Published
Non-uniform Euler-Bernoulli beams´ natural frequencies
Frecuencias propias de vigas Euler-Bernoulli no uniformes
DOI:
https://doi.org/10.15446/ing.investig.v31n1.20514Keywords:
Euler-Bernoulli beam, WKB method. (en)viga Euler-Bernoulli, método WKB. (es)
Downloads
This paper has studied the problem of natural frequencies for Euler-Bernoulli beams having non-uniform cross-section. The numerically-obtained solutions were compared to asymptotic solutions obtained by the Wentzel-Kramers-Brillouin (WKB) method. It was established that WKB formula precision was higher than 3% for high frequencies (≥ 4 mode).
En el presente trabajo se estudia el problema de frecuencias propias de la viga Euler-Bernoulli de sección no uniforme; se comparan las soluciones del problema obtenidas numéricamente con la solución asintótica lograda mediante el método Wentzel-Kramers-Brillouin (WKB). Se establece que la precisión de las fórmulas WKB es mayor del 3% para frecuencias altas (número de modo ≥ 4).
References
Abrate, S., Vibration of non-uniform rods and beams., Journal of Sound and Vibration, Vol. 185, 1995, pp. 703-716.
Akulenko, L. P., Nesterov, S. V., High-precision Methods in Eigenvalue Problems and Their Applications., Chapman & Hall, 2005.
Fedoryuk, M. V., Asymptotic Analysis., Linear Ordinary Differential Equations, Springer, 1993.
Geist, B., McLaughlin, J. R., Asymptotic formulas for the eigenvalues of the Timoshenko beam., J. Math. Anal. Appl., Vol. 53, 2001, pp. 341-380.
Hsu, J-Ch., Lai, H-Y., Chen, C. K., Free vibration of non-uniform Euler-Bernoulli beams whit general elastically end constraints using Adomian modified decomposition method., Journal of Sound and Vibration, Vol. 318, 2008, pp. 965-981.
Landau, L. D., Lifshitz, E. M., Theory of Elasticity, Course of Theoretical Physics, Vol.7, Pergamon Press, 1975.
Tijonov, A. N., Samarsky, A. A., Ecuaciones de la Física Matemática, Editorial Mir-Moscú., 1972.
Todhunter, I., A History of the Theory of Elasticity and the Strength of Materials., Vol. II, Pt.2, Cambridge. Univ. Press, 1893.
Dimensions
PlumX
Article abstract page views
Downloads
How to Cite
License
Copyright (c) 2011 Hugo Aya, Ricardo Cano, Petr Zhevandrov
This work is licensed under a Creative Commons Attribution 4.0 International License.
The authors or holders of the copyright for each article hereby confer exclusive, limited and free authorization on the Universidad Nacional de Colombia's journal Ingeniería e Investigación concerning the aforementioned article which, once it has been evaluated and approved, will be submitted for publication, in line with the following items:
1. The version which has been corrected according to the evaluators' suggestions will be remitted and it will be made clear whether the aforementioned article is an unedited document regarding which the rights to be authorized are held and total responsibility will be assumed by the authors for the content of the work being submitted to Ingeniería e Investigación, the Universidad Nacional de Colombia and third-parties;
2. The authorization conferred on the journal will come into force from the date on which it is included in the respective volume and issue of Ingeniería e Investigación in the Open Journal Systems and on the journal's main page (https://revistas.unal.edu.co/index.php/ingeinv), as well as in different databases and indices in which the publication is indexed;
3. The authors authorize the Universidad Nacional de Colombia's journal Ingeniería e Investigación to publish the document in whatever required format (printed, digital, electronic or whatsoever known or yet to be discovered form) and authorize Ingeniería e Investigación to include the work in any indices and/or search engines deemed necessary for promoting its diffusion;
4. The authors accept that such authorization is given free of charge and they, therefore, waive any right to receive remuneration from the publication, distribution, public communication and any use whatsoever referred to in the terms of this authorization.
