Effect of intermediate supports location on natural frequencies of multiple cracked continuous beams

Do Nam, Nguyen Tien Khiem, Le Khanh Toan, Nguyen Thi Thao, Pham Thi Ba Lien
Author affiliations


  • Do Nam VNU University of Engineering and Technology, Hanoi, Vietnam
  • Nguyen Tien Khiem Institute of Mechanics, Vietnam Academy of Science and Technology, Hanoi, Vietnam
  • Le Khanh Toan Institute of Mechanics, Vietnam Academy of Science and Technology, Hanoi, Vietnam
  • Nguyen Thi Thao Institute of Mechanics, Vietnam Academy of Science and Technology, Hanoi, Vietnam
  • Pham Thi Ba Lien University of Transport and Communication, Vietnam




continuous beam, multi-span beam, multiple cracked beam, natural frequency


The present paper deals with free vibration of multiple cracked continuous beams with intermediate rigid supports. A simplified method is proposed to obtain general solution of free vibration in cracked beam with intermediate supports that is then used for natural frequency analysis of the beam in dependence upon cracks and support locations. Numerical results show that the support location or ratio of span lengths in combination with cracks makes a significant effect on eigenfrequency spectrum of beam. The discovered effects of support locations on eigenfrequency spectrum of cracked continuous beam are useful for detecting not only cracks but also positions of vanishing deflection on the beam.


Download data is not yet available.


Y. K. Lin. Free vibrations of a continuous beam on elastic supports. International Journal of Mechanical Sciences, 4, (5), (1962), pp. 409–423. doi:10.1016/s0020-7403(62)80027-7.

H. P. Lin and S. C. Chang. Free vibration analysis of multi-span beams with intermediate flexible constraints. Journal of Sound and Vibration, 281, (1-2), (2005), pp. 155–169. doi:10.1016/j.jsv.2004.01.010.

D. Zhou. Free vibration of multi-span Timoshenko beams using static Timoshenko beam functions. Journal of Sound and Vibration, 241, (4), (2001), pp. 725–734. doi:10.1006/jsvi.2000.3266.

K. Saeedi and R. B. Bhat. Clustered natural frequencies in multi-span beams with constrained characteristic functions. Shock and Vibration, 18, (5), (2011), pp. 697–707. doi:10.1155/2011/940461.

D. Y. Zheng, Y. K. Cheung, F. T. K. Au, and Y. S. Cheng. Vibration of multi-span non-uniform beams under moving loads by using modified beam vibration functions. Journal of Sound and Vibration, 212, (3), (1998), pp. 455–467. doi:10.1006/jsvi.1997.1435.

M. Ichikawa, Y. Miyakawa, and A. Matsuda. Vibration analysis of the continuous beam subjected to a moving mass. Journal of Sound and Vibration, 230, (3), (2000), pp. 493–506. doi:10.1006/jsvi.1999.2625.

Y. Yesilce and O. Demirdag. Effect of axial force on free vibration of Timoshenko multi-span beam carrying multiple spring-mass systems. International Journal of Mechanical Sciences, 50, (6), (2008), pp. 995–1003. doi:10.1016/j.ijmecsci.2008.03.001.

Y. Yesilce. Free and forced vibrations of an axially-loaded Timoshenko multi-span beam carrying a number of various concentrated elements. Shock and Vibration, 19, (4), (2012), pp. 735–752. doi:10.1155/2012/579287.

K. Henchi, M. Fafard, G. Dhatt, and M. Talbot. Dynamic behaviour of multi-span beams under moving loads. Journal of Sound and Vibration, 199, (1), (1997), pp. 33–50. doi:10.1006/jsvi.1996.0628.

N. Azizi, M. M. Saadatpour, and M. Mahzoon. Using spectral element method for analyzing continuous beams and bridges subjected to a moving load. Applied Mathematical Modelling, 36, (8), (2012), pp. 3580–3592. doi:10.1016/j.apm.2011.10.019.

H. B. Liu, H. H. Nguyen, and Y. M. Xiang. Vibration analysis of a multi-span continuous beam with cracks. Applied Mechanics and Materials, 256, (2013), pp. 964–972. doi:10.4028/www.scientific.net/AMM.256-259.964.

T. V. Lien and T. A. Hao. Determination of mode shapes of a multiple cracked beam element and its application for free vibration analysis of a multi-span continuous beam. Vietnam Journal of Mechanics, 35, (4), (2013), pp. 313–323. doi:10.15625/0866-7136/35/4/2520.

D. S. Sharma, M. J. Mungla, and K. H. Barad. Vibration-based non-destructive technique to detect crack in multi-span beam. Nondestructive Testing and Evaluation, 30, (4), (2015), pp. 291–311. doi:10.1080/10589759.2015.1029475.

M. J. Mungla, D. S. Sharma, and R. R. Trivedi. Inverse method to identify crack parameters in multi-span beam using genetic algorithm. Nondestructive Testing and Evaluation, 32, (3), (2017), pp. 301–318. doi:10.1080/10589759.2016.1226302.

G. Tan, Z. Zhu,W.Wang, and Y. Cheng. Free vibration analysis of a uniform continuous beamwith an arbitrary number of cracks and spring-mass systems. Arabian Journal for Science and Engineering, (2017), pp. 1–16. doi:10.1007/s13369-017-2933-0.

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, (3-5), (2009), pp. 473–489. doi:10.1016/j.jsv.2009.07.008.

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.






Research Article

Most read articles by the same author(s)

1 2 3 4 > >>