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In-Plane Vibration Analysis of Asymmetric Curved Beams Using DQM

DQM을 이용한 비대칭 곡선보의 내평면 진동해석

  • Kang, Ki-Jun (Department of Automotive Engineering, Hoseo University) ;
  • Kim, Young-Woo (Department of Automotive Engineering, Hoseo University)
  • 강기준 (호서대학교 공과대학 자동차공학과) ;
  • 김영우 (호서대학교 공과대학 자동차공학과)
  • Received : 2010.06.09
  • Accepted : 2010.08.10
  • Published : 2010.08.31

Abstract

The free in-plane vibration of asymmetric circular curved beams with varying cross-section is analyzed by the differential quadrature method (DQM) neglecting transverse shearing deformation. Natural frequencies are calculated for the beams with various opening angles and boundary conditions. Results obtained by the DQM are compared with available results by other methods in the literature. It is found that the DQM gives the good accuracy even with a small number of grid points.

미분구적법을 이용하여, 전단변형을 고려하지 않은, 단면적이 변하는 비대칭 곡선 보의 면내 자유진동을 해석하였다. 다양한 경계조건 및 굽힘 각에 따른 진동수를 계산하였고, 그 결과를 다른 수치해석들과 비교하였다. 미분구적법은 비교적 적은 요소를 사용하고도 정확한 해석결과를 보여준다.

Keywords

References

  1. R. Hoppe, "The Bending Vibration of a Circular Ring", Crelle's J. Math., Vol. 73, pp. 158-170, 1871.
  2. A. E. H. Love, "A Treatise of the Mathematical Theory of Elasticity", 4th ed, Dover, New York, 1944.
  3. R. R. Archer, "Small Vibration of Thin Incomplete Circular Rings", Int. J. Mech. Sci., Vol. 1, pp. 45-56, 1960. https://doi.org/10.1016/0020-7403(60)90029-1
  4. N. M. Auciello and M. A. De Rosa, "Free Vibrations of Circular Arches: A Review", J. Sound Vibr., Vol. 176, No. 4, pp. 433-458, 1994. https://doi.org/10.1006/jsvi.1994.1388
  5. R. E. Bellman and J. Casti, "Differential Quadrature and Long-Term Integration", J. Math. Anal. Applic., Vol. 34, No. 2, pp. 235-238, 1971. https://doi.org/10.1016/0022-247X(71)90110-7
  6. J. Park, "A Numerical Study on flexural Strength with the Spreading of Upper Reinforcement of Girder into the Adjoining Slab, J. KAIS, Vol. 8, No. 5, pp. 1179-1185. 2007.
  7. S. K. Jang, et al., "Application of Differential Quadrature to Static Analysis of Structural Components", Int. J. Numer. Mech. Engng, Vol. 28, No. 3, pp. 561-577, 1989. https://doi.org/10.1002/nme.1620280306
  8. K. Kang and J. Han, "Analysis of a Curved beam Using Classical and Shear Deformable Beam Theories", Int. J. KSME., Vol. 12, No. 2, pp. 244-256, 1998. https://doi.org/10.1007/BF02947169
  9. K. Kang and B. Kim, "In-Plane Vibration Analysis of Curved Beams Considering Shear Deformation Using DQM", J. KAIS, Vol. 7, No. 5, pp. 793-800. 2006.
  10. R. W. Hamming, "Numerical Methods for Scientists and Engineers", 2nd ed, McGraw-Hill, New York, 1973.
  11. A. R. Kukreti, et al., "Differential Quadrature and Rayleigh-Ritz Methods to Determine the Fundamental Frequency of Simply Supported Rectangular Plate with Linearly Varying Thickness", J. Sound Vibr., Vol. 189, No. 1, pp. 103-122. 1996. https://doi.org/10.1006/jsvi.1996.0008

Cited by

  1. In-Plane Buckling Analysis of Asymmetric Curved Beam Using DQM vol.14, pp.10, 2013, https://doi.org/10.5762/KAIS.2013.14.10.4706