Journal of the Computational Structural Engineering Institute of Korea (한국전산구조공학회논문집)

Computational Structural Engineering Institute of Korea (한국전산구조공학회)
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Free Vibrations of Tapered Timoshenko Beam by using 4th Order Ordinary Differential Equation

4계 상미분방정식에 의한 변단면 Timoshenko 보의 자유진동

  • 이병구 (원광대학교 토목환경공학과) ;
  • 박광규 (대전대학교 토목공학과) ;
  • 이태은 (원광대학교 토목환경공학과)
  • Received : 2011.11.23
  • Accepted : 2012.06.05
  • Published : 2012.06.30
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Abstract

This paper deals with free vibrations of the tapered Timoshenko beam in which both the rotatory inertia and shear deformation are included. The cross section of the tapered beam is chosen as the rectangular cross section whose depth is constant but breadth is varied with the parabolic function. The fourth order ordinary differential equation with respect the vertical deflection governing free vibrations of such beam is derived based on the Timoshenko beam theory. This governing equation is solved for determining the natural frequencies corresponding with their mode shapes. In the numerical examples, three end constraints of the hinged-hinged, hinged-clamped and clamped-clamped ends are considered. The effects of various beam parameters on natural frequencies are extensively discussed. The mode shapes of both the deflections and stress resultants are presented, in which the composing rates due to bending rotation and shear deformation are determined.

이 연구는 회전관성과 전단변형을 동시에 고려한 변단면 Timoshenko 보의 자유진동에 관한 연구이다. 변단면 보의 단면은 폭이 포물선 함수로 변화하는 변화폭 직사각형 단면으로 채택하였다. 이러한 보의 자유진동을 지배하는 수직변위에 대한 4계 상미분방정식을 유도하였다. 이 상미분방정식을 수치해석하여 고유진동수와 진동형을 산출하였다. 수치해석 예에서는 회전-회전, 회전-고정, 고정-고정 지점을 고려하였다. 진동형은 변위의 진동형뿐만 아니라 합응력의 진동형도 산출하여 그림에 나타내었다. 휨 회전각과 전단변형에 의한 수직변위 및 전단면 회전각의 구성비율을 산정하였다.

Keywords

References

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