Journal of the Korea Academia-Industrial cooperation Society (한국산학기술학회논문지)

The Korea Academia-Industrial cooperation Society (한국산학기술학회)
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Extensional Vibration Analysis of Curved Beams Including Rotatory Inertia and Shear Deformation Using DQM

미분구적법(DQM)을 이용 회전관성 및 전단변형을 포함한 곡선 보의 신장 진동해석

  • Kang, Ki-Jun (Department of Mechanical Engineering, Hoseo University) ;
  • Park, Cha-Sik (Department of Mechanical Engineering, Hoseo University)
  • 강기준 (호서대학교 공과대학 기계공학부) ;
  • 박차식 (호서대학교 공과대학 기계공학부)
  • Received : 2016.02.17
  • Accepted : 2016.05.12
  • Published : 2016.05.31
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Abstract

One of the most efficient procedures for the solution of partial differential equations is the method of differential quadrature. The differential quadrature method (DQM) has been applied to a large number of cases to overcome the difficulties of complex algorithms of computer programming, as well as the excessive use of storage due to the conditions of complex geometry and loading. The in-plane vibrations of curved beams with extensibility of the arch axis, including the effects of rotatory inertial and shear deformation, are analyzed by the DQM. The fundamental frequencies are calculated for members with various slenderness ratios, shearing flexibilities, boundary conditions, and opening angles. The results are compared with the numerical results obtained by other methods for cases in which they are available. The DQM gives good mathematical precision even when only a limited number of grid points is used, and new results according to diverse variations are also suggested.

편미분방정식의 해를 구하기 위한 효율적인 방법 중의 하나는 미분구적법이다. 복잡한 기하학적 구조 및 하중은 컴퓨터 용량을 과도하게 사용할 뿐만 아니라, 복합알고리즘 프로그램을 어렵게 해 이를 극복하기위하여 미분구적법(DQM)이 많은 분야에 적용되어왔다. 곡선 보의 아크 축 신장에 회전관성 및 전단변형을 포함하여 DQM을 이용 곡선 보의 내 평면진동을 해석하였다. 다양한 세장비 및 전단신축성 그리고 경계조건 및 열림 각에 따른 기본진동수를 계산하였다. DQM 결과는 활용 가능한 다른 수치해석결과와 비교하였다. DQM은 적은 격자점을 사용하고도 정확한 해석을 보여주었고, 다양한 변경에 따른 새로운 결과 또한 제시하였다.

Keywords

References

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