• Title/Summary/Keyword: 면외 고유진동

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Semi-analytical Annular Mindlin Plate Element for Out-of-plane Vibration Analysis of Thick Disks (두꺼운 디스크의 면외 진동 해석을 위한 준-해석적 환상 민드린 평판 요소)

  • Kim, Chang-Boo;Cho, Hyeon Seok;Beom, Hyeon Gyu
    • Journal of the Korean Society for Railway
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    • v.15 no.6
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    • pp.588-596
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    • 2012
  • This paper presents a new semi-analytical annular Mindlin plate element with which out-of-plane natural vibration of thick disks can be analyzed simply, efficiently, and accurately through FEM by including effects of rotary inertia and transverse shear deformation. Using static deformation modes which are exact solutions of equilibrium equations of annular Mindlin plate, the element interpolation functions, stiffness and mass matrices corresponding to each number of nodal diameters are derived. The element is capable of representing out-of-plane rigid-body motions exactly and free from shear locking. Natural frequencies of uniform and multi-step disks with or without concentric ring support are analyzed by applying the presented element. Such results are compared with theoretical predictions of previous works or FEA results obtained by using two-dimensional shell element to investigate the convergence and accuracy of the presented element.

Out of Plane Free Vibrations of Circular Curved Beams (원호형 곡선보의 면외 자유진동에 관한 수치해석적 연구)

  • 이병구;오상진
    • Computational Structural Engineering
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    • v.9 no.1
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    • pp.133-139
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    • 1996
  • In this paper, an approximate method is developed to obtain the natural frequencies of the out of plane vibration of circular curved beams. The governing differential equations are derived using the dynamic equilibrium equations with the Timoshenko theory, and solved numerically. The Runge-Kutta method and Regula-Falsi method are used to integrate the differential equations and to determine the natural frequencies, respectively. In numerical examples, the hinged-hinged and clamped-clamped end constraints are considered. For each case, the four lowest natural frequencies are reported as functions of four non-dimensional system parameters.

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Free Vibration Analysis of horizontally Curved Beams considering Warping and Rotatory Inertia (?과 회전관성을 고려한 수평 곡선보의 자유진동 해석)

  • 이병구;박광규;오상진;진태기
    • Journal of the Computational Structural Engineering Institute of Korea
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    • v.14 no.1
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    • pp.35-42
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    • 2001
  • 본 연구는 변화곡률 수평 곡선보의 면외 자유진동에 관한 연구이다. 뒴과 회전관성을 고려한 변화곡률 수평 곡선보의 자유진동을 지배하는 상미분방정식이 유도되었고, 이 지배미분방정식을 수치해석하여 곡선보의 고유진동수를 산출하였다. 지배미분방정식을 수치적분하기 위하여 Runge-Kutta method를 이용하였고, 고유진동수를 산출하기 위하여 Regula-Falsi method와 결합한 행렬값 탐사법을 이용하였다. 본 연구의 이론적 타당성을 검증하기 위하여 타문헌의 고유진동수와 비교하였고, 실험실 규모의 모형실험을 실시하여 이론값과 실험값의 고유진동수를 비교하였다. 수치해석의 결과로 무차원 재변수들의 변화에 따른 무차원 고유진동수를 제 3모드까지 산출하였고, 그 결과들을 고찰하였다. 본 연구의 결과는 곡선형 교량 등과 같이 곡선부재로 이루어진 구조물의 설계시에 유용하게 이용될 수 있을 것으로 기대된다.

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Flapwise Bending Vibration Analysis of Rotating Cantilever Plates (회전 외팔평판의 면외 방향 굽힘진동 해석)

  • Kim, Sung-Kyun;Yoo, Hong-Hee
    • Proceedings of the KSME Conference
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    • 2000.04a
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    • pp.613-618
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    • 2000
  • It is well known that the rotating motion of a blade-like structure induces centrifugal inertia force that causes the variation of the natural frequencies of the structure. Even though most of blade-like structures can be successfully Idealized as beams, some behave like plates rather than beams. This paper presents a modeling method for the flapwise bending vibration analysis of rotating cantilever plates. The dependence of natural frequencies and free vibration modes on the angular speed as well as the aspect ratio of a rotating plate is investigated. Particularly. the natural frequency loci crossing is observed and discussed In the present study.

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Flapwise Bending Vibration of Rotating Timpshenko Beams with Concentrated Mass and Mass Moment of Inertia (집중 질량및 관성 모멘트를 갖는 회전하는 티모센코 보의 면외굽힘 진동)

  • 박정훈;유홍희
    • Journal of KSNVE
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    • v.8 no.2
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    • pp.353-360
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    • 1998
  • In this paper, a modeling method for the bending vibration analysis of rotating Timoshenko beams with concentrated mass and mass moment of inertia is presented. The shear and rotary inertia effects become critical for the accurate estimation of the natural frequencies and mode shapes as the slenderness ratio decreases. The natural frequencies obtained by using the Timoshenko beam theory are lower than those by using the Euler beam theory. The critical angular speed, which does not exist only with the concentrated mass, exists with the concentrated mass moment of inertia.

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Flapwise Bending Vibration Analysis of Rotating Cross-ply Composite Beams (전단 및 단면 관성효과를 고려한 Cross-ply 복합재 회전 외팔보의 면외방향 굽힘 진동해석)

  • 이승현;신상하;유홍희
    • Proceedings of the Korean Society for Noise and Vibration Engineering Conference
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    • 2003.11a
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    • pp.994-999
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    • 2003
  • A modeling method for the modal analysis of a rotating cross-ply composite beam based on Timoshenko beam theory is presented. To analyze the composite beam exactly, the effects of shear deformation and rotary inertia are included. Linear differential equations of motion are derived using the assumed mode method. For the modeling, hybrid deformation variables are employed and approximated to derive the equations of motion. The effects of the dimensionless angular velocity and the slenderness ratio parameter on the variations of modal characteristics are investigated

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Flapwise bending vibration analysis of rotating cantilever beams considering shear and rotary inertial effects (전단 및 단면 회전관성효과를 고려한 회전 외팔보의 면외 굽힘진동해석)

  • Shin, Sang-Ha;Yoo, Hong-Hui
    • Transactions of the Korean Society of Mechanical Engineers A
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    • v.21 no.10
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    • pp.1580-1588
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    • 1997
  • A modeling method for the flapwise bending vibration of a rotating cantilever beam which has small slenderness ratio is presented in this paper. It is shown that as the slenderness ratio decreases the shear and rotary inertia effects increase. Such effects become critical for the accurate estimation of the natural frequencies and modeshapes, especially higher frequencies and modes, as the angular speed increases. It is also shown that the flapwise bending natural frequencies are higher than the chordwise bending natural frequencies. The discrepancy between first natural frequencies are especially significant when the hub radius ratio is small.

Free Vibrations of Horizontally Curved Beams with Variable Cross Section (변다면 수평 곡선보의 자유진동에 관한 연구)

  • 이병구;박광규;모정만;이재만
    • Computational Structural Engineering
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    • v.11 no.3
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    • pp.155-164
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    • 1998
  • 이 논문은 변단면을 고려한 수평 곡선보의 자유진동에 관한 연구이다. 진동시 곡선보 요소에 작용하는 합응력과 관성력의 동적평형방정식을 이용하여 변단면 원호형 수평 곡선보의 자유진동을 지배하는 상미분방정식을 유도하였다. 이 미분방정식을 원형 단면을 갖는 선형변변단면에 적용하여 고유진동수, 진동형 및 합응력을 산출하였다. 수치 해석예에서는 양단고정 및 양단회전 곡선보를 채택하였으며, 수치해석 결과로서 고유진동수와 단면비, 세장비 및 중심각 사이의 관계를 그림에 나타내었다. 또한 실험실 규모의 실험을 통하여 본 연구결과의 타당성을 보였다.

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Flapwise Bending Vibration of Rotating Cantilever Beams (회전 외팔보의 면외방향 굽힘진동 해석)

  • 유홍희
    • Transactions of the Korean Society of Mechanical Engineers
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    • v.19 no.2
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    • pp.348-353
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    • 1995
  • When cantilever beams rotate, their bending stiffnesses change due to the stretching caused by centrifugal inertia forces. Such phenomena result in variations of natural frequencies and mode shapes associated with constant speed rotational motions of the beams. These variations are important in many practical applications such as helicopter blades, turbomachines, and space structures. This paper presents the formulation of a set of linear equations governing the flapwise bending vibration of rotating cantilever beams. These equations can be used to provide accurate predictions of the variations of natural frequencies and mode shapes due to rotation.

Flapwise Bending Vibration Analysis of Rotating Composite Cantilever Beams (복합재 회전 외팔보의 면외방향 굽힘진동 해석)

  • Lee, Seung-Hyun;Shin, Sang-Ha;Yoo, Hong-Hee
    • Proceedings of the KSME Conference
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    • 2003.04a
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    • pp.887-892
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    • 2003
  • A modeling method for the modal analysis of a rotating composite beam is presented in this paper. Linear differential equations of motion are derived by using the assumed mode method. For the modeling, hybrid deformation variables are employed and approximated to derive the equations of motion Symmetrical laminated layers are considered for the composite beam. The effects of the dimensionless angular velocity, the hub radius and the fiber orientation angle parameter on the variations of modal characteristics are investigated.

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