Browse > Article
http://dx.doi.org/10.5050/KSNVN.2005.15.11.1318

Vibration Analysis for the Euler-Bernoulli Wedge Beam by Using Differential Transformation Method  

Yun, Jong-Hak (안동대학교 대학원 기계공학부)
Shin, Young-Jae (안동대학교 대학원 기계공학부)
Publication Information
Transactions of the Korean Society for Noise and Vibration Engineering / v.15, no.11, 2005 , pp. 1318-1323 More about this Journal
Abstract
In this paper, the vibration analysis for the Euler-Bernoulli complete and truncate wedge beams by differential Transformation method(DTM) was investigated. The governing differential equation of the Euler-Bernoulli complete and truncate wedge beams with regular singularity is derived and verified. The concepts of DTM were briefly introduced. Numerical calculations are carried out and compared with previous published results. The usefulness and the application of DTM are discussed.
Keywords
Differential Transformation Method; Wedge Beam; Regular Singularity;
Citations & Related Records
연도 인용수 순위
  • Reference
1 Lee, T. W., 1976, 'Transverse Vibrations of a Tapered Beam Carrying a Concentrated Mass', Transactions of the American Society of Mechanical Engineers, Journal of Applied Mechanics (series E), 43, pp. 366-367   DOI
2 Goel, R. P., 1976, 'Transverse Vibration of Taper Beams', Journal of Sound and Vibraion, Vol. 47, pp. 1-7   DOI   ScienceOn
3 Yang, K. Y., 1990, 'The Natural Frequencies of a Non-uniform Beam with a Tip Mass and with Translational and Rotational Springs', Journal of Sound and Vibration, Vol. 137, pp. 339-341   DOI   ScienceOn
4 Naguleswaran, S., 1994, 'Vibration in the Two Principal Planes of a Non-uniform Beam of Rectangular Cross-section, One Side of which Varies as the Square Root of the Axial Coordianate', Journal of Sound and Vibration, Vol. 172, pp. 305-319   DOI   ScienceOn
5 Todhunter, I. and Pearson, K., 1960, A History of the Theory of Elasticity and of the Strength of Materials, 2(2) 92-98. New York: Dover(Reprint of 1893 Publication of Cambridge University Press)
6 Ward, P. F., 1913, 'Transverse Vibration of a Rod of Varying Cross Section', Philosophical Magazine (series 6), 46, pp. 85-106
7 Nicholson, J. W., 1920, 'The Lateral Vibration of Sharply Pointed Bars', Proceedings of the Royal Society of London (series A), 97, pp. 172-181   DOI
8 Wrinch, D. M., 1992, 'On the Lateral Vibration of Bars of Conical Type', Proceedings of the Royal Society of London(Series A), 101, pp. 493-508
9 Conway, H. D. and Dubil, J. F., 1965, 'Vibration Frequencies of Truncated Cone and Wedge Beams', Transactions of the American Society of Mechanical Engineers, Journal of Applied Mechanics (series E), 32, pp. 923-925
10 Sanger, D. J., 1986, 'Transverse Vibration of a Class of Non-uniform Beams', Journal of Mechanical Engineering Science, 16, pp. 111-120
11 Naguleswaran, S., 1994, 'A Direct Solution for the Transverse Vibration of Euler-Bernoulli Wedge and Cone Beams', Journal of Sound and Vibration, Vol. 172, No. 3, pp. 289-304   DOI   ScienceOn
12 Zhou, J. K., 1986, 'Differential Transformation and its Application for Electrical Circuits', Huazhong University Press, Wuhan China(in Chinese)
13 Malik, M. and Dang, H. H., 1998, 'Vibration Analysis of Continuous Systems by Differential Transformation', Applied Mathematics and Computation, 96, pp. 17-26   DOI   ScienceOn
14 Chen, C. K. and. Ho, S. H., 1996, 'Application of Differential Transformation to Eigenvalue Problems', Applied Mathematics and Computation, 79, pp. 173-188   DOI   ScienceOn
15 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
16 Wang, H. C., 1997, 'Generalized Hyper-geometric Function Solutions on the Transverse Vibrations of a Class of Non-uniform Beams', Transactions of the American Society of Mechanical Engineers, Journal of Applied Mechanics (series E), 34, pp. 702-708
17 Naguleswaran, S., 1992, 'Vibration on an Euler-Benroulli Beam of Constant Depth and with Inearly Varying Breadth', Journal of Sound and Vibration, Vol. 153, pp. 509-522   DOI   ScienceOn