DOI QR코드

DOI QR Code

The Effect of Series Center on the Convergence of the Solution in Vibration Analysis by Differential Transformation Method(DTM)

미분변환법에 의한 진동 해석시 급수중심이 해의 수렴에 미치는 영향

  • 신영재 (안동대학교 기계공학부) ;
  • 윤종학 (안동대학교 기계공학부) ;
  • 유영찬 (안동대학교 건축공학부)
  • Published : 2007.02.01

Abstract

This paper presents the effect of the center of the series on convergence in solving vibration problems by Differential Transformation Method(DTM) to the transverse vibration of the Euler-Bernoulli beam under varying axial force. The governing differential equation of the transverse vibration of the Euler-Bernoulli beam under varying axial force is derived. The concepts of DTM were briefly introduced. Numerical calculations are carried out and compared with previously published results. The effect of the center of the series on convergence in solving the problem by DTM is discussed.

Keywords

Center of the Series;Differential Transformation Method;Axial Force

References

  1. Naguleswaran, S., 1991, 'Vibration of a Vertical Cantilever with and Without Axial Freedom at Clamped End,' Journal of Sound and Vibration, 146 (2), pp. 191-198 https://doi.org/10.1016/0022-460X(91)90758-C
  2. Naguleswaran, S., 2004, 'Transverse Vibration of a uniform Euler-Bernoulli Beam Under Linearly Varying Axial Force,' Journal of Sound and Vibration, 275, pp. 47-57 https://doi.org/10.1016/S0022-460X(03)00741-7
  3. Zhou, J. K., 1986, Differential Transformation and its Application for Electrical Circuits, Huazhong University Press, Wuhan China(in Chinese)
  4. Chen, C. K. and Ho, S. H., 1996, 'Application of Differential Transformation to Eigenvalue Problems,' Applied Mathematics and Computation, 79, pp. 173-188 https://doi.org/10.1016/0096-3003(95)00253-7
  5. Shin, Y. J. and Yun, J. H., 2006, 'Transverse Vibration of a Uniform Euler-Bernoulli Beam Under Varying Axial Force Using Differential Transformation Method,' Journal of Mechanical Science and Technology (KSME Int. J.), Vol. 20, No. 2, pp. 191-196 https://doi.org/10.1007/BF02915820
  6. Shin, Y. J., Jaun, S. J., Yun, J. H., Dioyan, N. M., Hwang, K. S. and Jy, Y. C., 2004, 'Vibration Analysis for the Circular Plates by Using the Differential Transformation Method,' Eleventh International Congress on Sound and Vibration, pp. 3723-3732
  7. Han, J. B. and Liew, K. M., 1999, 'Axisymmetric Free Vibration of Thick Annular Plates,' International Journal of Mechanical Sciences, 41, pp. 1089-1109 https://doi.org/10.1016/S0020-7403(98)00057-5
  8. Leissa, W. and Kang, J. H., 2002, 'Exact Solutions for Vibration and Buckling of an SS-C-SS-C Rectangular Plate Loaded by Linearly Varying In-Plane Stresses,' International Journal of Mechanical Sciences, 44, pp. 1923-1945 https://doi.org/10.1016/S0020-7403(02)00069-3