### A closed-form solution for free vibration of multiple cracked Timoshenko beam and application

#### Abstract

#### Keywords

#### Full Text:

PDF#### References

I. Elishakoff, J. Kaplunov, and E. Nolde. Celebrating the centenary of Timoshenko’s study of effects of shear deformation and rotary inertia. Applied Mechanics Reviews, 67, (6), (2015). doi:10.1115/1.4031965.

L. Majkut. Free and forced vibrations of Timoshenko beams described by single difference equation. Journal of Theoretical and Applied Mechanics, 47, (1), (2009), pp. 193–210, http://ptmts.org.pl/jtam/index.php/jtam/article/view/v47n1p193.

I. Karnovsky and O. Lebed. Formulas for structural dynamics: tables, graphs and solutions. Mc-Graw Hill, Inc., (2000).

T. Kocaturk and M. Simsek. Free vibration analysis of Timoshenko beams under various boundary conditions. Journal of Engineering and Natural Sciences, 1, (2005), pp. 30–40, http://eds.yildiz.edu.tr/ArticleContent/Journal/sigma/Volumes/2005/Issues/Regular-1/YTUJENS-2005-23-1.311.pdf.

R. D. Adams, P. Cawley, C. J. Pye, and B. J. Stone. A vibration technique for non-destructively assessing the integrity of structures. Journal of Mechanical Engineering Science, 20, (2), (1978), pp. 93–100. doi:10.1243/jmes jour 1978 020 016 02.

R. Y. Liang, J. Hu, and F. Choy. Quantitative NDE technique for assessing damages in beam structures. Journal of Engineering Mechanics, 118, (7), (1992), pp. 1468–1487. doi:10.1061/(asce)0733-9399(1992)118:7(1468).

Y. Narkis. Identification of crack location in vibrating simply supported beams. Journal of Sound and Vibration, 172, (4), (1994), pp. 549–558. doi:10.1006/jsvi.1994.1195.

T. G. Chondros, A. D. Dimarogonas, and J. Yao. A continuous cracked beam vibration theory. Journal of Sound and Vibration, 215, (1), (1998), pp. 17–34. doi:10.1006/jsvi.1998.1640.

N. T. Khiem and T. V. Lien. A simplified method for natural frequency analysis of a multiple cracked beam. Journal of Sound and Vibration, 245, (4), (2001), pp. 737–751. doi:10.1006/jsvi.2001.3585.

N. T. Khiem and H. T. Tran. A procedure for multiple crack identification in beam-like structures from natural vibration mode. Journal of Vibration and Control, 20, (9), (2014), pp. 1417–1427. doi:10.1177/1077546312470478.

S. Caddemi and I. Calio. Exact closed-form solution for the vibration modes of the Euler–Bernoulli beam with multiple open cracks. Journal of Sound and Vibration, 327, (3), (2009), pp. 473–489. doi:10.1016/j.jsv.2009.07.008.

N. T. Khiem and T. T. Hai. A closed-form solution for free vibration of beams with arbitrary number of cracks. In Proceedings of the Scientific Conference dedicated to 35th Anniversary of Vietnam Academy of Science and Technology, Vol. 1, Hanoi, Vietnam, (2010). pp. 30–42.

T. C. Tsai and Y. Z.Wang. Vibration analysis and diagnosis of a cracked shaft. Journal of Sound and Vibration, 192, (3), (1996), pp. 607–620. doi:10.1006/jsvi.1996.0209.

S. P. Lele and S. K. Maiti. Modelling of transverse vibration of short beams for crack detection and measurement of crack extension. Journal of Sound and Vibration, 257, (3), (2002), pp. 559–583. doi:10.1006/jsvi.2002.5059.

Q. S. Li. Vibratory characteristics of Timoshenko beams with arbitrary number of cracks. Journal of Engineering Mechanics, 129, (11), (2003), pp. 1355–1359. doi:10.1061/(asce)0733-9399(2003)129:11(1355).

J. A. Loya, L. Rubio, and J. Fernández-Sáez. Natural frequencies for bending vibrations of Timoshenko cracked beams. Journal of Sound and Vibration, 290, (3), (2006), pp. 640–653. doi:10.1016/j.jsv.2005.04.005.

A. S. J. Swamidas, X. Yang, and R. Seshadri. Identification of cracking in beam structures using Timoshenko and Euler formulations. Journal of Engineering Mechanics, 130, (11), (2004), pp. 1297–1308. doi:10.1061/(asce)0733-9399(2004)130:11(1297).

K. Aydin. Influence of crack and slenderness ratio on the eigenfrequencies of Euler–Bernoulli and Timoshenko beams. Mechanics of Advanced Materials and Structures, 20, (5), (2013), pp. 339–352. doi:10.1080/15376494.2011.627635.

N. Khaji, M. Shafiei, and M. Jalalpour. Closed-form solutions for crack detection problem of Timoshenko beams with various boundary conditions. International Journal of Mechanical Sciences, 51, (9), (2009), pp. 667–681. doi:10.1016/j.ijmecsci.2009.07.004.

S. Fekrazadeh and N. Khaji. An analytical method for crack detection of Timoshenko beams with multiple open cracks using a test mass. European Journal of Environmental and Civil Engineering, 21, (1), (2017), pp. 24–41. doi:10.1080/19648189.2015.1090929.

### Refbacks

- There are currently no refbacks.

3rd Floor, A16 Building, 18B Hoang Quoc Viet Street, Cau Giay District, Hanoi, Vietnam Tel: (+84) 24 3791 7103 Email: vjmech@vjs.ac.vn |