Maio 2014 vol. 1 num. 1 - 10th World Congress on Computational Mechanics
Full Article - Open Access.
DYNAMICS OF STEPPED EULER-BERNOULLI BEAMS WITH ELASTIC END SUPPORTS
Stepped beams with elastic end supports have been extensively investigated due to their importance in structural engineering fields, including active structures, structural elements with integrated piezoelectric materials, shaft-disc system components, turbomachinery blades, etc. In the present work, a mathematical modeling is proposed for stepped beams with elastic end supports. The analysis is based on the classical Euler- Bernoulli beam theory. In comparison with the published literature on the transverse vibration of single cross-section change beams, there are relatively few works covering beam vibration when there is more than one change in the beam cross-section. In the present study, the natural frequencies and the mode shapes of beams with two step changes in cross-sections are investigated. Combinations of the classical clamped, pinned, sliding and free type end supports are considered. The first three natural frequencies of the studied beams are evaluated for some types of end supports. The proposed method can be extended to beams with any number of changes in cross-section.
Palavras-chave: stepped beam, natural frequency, mode shape.,
-  De Rosa, M. A., 1994, " Free vibration of Stepped Beams with Elastic Ends", Journal of Sound and Vibartion, vol. 173, no. 5, pp. 557-565.
-  Dong, Xing-Jian, Meng., G., Li, Hong-Guang, Ye, L., 2005, "Vibration Analysis of a Stepped Laminated Composite Timoshenko Beam", Mechanics Research Communications, vol. 32, pp. 572-581.
-  Heidebrecht, A. C., 1967, "Vibration of Non-Uniform Simply-Supported Beams", Journal of the Engineering Mechanics Division, Proceedings of the American Society of Civil Engineers, vol. 93, pp. 1-15.
-  Levinson, M., 1976, "Vibration of Stepped Strings and Beams Euler-Bernoulli", Journal of Sound and Vibration, vol. 49, pp. 187-291.
-  Jang, S. K., Bert, C. W., 1989, "Free Vibration of Stepped Beams: exact and numerical solutions", Journal of Sound and Vibration, vol. 130, no. 2, pp. 342-346.
-  Jang, S. K., Bert, C. W., 1989, "Free Vibration of Stepped Beams: Higher Mode Frequencies and Effects of Steps on Frequency", Journal of Sound and Vibration, vol. 132, no. 1, pp. 164-168.
-  Maurini, C., Porfiri, M., Pouget, J., 2006, "Numerical Methods for Modal Analysis of Stepped Piezelectric Beams", Journal of Sound and Vibration, vol. 298, pp. 918-933.
-  Maurizi, M. J., Bellés, P. M., 1993, "Natural Frequencies of One-Span Beams with Stepwise Variable Cross-Section", Journal of Sound and Vibration, vol. 168, no. 1, pp. 184- 18
-  Neguleswaran, S., 2002, "Vibration of an Euler-Bernoulli Beam on Elastic End Supports and with up to Three Step Changes in Cross-Section", International Journal of Mechanical Sciences, no. 44, pp. 2541-2555.
-  Stanton, S. C., .Mann, B. P, 2010, “On the dynamic response of beams with multiple geometric or material discontinuities”, Mechanical Systems and Signal Processing, vol. 24, 1409–1419.
-  Taleb, N. J., Suppiger, E. W., 1961, " Vibration of Stepped Beams", Journal of Aerospace Engineering, vol. 28, pp. 295-298.
-  Vaz, J. D. C., 2009, "Analyis of the Dynamic Behavior of an Euler-Bernoulli stepped Beam with Elastically Variable Supports", MSc. thesis, Mechanical Engineering Institute, Federal University of Itajubá, 94 p.
Vaz Junior, J.D.C.; Lima, J. J.; "DYNAMICS OF STEPPED EULER-BERNOULLI BEAMS WITH ELASTIC END SUPPORTS", p. 78-88 . In: In Proceedings of the 10th World Congress on Computational Mechanics [= Blucher Mechanical Engineering Proceedings, v. 1, n. 1].
São Paulo: Blucher,
ISSN 2358-0828, DOI 10.5151/meceng-wccm2012-16636
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