문집
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• 대한기계학회 2008년도 추계학술대회A
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• pp.832-837
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• 2008

A modeling method for the modal analysis of a multi-packet blade system having tapered cross section undergoing rotational motion is presented in this paper. Blades are idealized as tapered cantilever beams that are fixed to a rotating disc. The stiffness coupling effects between blades due to the flexibilities of the disc and the shroud are modeled with discrete springs. Hybrid deformation variables are employed to derive the equations of motion. To obtain more general information, the equations of motion are transformed into dimensionless forms in which dimensionless parameters are identified. The effects of the dimensionless parameters including tapered ratio and the number of packets as well as blades on the modal characteristics of the system are investigated with some numerical examples.

• Structural Engineering and Mechanics
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• 제5권3호
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• pp.269-281
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• 1997

The overall buckling mode in a composite steel-concrete beam over an internal support is necessarily lateral-distortional, in which the bottom compressive range displaces laterally and twists, since the top flange is restrained by the nearly rigid concrete slab. An efficient finite element method is used to study elastic lateral-distortional buckling in composite beams whose steel portion is tapered. The simplified model for a continuous beam that is presented herein is a fixed ended cantilever whose steel portion is tapered, and is subjected to moment gradient. This is intended to give an insight into distortion in a continuous beam that occurs in the negative bending region, and the differences between the cantilever representation and the continuous beam are highlighted. An eigenproblem is established, and the buckling modes and loads are determined in the elastic range of structural response. It is found from the finite element study that the buckling moment may be enhanced significantly by using a vertical stiffener in the region where the lateral movement of the bottom range is greatest. This enhancement is quantified in the paper.

• 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.

• 대한기계학회논문집A
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• 제23권6호
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• pp.1026-1038
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• 1999

Interlaminar fracture toughness of carbon/epoxy composite materials has been studied under tensile and flexural loading by the use of width tapered double cantilever beam(WTDCB) and end notched flexure(ENF) specimens. This study has significantly examined the effect of various interfacial ply orientation, ${\alpha}(0^{\circ},\;45^{\circ}\;and\;90^{\circ})$ and crack propagation direction, ${\theta}(0^{\circ},\;15^{\circ},\;30^{\circ}\;and\;45^{\circ})$ in terms of critical strain energy release rate through experiments. Twelve differently layered laminates were investigated. The data reduction for evaluating the fracture energy is based on compliance method and beam theory. Beam theory is used to analyze the effect of crack propagation direction. The geometry and lay-up sequence of specimens are considered various conditions such as skewness parameter, beam volume, and so on. The results show that the fiber bridging occurred due to the non-midplane crack propagation and causes the difference of fracture energy evaluated by both methods. For safer and more reliable composite structures, we obtain the optimal stacking sequence from initial fracture energy in each mode.