• 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.

• Structural Engineering and Mechanics
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• 제10권5호
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• pp.479-489
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• 2000

Based on the stiffness equation of the tapered beam element involving the effects of axial force and shear deformation, numerical investigations are carried out on elastic instability for web-linearly tapered columns with I-section of steel portal frames. Effects of shear deformation on the effective length of the tapered columns with I-section are studied. An efficient approach for determining the effective length of the tapered portal frame columns considering effects of shear deformation is proposed.

• 한국소음진동공학회논문집
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• 제20권1호
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• pp.10-21
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• 2010

Equations of chordwise and flapwise bending motions for the vibration analysis of rotating pre-twisted blades having tapered cross section and setting angle are derived by using hybrid deformation variable modeling. The two motions are couples to each other due to the pre-twisted angle of the beam cross section. The derived equations are transformed into dimensionless forms in which dimensionless parameters are identified. The effects of the dimensionless parameters on the modal characteristics of rotating pre-twisted blades having tapered cross section and orientation angle are investigated. The eigenvalue loci veering phenomena are also investigated and discussed in this work.

• 한국소음진동공학회:학술대회논문집
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• 한국소음진동공학회 2009년도 춘계학술대회 논문집
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• pp.288-295
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• 2009

Equations of chordwise and flapwise bending motions for the vibration analysis of rotating pre-twisted blades having tapered cross section and orientation angle are derived by using hybrid deformation variable modeling. The two motions are couples to each other due to the pre-twisted angle of the beam cross section. The derived equations are transformed into dimensionless forms in which dimensionless parameters are identified. The effects of the dimensionless parameters on the modal characteristics of rotating pre-twisted blades having tapered cross section and orientation angle are investigated. The eigenvalue loci veering phenomena is also investigated and discussed in this work.

• 한국소음진동공학회:학술대회논문집
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• 한국소음진동공학회 2006년도 춘계학술대회논문집
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• pp.1338-1342
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• 2006

This paper presents the theoretical approach to describe the wave propagation in the waveguide with varying cross-section. The waveguides considered in this paper are stepped-rod, tapered-rod, and stepped rod with a tapered section at the middle of wave-transmission. The wave transmission ratio for displacement, stress, and power was calculated for these three rods. The distribution of the stress and displacement along the stepped rod with a tapered section was calculated and compared with the results obtained by FEM analysis.

• 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.

• Steel and Composite Structures
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• 제28권4호
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• pp.403-414
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• 2018

In this paper, the lateral-torsional buckling of axially-transversally functionally graded tapered beam is investigated. The structure cross-section is assumed to be symmetric I-section, and it is continuously laterally supported by torsional springs through the length. In addition, the height of cross-section varies linearly throughout the length of structure. The proposed formulation is obtained for the case that the elastic and shear modulus change as a power function along the beam length and section height. This structure carries two concentrated moments at the ends. In this study, the lateral displacement and twisting angle relation of the beam are defined by sinusoidal series. After establishing the eigenvalue equation of unknown constants, the beam critical bending moment is found. To validate the accuracy and correctness of results, several numerical examples are solved.

• 소음진동
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• 제6권5호
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• pp.587-594
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• 1996

이 논문에서는 일정체적의 정다각형 단면을 갖는 보-기둥의 자유진동 및 좌굴하중을 지배하는 비분방정식을 유도하고 이를 수치해석하였다. 정다각형 단면의 단면깊이 변화식으로는 포물선식과 정현식을 채택하였고, 고정-고정, 회전-고정 및 회전-회전의 단부조건에 대하여 고유진동수 및 좌굴하중을 산출하였다. 수치해석의 결과로 무차원 고유진동수와 무차원변들 사이의 관계 및 무차원 좌굴하중과 단면비 사이의 관계를 그림에 나타내었다. 또한, 최강기둥의 단면비와 좌국하중을 산출 하였다.

• Structural Engineering and Mechanics
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• 제66권1호
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• pp.125-138
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• 2018

This paper proposes a transfer matrix method for the bending vibration of two types of tapered beams subjected to axial force, and it is applied to analyze tapered beams with an edge or multiple edge open cracks. One beam type is assumed to be reduced linearly in the cross-section height along the beam length. The other type is a tapered beam in which the cross-section height and width with the same taper ratio is linearly reduced simultaneously. Each crack is modeled as two sub-elements connected by a rotational spring, and the method can evaluate the effect of cracking on the desired number of eigenfrequencies using a minimum number of subdivisions. Among the power series available for the solutions, the roots of the differential equation are computed using the Frobenius method. The computed results confirm the accuracy of the method and are compared with previously reported results. The effectiveness of the proposed methods is demonstrated by examining specific examples, and the effects of cracking and axial loading are carefully examined by a comparison of the single and double tapered beam results.