Damage-Caused Frequency Shifts in Beams and their Use in Structural Health Assessment

Abstract:

Transverse cracks affect the stiffness and consequently the dynamic behavior of beams, by altering the natural frequencies. Actual cracked beam models are not able to explain in-deep the vibration mechanism and, therefore, no mathematical relation able to predict frequency changes due to damage exist. This paper proposes a new damage model which better explain the dynamic behavior of beams with open and closed cracks and a mathematical relation able to predict the frequency changes due to damage. In contrast to actual models, a global approach is used, by considering the influence of the stored energy distribution for each transversal vibration mode. Since the energy loss globally quantifies the state change due to damage, it was possible to replace the cracked beam with an equivalent one having constant but reduced stiffness. Based on it, a relation indicating the frequency drop damage was contrived and tested, by means of the finite element analysis, for various damage types and locations along the beam. Simulations have shown that accurate prediction about the natural frequency shifts can be made with the proposed relation.

• Periodical: Applied Mechanics and Materials (Volume 801)
• Pages: 142-147
• DOI: https://doi.org/10.4028/www.scientific.net/AMM.801.142
• Online since: October 2015
• Authors: Gilbert Rainer Gillich*, Horia Furdui, Marius Tufoi, Zeno Iosif Praisach, Silviu Razvan Avram
• Keywords: Bilinear Model, Breathing Crack, Damage Detection, Euler-Bernoulli Beam, Frequency Shift, Open Crack

References

[1] Z. Praisach, G.R. Gillich, D.E. Birdeanu, Considerations on Natural Frequency Changes in Damaged Cantilever Beams Using FEM, Latest Trends on Engineering Mechanics, Structures, Engineering Geology (2010) 214-219.

[2] W.T. Thomson, Vibration of slender bars with discontinuities in stiffness, J. Appl. Mech. 16 (1949) 203-207.

DOI: 10.1115/1.4010044

[3] M.H.H. Shen, Y.C. Chu, Vibrations of beams with a fatigue crack, Comput. Struct. 45 (1992) 79–93.

[4] A. Rivola, P.R. White, Bispectral analysis of the bilinear oscillator with application to the detection of fatigue cracks, J. Sound Vib. 216 (1998) 889-910.

DOI: 10.1006/jsvi.1998.1738

[5] R. Ruotolo, C. Surace, P. Crespo, D. Storer, Harmonic analysis of the vibrations of a cantilevered beam with a closing crack, Comput. Struct. 61 (1996) 1057–1074.

DOI: 10.1016/0045-7949(96)00184-8

[6] G. Yan, A. de Stefano, E. Matta, R. Feng A novel approach to detecting breathing-fatigue cracks based on dynamic characteristics, J. Sound Vib. 332 (2013) 407–422.

DOI: 10.1016/j.jsv.2012.09.008

[7] A. Bovsunovsky, C. Surace Non-linearities in the vibrations of elastic structures with a closing crack: A state of the art review, Mech. Syst. Signal Pr. In Press, Corrected Proof (2015).

DOI: 10.1016/j.ymssp.2015.01.021

[8] G.R. Gillich, Z.I. Praisach, Modal identification and damage detection in beam-like structures using the power spectrum and time–frequency analysis, Signal Process. 96 (2014) 29–44.

DOI: 10.1016/j.sigpro.2013.04.027

[9] G.R. Gillich, Z.I. Praisach, C.M. Iavornic, Reliable method to detect and assess damages in beams based on frequency changes, Proceedings of the ASME International Design Engineering Technical Conferences and Computers and Information in Engineering Conference 2012, VOL 1, PTS A and B, (2012).

DOI: 10.1115/detc2012-70094

[10] G.R. Gillich, Z.I. Praisach, M.A. Wahab, O. Vasile, Localization of Transversal Cracks in Sandwich Beams and Evaluation of Their Severity, Shock Vib. (2014) Article Number: 607125.

DOI: 10.1155/2014/607125