KSCE Journal of Civil and Environmental Engineering Research (대한토목학회논문집)

Korean Society of Civil Engeneers (대한토목학회)
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Free Vibrations of Timoshenko Beam with Elastomeric Bearings at Two Far Ends

양단이 탄성받침으로 지지된 Timoshenko 보의 자유진동

  • 이병구 (원광대학교 토목환경공학과) ;
  • 이태은 (원광대학교 토목환경공학과) ;
  • 박창은 (원광대학교 대학원 토목환경공학과)
  • Received : 2010.12.29
  • Accepted : 2011.03.16
  • Published : 2011.06.30
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Abstract

This paper deals with free vibrations of the Timoshenko beam supported by two elastomeric bearings at two far ends. The ordinary differential equation governing free vibrations of such beam is derived, in which both effects of rotatory inertia and shear deformation are included as the Timoshenko beam theory. Also, boundary conditions of the free end are derived based on the Timoshenko beam theory. The ordinary differential equation is solved by the numerical methods for calculating natural frequencies and mode shapes. Both effects of the rotatory inertia and shear deformation on natural frequencies are extensively discussed. Also, relationships between natural frequencies and slenderness ratio, foundation modulus and bearing length are presented. Typical mode shapes of bending moment and shear force as well as deflection are given in figures which show the positions of maximum amplitudes and nodal points.

이 연구는 양단이 탄성받침으로 지지된 Timoshenko 보의 자유진동에 관한 연구이다. 회전관성과 전단변형을 동시에 고려하는 Timoshenko 보 이론을 적용하여 탄성받침 보의 자유진동을 지배하는 상미분방정식과 자유단의 경계조건을 유도하였다. 이 상미분방정식을 수치해석하여 고유진동수와 진동형상을 산출하였다. 회전관성과 전단변형이 자유진동에 미치는 영향을 분석하고, 변수연구를 통하여 세장비, 지반계수, 탄성받침 길이 등이 자유진동에 미치는 영향을 그림에 나타내었다. 변위 및 휨 모멘트, 전단력의 진동형상을 그림에 나타내어 최대진폭 및 무변위의 위치를 알 수 있도록 하였다.

Keywords

References

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