Exact receptance function and receptance curvature of a clamped-clamped continuous cracked beam

Nguyen Viet Khoa, Cao Van Mai, Dao Thi Bich Thao
Author affiliations

Authors

  • Nguyen Viet Khoa Institute of Mechanics, VAST, 18 Hoang Quoc Viet, Hanoi, Vietnam
  • Cao Van Mai Institute of Mechanics, VAST, 18 Hoang Quoc Viet, Hanoi, Vietnam
  • Dao Thi Bich Thao Institute of Mechanics, VAST, 18 Hoang Quoc Viet, Hanoi, Vietnam

DOI:

https://doi.org/10.15625/0866-7136/14566

Keywords:

receptance, curvature of receptance, frequency response function, crack, crack detection

Abstract

The receptance function has been studied and applied widely since it interrelates the harmonic excitation and the response of a structure in the frequency domain. This paper presents the derivation of the exact receptance function of continuous cracked beams and its application for crack detection. The receptance curvature is defined as the second derivative of the receptance. The influence of the crack on the receptance and receptance curvature is investigated. It is concluded that when there are cracks the receptance curvature has sharp changes at the crack positions. This can be applied for the crack detection purpose. In this paper, the numerical simulations are provided.

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References

R. E. D. Bishop and D. C. Johnson. The mechanics of vibration. Cambridge University Press, (1960).

B. Yang. Exact receptances of nonproportionally damped dynamic systems. Journal of Vibration and Acoustics, 115, (1), (1993), pp. 47–52.

J. E. Mottershead. On the zeros of structural frequency response functions and their sensitivities. Mechanical Systems and Signal Processing, 12, (5), (1998), pp. 591–597. https://doi.org/10.1006/mssp.1998.0167. https://doi.org/10.1006/mssp.1998.0167.">

M. Gurgoze. Receptance matrices of viscously damped systems subject to several constraint equations. Journal of Sound and Vibration, 230, (5), (2000), pp. 1185–1190.

A. Karakas and M. Gurgoze. A novel formulation of the receptance matrix of nonproportionally damped dynamic systems. Journal of Sound and Vibration, 264, (2003), pp. 733–740. https://doi.org/10.1016/S0022-460X(02)01507-9. https://doi.org/10.1016/S0022-460X(02)01507-9.">

P. Albertelli, M. Goletti, and M. Monno. A new receptance coupling substructure analysis methodology to improve chatter free cutting conditions prediction. International Journal of Machine Tools and Manufacture, 72, (2013), pp. 16–24. https://doi.org/10.1016/j.ijmachtools.2013.05.003. https://doi.org/10.1016/j.ijmachtools.2013.05.003.">

G. Muscolino and R. Santoro. Explicit frequency response function of beams with crack of uncertain depth. Procedia Engineering, 199, (2017), pp. 1128–1133. https://doi.org/10.1016/j.proeng.2017.09.239. https://doi.org/10.1016/j.proeng.2017.09.239.">

Y.-S. Lee and M.-J. Chung. A study on crack detection using eigenfrequency test data. Computers & Structures, 77, (3), (2000), pp. 327–342. https://doi.org/10.1016/S0045-7949(99)00194-7. https://doi.org/10.1016/S0045-7949(99)00194-7.">

D. Y. Zheng and N. J. Kessissoglou. Free vibration analysis of a cracked beam by finite element method. Journal of Sound and Vibration, 273, (3), (2004), pp. 457–475. https://doi.org/10.1016/S0022-460X(03)00504-2. https://doi.org/10.1016/S0022-460X(03)00504-2.">

P. Gudmundson. The dynamic behaviour of slender structures with cross-sectional cracks. Journal of the Mechanics and Physics of Solids, 31, (4), (1983), pp. 329–345. https://doi.org/10.1016/0022-5096(83)90003-0. https://doi.org/10.1016/0022-5096(83)90003-0.">

J. Thalapil and S. K. Maiti. Detection of longitudinal cracks in long and short beams using changes in natural frequencies. International Journal of Mechanical Sciences, 83, (2014), pp. 38–47. https://doi.org/10.1016/j.ijmecsci.2014.03.022. https://doi.org/10.1016/j.ijmecsci.2014.03.022.">

N. V. Khoa. Monitoring a sudden crack of beam-like bridge during earthquake excitation. Vietnam Journal of Mechanics, 35, (3), (2013), pp. 189–202. https://doi.org/10.15625/0866-7136/35/3/2561. https://doi.org/10.15625/0866-7136/35/3/2561.">

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. https://doi.org/10.1016/j.jsv.2009.07.008. https://doi.org/10.1016/j.jsv.2009.07.008.">

S. Caddemi and I. Caliò. Exact reconstruction of multiple concentrated damages on beams. Acta Mechanica, 225, (11), (2014), pp. 3137–3156. https://doi.org/10.1007/s00707-014-1105-5. https://doi.org/10.1007/s00707-014-1105-5.">

T. V. Lien, N. T. Duc, and N. T. Khiem. Mode shape analysis of multiple cracked functionally graded beam-like structures by using dynamic stiffness method. Vietnam Journal of Mechanics, 39, (3), (2017), pp. 215–228. https://doi.org/10.15625/0866-7136/8631. https://doi.org/10.15625/0866-7136/8631.">

K. V. Nguyen. Mode shapes analysis of a cracked beam and its application for crack detection. Journal of Sound and Vibration, 333, (3), (2014), pp. 848–872. https://doi.org/10.1016/j.jsv.2013.10.006. https://doi.org/10.1016/j.jsv.2013.10.006.">

R. F. Hoskins. Delta function. Horwood Publishing Limited, second edition, (2009).

R. Lyons. Understanding digital signal processing. Prentice Hall, Boston, USA, third edition, (2011).

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Published

28-12-2019

How to Cite

[1]
N. V. Khoa, C. V. Mai and D. T. B. Thao, Exact receptance function and receptance curvature of a clamped-clamped continuous cracked beam, Vietnam J. Mech. 41 (2019) 349–361. DOI: https://doi.org/10.15625/0866-7136/14566.

Issue

Vol. 41 No. 4 (2019)

Section

Research Article

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Creative Commons License

This work is licensed under a Creative Commons Attribution-ShareAlike 4.0 International License.

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