Damage Localization Beyond Modal Curvature Methods

Damage Localization Beyond Modal Curvature Methods

Giada FARACO, Andrea Vincenzo DE NUNZIO, Nicola Ivan GIANNOCCARO, Arcangelo MESSINA

Abstract. Structural health monitoring and damage localization using non-destructive techniques have long been key research topics, aimed at detecting defects that may evolve into critical failures if left unnoticed. In this context, reference-free approaches are particularly important, since information about the undamaged state is often unavailable. Among the various techniques, vibration-based methods, and particularly the analysis of mode shapes, have been widely investigated. The curvature method, based on the second derivative of mode shapes, has attracted significant attention, proving to be one of the most reliable and established techniques for identifying localized stiffness reductions associated with damage without requiring baseline data. However, the use of second- or higher-order derivatives poses notable challenges when dealing with experimental data, as these operations tend to amplify measurement noise and complicate the estimation process. To overcome these limitations, the authors have proposed an extension of traditional curvature-based methods by introducing a novel damage indicator based on the first derivative of mode shapes, combined with appropriate filtering techniques. The aim of this manuscript is to provide an experimental validation of this previously developed approach, showing how it simplifies the computational procedure while preserving, and in some cases enhancing, the accuracy of damage detection and localization. As in conventional curvature-based methods, damage is identified through the presence of localized peaks in the derived indicators. The effectiveness of the proposed approach is demonstrated numerically, through a case study of a stepped beam with a circular cross-section.

Keywords
Damage Detection, Damage Localization, Mode Shapes, Mode Shapes Derivatives

Published online 11/8/2026, 5 pages
Copyright © 2026 by the author(s)
Published under license by Materials Research Forum LLC., Millersville PA, USA

Citation: Giada FARACO, Andrea Vincenzo DE NUNZIO, Nicola Ivan GIANNOCCARO, Arcangelo MESSINA, Damage Localization Beyond Modal Curvature Methods, Materials Research Proceedings, Vol. 73, pp 302-306, 2026

DOI: https://doi.org/10.21741/9781644904459-59

The article was published as article 59 of the book Mechanics of Advanced Materials and Structures

Content from this work may be used under the terms of the Creative Commons Attribution 3.0 license. Any further distribution of this work must maintain attribution to the author(s) and the title of the work, journal citation and DOI.

References
[1] A.K. Pandey, M. Biswas, M.M. Samman, Damage detection from changes in curvature mode shapes, J. Sound Vib. 145 (1991) 321–332. https://doi.org/10.1016/0022-460X(91)90595-B
[2] C.P. Ratcliffe, Damage detection using a modified Laplacian operator on mode shape data, J. Sound Vib. 204 (1997) 505–517. https://doi.org/10.1006/jsvi.1997.0961
[3] R.P.C. Sampaio, N.M.M. Maia, J.M.M. Silva, Damage detection using the frequency-response-function curvature method, J. Sound Vib. 226 (1999) 1029–1042. https://doi.org/10.1006/jsvi.1999.2340
[4] A. Gentile A, A. Messina, Detection of crack by only measured mode shapes in damaged conditions, in: The Cromwell Press Ltd., University of Wales Swansea, 2002.
[5] E. Parloo, P. Guillaume, M. Van Overmeire, Damage assessment using mode shape sensitivities, Mech. Syst. Signal Process. 17 (2003) 499–518. https://doi.org/10.1006/mssp.2001.1429
[6] Q. Wang, X. Deng, Damage detection with spatial wavelets, Int. J. Solids Struct. 36 (1999) 3443–3468. https://doi.org/10.1016/S0020-7683(98)00152-8
[7] S.-T. Quek, Q. Wang, L. Zhang, K.-K. Ang, Sensitivity analysis of crack detection in beams by wavelet technique, Int. J. Mech. Sci. 43 (2001) 2899–2910. https://doi.org/10.1016/S0020-7403(01)00064-9
[8] J.-C. Hong, Y.Y. Kim, H.C. Lee, Y.W. Lee, Damage detection using the Lipschitz exponent estimated by the wavelet transform: applications to vibration modes of a beam, Int. J. Solids Struct. 39 (2002) 1803–1816. https://doi.org/10.1016/S0020-7683(01)00279-7
[9] A. Gentile, A. Messina, On the continuous wavelet transforms applied to discrete vibrational data for detecting open cracks in damaged beams, Int. J. Solids Struct. 40 (2003) 295–315. https://doi.org/10.1016/S0020-7683(02)00548-6
[10] S. Rucevskis, M. Wesolowski, Identification of Damage in a Beam Structure by Using Mode Shape Curvature Squares, Shock Vib. 17 (2010) 601–610. https://doi.org/10.1155/2010/729627
[11] Yazdanpanah, O., Seyedpoor, S.M., Bengar, H. Akbarzadeh, A new damage detection indicator for beams based on mode shape data, Struct. Eng. Mech. 53 (2015) 725–744. https://doi.org/10.12989/SEM.2015.53.4.725
[12] D. Dessi, G. Camerlengo, Damage identification techniques via modal curvature analysis: Overview and comparison, Mech. Syst. Signal Process. 52–53 (2015) 181–205. https://doi.org/10.1016/j.ymssp.2014.05.031
[13] M.C. Porcu, D.M. Patteri, S. Melis, F. Aymerich, Effectiveness of the FRF curvature technique for structural health monitoring, Constr. Build. Mater. 226 (2019) 173–187. https://doi.org/10.1016/j.conbuildmat.2019.07.123
[14] G. Faraco, A.V. De Nunzio, N.I. Giannoccaro, A. Messina, A Non-destructive Approach for Damage Localization in Civil or Mechanical Structures Without Reference Model, in: E. Caetano, Á. Cunha (Eds.), Exp. Vib. Anal. Civ. Eng. Struct., Springer Nature Switzerland, Cham, 2025: pp. 671–680. https://doi.org/10.1007/978-3-031-96110-6_65
[15] G. Faraco, A.V.D. Nunzio, N.I. Giannoccaro, A. Messina, Experimental Validation on a Real-World Truss Structure of a Damage Localization Method Based on Mode Shape Derivatives, Struct. Durab. Health Monit. 0 (2025) 1–10. https://doi.org/10.32604/sdhm.2025.075327
[16] W.E. Boyce, R.C. DiPrima, Elementary differential equations and boundary value problems, Jonh Wily & Sons, New York, NY, 1997.