Browse > Article

Error Analysis and Improvement of the Timoshenko Beam based Finite Element Model for Multi-Stepped Beam Structures  

홍성욱 (금오공과대학교 기계공학부)
이용덕 (LG 이노텍)
김만달 (금오공과대학교 대학원)
Publication Information
Abstract
The Timoshenko beam model has been known as the most accurate model for representing beam structures. However, the Timoshenko beam model may give rise to a significant error when it is applied to multi-stepped beam structures. This paper is intended to demonstrate the modeling error of Timoshenko beam based finite element model for multi-stepped beam structures and to suggest a new modeling method to improve the accuracy. A tentative bending spring is introduced into the stepped section to represent the softening effect due to the presence of step. This paper also proposes a finite element modeling method in the light with the tentative bending spring model for the step softening effect. The proposed method rigorously adapts computation results from a commercial finite element code. The validity of the proposed method is demonstrated through a series of simulation and experiment.
Keywords
Timoshenko beam; Multi-stepped beam; Stress concentration; Natural frequency;
Citations & Related Records
Times Cited By KSCI : 3  (Citation Analysis)
연도 인용수 순위
1 Timoshenko, S., Young, D. and Weaver, W. Jr, Vibration Problems in Engineering, 4th ed., John Wiley & Sons, 1974
2 Han, S. M., Benaroya, H. and Wei, T., 'Dynamics of Transversely Vibrating Beams using Four Engineering Theories,' Journal of Sound and Vibration, Vol. 225, No.5, pp. 935-988, 1999   DOI   ScienceOn
3 Nagaraj, V. T., 'Relation between Fundamental Natural Frequency and Maximum Static Deflection for Rotating Timoshenko Beams,' Journal of Sound and Vibration, Vol. 201, No.3, pp. 404-406, 1997   DOI   ScienceOn
4 Rao, S. S. and Gupta, R. S., 'Finite Element Vibration Analysis of Rotating Timoshenko Beams,' Journal of Sound and Vibration, Vol. 242, No. 1, pp. 103-124, 2001   DOI   ScienceOn
5 Nelson, H. D., 'A Finite Rotating Shaft Element using Timoshenko Beam Theory,' ASME, Journal of Mechanical Design, Vol. 102, pp. 793-803, 1980   DOI
6 Wu, T. X. and Thompson, D. J., 'A Double Timoshenko Beam Model for Vertical Vibration Analysis of Railway Track at High Frequencies,' Journal of Sound and Vibration, Vol. 224, No.2, pp. 329-348, 1999   DOI   ScienceOn
7 Wang, R. T. and Lin, T. Y., 'Vibration of MultiSpan Timoshenko Frames due to a Moving Load,' Journal of Sound and Vibration, Vol. 212, pp. 417-434, 1998   DOI   ScienceOn
8 Abramovich, H., 'Shear Deformation and Rotatory Inertia Effects of Vibrating Composite Beams,' Composite Structures, Vol. 20, pp. 165-173, 1992   DOI   ScienceOn
9 Lee, S. P. and Maiti, S. K., 'Modelling of Transverse Vibration of Short Beams for Crack Identification and Measurement of Crack Extension,' Journal of Sound and Vibration, Vol. 257, No.3, pp. 559-583, 2002   DOI   ScienceOn
10 Pilkey, W. D., Formulas for Stress, Strain, and Structural Matrices, John Wiley & Sons, Inc., 1994
11 Hong, S. W., Kim, J. W. and Park, J. H., 'A Method for Determining Exact Modal Parameters of Non-uniform, Continuous Beam Structures with Damping Elements,' Journal of the KSPE, Vol. 15, No. 12, pp. 202-211, 1998   과학기술학회마을
12 Hong, S. W., Kim, M. D. and Lee, C. W., 'Dynamic Modeling and Analysis of Beam Structures with Cracks,' Journal of the KSPE, Vol. 20, No.6, pp. 197-204, 2003   과학기술학회마을
13 Hong, S. W., Cho, Y. J. and Kim, J. S., 'A Study on the Combined Use of Exact Dynamic Elements and Finite Elements,' Journal of the KSNVE, Vol. 12, No.2, pp. 141-149, 2002   과학기술학회마을   DOI
14 I-DEAS Design User's Guide, Samsung SDS, Co., 1996