Transactions of the Korean Society for Noise and Vibration Engineering (한국소음진동공학회논문집)

The Korean Society for Noise and Vibration Engineering (한국소음진동공학회)
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Free Vibrations of Timoshenko Beam with Constant Volume

일정체적 Timoshenko 보의 자유진동

  • 이병구 (원광대학교 토목환경공학과) ;
  • 이태은 (원광대학교 토목환경공학과) ;
  • 윤희민 (원광대학교 대학원 토목환경공학과)
  • Received : 2011.11.24
  • Accepted : 2011.12.30
  • Published : 2012.03.20
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Abstract

This paper deals with free vibrations of the tapered Timoshenko beam with constant volume, in which both the rotatory inertia and shear deformation are included. The cross section of the tapered beam is chosen as the regular polygon cross section whose depth is varied with the parabolic function. The ordinary differential equations governing free vibrations of such beam are derived based on the Timoshenko beam theory by decomposing the displacements. Governing equations are 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.

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References

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