Reconstruction Method for Damage Detection in Beams Based on Natural Frequency and Antiresonant Frequency Measurements
Publication: Journal of Engineering Mechanics
Volume 136, Issue 3
Abstract
This paper deals with a dynamic method for damage detection in beams. Under the assumption that the damaged beam is a perturbation of the undamaged one, it is shown that natural frequency and antiresonant frequency shifts induced by structural damage contain information on certain generalized Fourier coefficients of the stiffness variation caused by the degradation. A reconstruction method based on this property is proposed to solve the inverse problem. Cases with pseudoexperimental and experimental data are discussed. The results are in good agreement with the theory, provided that average frequency and antiresonant frequency shifts are bigger than modeling/measurement errors.
Get full access to this article
View all available purchase options and get full access to this article.
References
Adams, R. D., Cawley, P., Pye, C. J., and Stone, B. J. (1978). “A vibration technique for non-destructively assessing the integrity of structures.” J. Mech. Eng. Sci., 20(2), 93–100.
Barcilon, V. (1976). “Inverse problem for a vibrating beam.” Appl. Math. Phys., 27, 347–358.
Barnes, D. C. (1991). “The inverse eigenvalue problem with finite data.” SIAM J. Math. Anal., 22(3), 732–753.
Borg, G. (1946). “Eine umkehrung der sturm-liouvilleschen eigenwertaufgabe. Bestimmung der differentialgleichung durch die eigenwerte.” Acta Math., 78, 1–96.
Brezis, H. (1986). Analisi funzionale, Liguore Editore, Naples, Italy.
Buda, G., and Caddemi, S. (2007). “Identification of concentrated damages in Euler-Bernoulli beams under static loads.” J. Eng. Mech., 133(8), 942–956.
Caddemi, S., Caliò, I., and Liseni, S. (2009). “A procedure for the identification of concentrated damages on beams by free vibration tests.” Proc., XIX AIMETA, Aras Editions, Ancona, Italy.
Caddemi, S., and Morassi, A. (2007). “Crack detection in elastic beams by static measurements.” Int. J. Solids Struct., 44(16), 5301–5315.
Capecchi, D., and Vestroni, F. (1999). “Monitoring of structural systems by using frequency data.” Earthquake Eng. Struct. Dyn., 28, 447–461.
Casas, J. R., and Aparicio, A. C. (1994). “Structural damage identification from dynamic-test data.” J. Struct. Eng., 120(8), 2437–2450.
Cerri, M. N., and Vestroni, F. (2000). “Detection of damage in beams subjected to diffused cracking.” J. Sound Vib., 234(2), 259–276.
D’Ambrogio, W., and Fregolent, A. (2000). “The use of antiresonances for robust model updating.” J. Sound Vib., 236, 227–243.
D’Ambrogio, W., and Fregolent, A. (2003). “Results obtained by minimising natural frequency and antiresonance errors of a beam model.” Mech. Syst. Signal Process., 17(1), 29–37.
Davini, C., Morassi, A., and Rovere, N. (1995). “Modal analysis of notched bars: Tests and comments on the sensitivity of an identification technique.” J. Sound Vib., 179(3), 513–527.
Dharmaraju, N., and Sinha, J. K. (2005). “Some comments on use of antiresonances for crack identification in beams.” J. Sound Vib., 286, 669–671.
Dilena, M., and Morassi, A. (2004). “The use of antiresonances for crack detection in beams.” J. Sound Vib., 276(1–2), 195–214.
Dilena, M., and Morassi, A. (2006). “Damage detection in discrete vibrating systems.” J. Sound Vib., 289(4–5), 830–850.
Dilena, M., and Morassi, A. (2009). “Structural health monitoring of rods based on natural frequency and antiresonant frequency measurements.” Struct. Health Monit., 8(2), 149–173.
Elcrat, A., and Papanicolau, V. G. (1997). “On the inverse problem of a fourth-order self-adjoint binomial operator.” SIAM J. Math. Anal., 28(4), 886–896.
Freund, L. B., and Herrmann, G. (1976). “Dynamic fracture of a beam or plate in plane bending.” J. Appl. Mech., 76, 112–116.
Gladwell, G. M. L. (1986). “The inverse problem for the Euler-Bernoulli beam from spectral data.” Proc. R. Soc. London, Ser. A, 407, 199–218.
Gladwell, G. M. L., England, A. H., and Wang, D. (1987). “Examples of reconstruction of an Euler-Bernoulli beam from spectral data.” J. Sound Vib., 119, 81–94.
Gladwell, G. M. L., and Morassi, A. (1999). “Estimating damage in a rod from changes in node positions.” Inverse Probl. Eng., 7(3), 215–233.
Gudmundson, P. (1982). “Eigenfrequency changes of structures due to cracks, notches or other geometrical changes.” J. Mech. Phys. Solids, 30(5), 339–353.
Hald, O. (1978). “The inverse Sturm-Liouville problem and the Rayleigh-Ritz method.” Math. Comput., 32(143), 687–705.
Hassiotis, S., and Jeong, G. D. (1993). “Assessment of structural damage from natural frequency measurements.” Comput. Struc., 49(4), 679–691.
Hearn, G., and Testa, R. B. (1991). “Modal analysis for damage detection in structures.” J. Struct. Eng., 117, 3042–3063.
Humar, J., Bagchi, A., and Xu, H. (2006). “Performance of vibration-based techniques for the identification of structural damage.” Struct. Health Monit., 5(3), 215–241.
Jones, K., and Turcotte, J. (2002). “Finite element model updating using antiresonant frequencies.” J. Sound Vib., 252, 717–727.
Khoo, L. M., Mantena, P. R., and Jadhav, P. (2004). “Structural damage assessment using vibration modal analysis.” Struct. Health Monit., 3(2), 177–194.
Knobel, R., and Lowe, B. D. (1993). “An inverse Sturm-Liouville problem for an impedance.” Z. Angew. Math. Phys., 44, 433–450.
Law, S. S., Shi, Z. Y., and Zhang, L. M. (1998). “Structural damage detection from incomplete and noisy modal test data.” J. Eng. Mech., 124(11), 1280–1288.
Lele, S. P., and Maiti, S. K. (2002). “Modeling of transverse vibration of short beams for crack detection and measurement of crack extension.” J. Sound Vib., 257(3), 559–583.
Liang, R. Y., Hu, J., and Choy, F. (1992). “Quantitative NDE technique for assessing damages in beam structures.” J. Eng. Mech., 118(7), 1468–1487.
Lowe, B. D. (1993). “On the construction of an Euler-Bernoulli beam from spectral data.” J. Sound Vib., 163(1), 165–171.
Morassi, A. (1993). “Crack-induced changes in eigenparameters of beam structures.” J. Eng. Mech., 119(9), 1798–1803.
Morassi, A. (2001). “Identification of a crack in a rod based on changes in a pair of natural frequencies.” J. Sound Vib., 242, 577–596.
Morassi, A. (2007). “Damage detection and generalized Fourier coefficients.” J. Sound Vib., 302, 229–259.
Morassi, A., and Rollo, M. (2001). “Identification of two cracks in a simply supported beam from minimal frequency measurements.” J. Vib. Control, 7, 729–739.
Morassi, A., and Rovere, N. (1997). “Localizing a notch in a steel frame from frequency measurements.” J. Eng. Mech., 123(5), 422–432.
Narkis, Y. (1994). “Identification of crack location in vibrating simply supported beams.” J. Sound Vib., 172, 549–558.
Niordson, F. I. (1967). “A method for solving inverse eigenvalue problems.” Recent progress in applied mechanics: The Folke Odqvist volume, B. Broberg, J. Hults, and F. I. Niordson, eds., Almqvist and Wiksell, Stockholm, Sweden.
Petroski, H. J. (1984). “Comments on ‘Free vibration of beams with abrupt changes in cross-section’.” J. Sound Vib., 93(1), 157–158.
Ren, W. X., and De Roeck, G. (2002). “Structural damage identification using modal data. I: Simulation verification.” J. Struct. Eng., 128(1), 87–95.
Rizos, P. F., Aspragathos, N., and Dimarogonas, A. D. (1990). “Identification of crack location and magnitude in a cantilever beam from the vibration modes.” J. Sound Vib., 138, 381–388.
Röhrl, N. (2005). “A least-squares functional for solving inverse Sturm-Liouville problems.” Inverse Probl., 21, 2009–2017.
Schueller, A. (2001). “Uniqueness for near-constant data in fourth-order inverse eigenvalue problems.” J. Math. Anal. Appl., 258, 658–670.
Sinha, J. K., Friswell, M. I., and Edwards, S. (2002). “Simplified models for the location of cracks in beam structures using measured vibration data.” J. Sound Vib., 251(1), 13–38.
Teughels, A., Maeck, J., and De Roeck, G. (2002). “Damage assessment by FE model updating using damage functions.” Comput. Struc., 80, 1869–1879.
Thomson, W. T. (1949). “Vibration of slender bars with discontinuities in stiffness.” J. Appl. Mech., 16, 203–207.
Vestroni, F., and Capecchi, D. (2000). “Damage detection in beam structures based on frequency measurements.” J. Eng. Mech., 126, 761–768.
Wahl, F., Schmidt, G., and Forrai, L. (1999). “On the significance of antiresonance frequencies in experimental structural analysis.” J. Sound Vib., 219, 379–394.
Wu, Q. (1994). “Reconstruction of integrated crack function of beams from eigenvalue shifts.” J. Sound Vib., 173(2), 279–282.
Information & Authors
Information
Published In
Copyright
© 2010 ASCE.
History
Received: Nov 20, 2007
Accepted: Oct 26, 2009
Published online: Feb 12, 2010
Published in print: Mar 2010
Notes
Note. Associate Editor: Erik A. Johnson
Authors
Metrics & Citations
Metrics
Citations
Download citation
If you have the appropriate software installed, you can download article citation data to the citation manager of your choice. Simply select your manager software from the list below and click Download.