Transactions of the Korean Society of Automotive Engineers (한국자동차공학회논문집)

The Korean Society of Automotive Engineers (한국자동차공학회)
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Vibration Analysis of Non-homogeneous Damped Beam Using the Differential Transformation Method

미분변환법에 의한 비균질 감쇠보의 진동 해석

  • Shin, Young-Jae (Department of Mechanical Engineering, Andong National University) ;
  • Jaun, Su-Ju (Department of Mechanical Engineering, Andong National University) ;
  • Yun, Jong-Hak (Department of Mechanical Engineering, Andong National University)
  • Published : 2005.09.01
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Abstract

In this paper, the natural frequencies of non-homogeneous damped beam are determined by using the differential transformation. The beam considered has different stiffness, damping and mass properties in each of two parts. The various boundary conditions are assumed at each end. The results obtained by the present method agree very well with those reported in the previous works. The present analysis shows the usefulness and validity of differential transformation in solving a non-homogeneous damped beam problem.

Keywords

References

  1. L. Klein, 'Transverse Vibrations of Non-uniform Beam,' Journal of Sound and Vibration, Vol. 37, pp. 491-505, 1974 https://doi.org/10.1016/S0022-460X(74)80029-5
  2. I. Elishakoff and S. Candan, 'Infinite Number of Closed-form Solutions for Reliability of Non-homogeneous Beam,' Applications of Statistics and Probability (R. E. Melchers and M. G. Stewart, editors), Vol. 2, pp. 1059-1067, 1999
  3. M. Gurgoze and H. Erol, 'On the 'modes' of Non-homogeneously Damped Rods Consisting of Two Parts,' Journal of Sound and Vibration, Vol. 260, pp. 357-367, 2003 https://doi.org/10.1016/S0022-460X(02)01047-7
  4. J. K. Zhou, 'Differential Transformation and its Application for Electrical Circuit,' Huazhong University Press, Wuhan China(in Chinese), 1986
  5. C. K. Chen and S. H. Ho, 'Transverse Vibration of a Rotating Twisted Timoshenko Beams Under Axial Loading Using Differential Transform,' International Journal of Mechanical Sciences, Vol. 41, pp.1339-1356, 1999 https://doi.org/10.1016/S0020-7403(98)00095-2
  6. M. Malik and H. H. Dang, 'Vibration Analysis of Continuous Systems by Differential Transformation Applied Mathematics and Computation,' Vol. 96, pp. 17-26, 1998 https://doi.org/10.1016/S0096-3003(97)10076-5
  7. C. K. Chen and W. J. Wu, 'Application of the Taylor Differential Transformation Method to Viscous Damped Vibration of Hard and Soft Spring System,' Computer and Structures, Vol. 59, No.4, pp.631-639, 1994 https://doi.org/10.1016/0045-7949(95)00304-5
  8. M. Gurgoze, 'The Modes of Non-homogeneous Damped Beams,' Journal of Sound and Vibration, Vol. 242, pp. 355-361, 2001 https://doi.org/10.1006/jsvi.2000.3323