Browse > Article
http://dx.doi.org/10.3795/KSME-A.2006.30.3.279

Vibration Analysis of Euler-Bernoulli Beam with Open Cracks on Elastic foundations Using Differential Transformation Method and Generalized Differential Quadrature Method  

Hwang Ki-Sup (안동대학교 대학원 기계공학부)
Yun Jong-Hak (안동대학교 대학원 기계공학부)
Shin Young-Jae (안동대학교 기계공학부 기계설계)
Publication Information
Transactions of the Korean Society of Mechanical Engineers A / v.30, no.3, 2006 , pp. 279-286 More about this Journal
Abstract
The main purpose of this paper is to apply differential transformation method(DTM) and generalized differential quadrature method(GDQM) to vibration analysis of Euler-Bernoulli beam with open cracks on elastic foundation. In this paper the concepts of DTM and GDQM were briefly introduced. The governing equation of motion of the beam with open cracks on elastic foundation is derived. The cracks are modeled by massless substitute spring. The effects of the crack location, size and the foundation constants, on the natural frequencies of the beam, are investigated. Numerical calculations are carried out and compared with previous published results.
Keywords
Differential Transformation Method; Generalized Differential Quadrature Method; Elastic Foundation;
Citations & Related Records
연도 인용수 순위
  • Reference
1 Hetenyi, M., 1946, 'Beams on Elastic Foundation,' (The University of Michigan Press, Michigan)
2 Rades, M., 1970, 'Steady-State Response of a Finite Beam on a Pasternak-type Foundation,' International Journal of Solids Structures, Vol. 6, pp. 739-756   DOI   ScienceOn
3 De Rosa, M. A., 1989, 'Stability and Dynamics of Beams on Winkler Elastic Foundations,' Earthquake Engineering and Structural Dynamnics, Vol. 18, pp. 377-388   DOI   ScienceOn
4 Farghaly, S. H. and Zeid, K. M., 1995, 'An Exact Frequency Equation for an Axially Loaded Beam-Mass-Spring System Resting on a Winkler Elastic Foundation,' Journal of Sound and Vibration, Vol. 185, No.2, 357-363   DOI   ScienceOn
5 BELLMAN, R., KASHEF, B. G. and CASTI, J., 1972, 'Differential Quadrature: a Technique for the ？Rapid Solution of Nonlinear Partial Differential Equation,' Journal of Computational Physics, Vol. 10, pp. 40-52   DOI   ScienceOn
6 ZHOU, J. K., 1986, 'Differential Transformation and its Application for Electrical Circuits,'Huazhong University Press, Wuhan China(in Chinese)
7 SHU, C. and DU, H., 1997, 'Implementation of Clamped and Simply Suppored Boundary Condition in the Generalized Differential Quadrature Free Vibration Analysis of Beams and Plate,' International Journal of Solids Structure, Vol. 34, No.7, pp. 819-835   DOI   ScienceOn
8 SHU, C., 1996, 'Free Vibration Analysis of Composite Laminated Conical Shells by Generalized Differential Quadrature, ' Journal of Sound and Vibration, Vol. 194, No.4, pp. 587-604   DOI   ScienceOn
9 Seong, K. Y., 2001, 'Natural frequencies of beam with open cracks on elastic foundations', The Degree of Master of Engineering, Thesis, University of Kyung-pook National University, Daegu, Korea
10 Malik, M. and Dang. H. H., 1998, 'Vibration Analysis of Continuous Systems by Differential Transformation,' Applied Mathematics and Computation, Vol. 96, pp 17-26   DOI   ScienceOn
11 CHEN, C. J. and WU, W. J., 1994, '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   DOI   ScienceOn
12 CHEN, C. K. and HO, S. H., 1999, 'Transverse Vibration of a Rotating Twisted Tirnoshenko Beams under Axial Loading using Differential Transform,' International Journal of Mechanical Sciences, Vol. 41, pp. 1339-1356   DOI   ScienceOn
13 HO, S. H. and CHEN, C. K., 1998, 'Analysis of ？General Elastically End Restrained Non-Uniform Beams using Differential Transform,' Applied Mathematical Modeling, Vol. 22, pp. 219-234   DOI   ScienceOn
14 Shin, Y. C. and Shin, Y. J., 2001, 'Longitudinal Vibration of Rods with Non-Uniform Cross-Section by Differential Transformation,' 2001 Spring the Korea Society of Ocean Engineers Conference, pp. 229-233
15 Kwon, K. M., Shin, Y. J. and Lu, Y. S., 2001, 'Vibration Analysis of Non-Uniform Beam by Differential Transformation,' 2001 Fall The Korean Society for Noise and Vibration Engineering Conference, pp. 617-621
16 SHU, C., 2000, 'Differential Quadrature and its Application in Engineering,' Springer, Inc
17 Maurizi, M. J., Rosales, M. and Belles, P., 1988 'A Further Note on the Free Vibrations of Beams Resting on an Elastic Foundation,' Journal of Sound and Vibration, Vol. 124, No.1, pp. 191-193   DOI   ScienceOn
18 Yuen, M. M. F., 1985, 'A Numerical Study of the ？Eigenparameters of a Damaged Cantilever,'Journal of Sound and Vibration, Vol. 103, No.3, pp. 301-310   DOI   ScienceOn
19 Razaqpur, A. G. and Shah, K. R., 1991, 'Exact Analysis of Beams on Two-Parameter Elastic Foundations,' International Journal of Solids Structures, Vol. 27, No.4, pp. 435-454   DOI   ScienceOn
20 Valsangkar, A. J. and Pradhanang, R., 1988, 'Vibrations of Beam-Columns on Two-Parameter Elastic Foundations,' Earthquake Engineering and Structural Dynamics, Vol. 16, pp. 217-225   DOI
21 Joshi, A. and Madhusudhan, B. S., 1991, 'A Unified Approach to Free Vibration of Locally Damaged Beams Having Various Homogeneous Boundary Conditions,' Journal of Sound and Vibration, Vol. 147, No.3, pp. 475-488   DOI   ScienceOn
22 Rizos, P. F., Aspragathos, N. and Dimarogonas, A. D., 1990, 'Identification of Crack Location and Magnitude in a Cantilever Beam from the Vibration Modes,' Journal of Sound and Vibration, Vol. 138, No.3, pp. 381-388   DOI   ScienceOn
23 Qian, G. L., Gu, S. N. and Jiang, J. S., 1990, 'The Dynamic Behavior and Crack Detection of a Beam with a Crack,' Journal of Sound and Vibration, Vol. 138, No.2, pp. 233-243   DOI   ScienceOn
24 Narkis, Y, 1994, 'Identification of Crack Location in Vibration Simply Supported Beams,' Journal of Sound and Vibration, Vol. 172, No.4, pp. 549-558   DOI   ScienceOn
25 Ostachowicz, W. M. and Krawczuk, M., 1991, 1991, 'Analysis of the Effect of Cracks on the Natural Frequencies of a Cantilever Beam,' Journal ofSound and Vibration, Vol. 150, No.2, pp. 191-201   DOI   ScienceOn