Keywords: damage quantification, modal curvature, direct approach, inverse approach, piezoelectric actuators and sensors, smart beams, finite element analysis.

Modal characteristics, such as frequencies, mode shapes and their derivatives, have been extensively investigated for vibration-based damage identification as attested by the reviews [1,2]. The latter indicates that the curvature or strain energy (that is directly related to curvature) mode shapes have superior performance than frequency or mode shape based damage indicators. Their effect is highly localized in the damage region. Thus, they are highly sensitive to damage and allow its location instantly. These attractive features were also confirmed by recent research in the framework of civil engineering applications [3,4,5,6,7,8].

However, the curvature values are generally computed from the displacement modal shapes using the central difference operator approximation. Hence, a proper sampling interval for the discretization is required in practice in order to achieve good quality of the damage detection [7] and to avoid loss of accuracy [8]. Thus, some researchers are still debating on measuring directly the curvature or computing it. Nevertheless, a good alternative is to use a piezoelectric sensor, such as PVDF or PZT, which measures the average curvature under its area, thus providing conveniently direct extraction of the curvature mode shapes as results of the corresponding modal analysis [8].

The above literature review indicates that modal curvatures have been rarely used for damage identification in piezoelectric smart composite structures. As expected, using a direct (or parametric) approach, the unique available work [8] has achieved only a location and magnitude damage evaluation. In fact, it is well known that further information on the damage extent, such as the damage depth, can be reached only using learning-evolution-based algorithms, such as artificial neural networks (ANN) [3]. This was demonstrated recently for piezoelectric laminated composite beams under different boundary conditions (BC) using static signatures [9,10], including the static curvature.

Therefore, the present contribution focuses on the use of the modal curvature (second derivative of the deflection) for the damage detection (presence) and full quantification (location, length and depth) in laminated composite beam structures under various BC. Built-in piezoceramic patches are used for the electric excitation of the finite element (FE) healthy and damaged smart beam models. The latter are constructed using an in-house MATLAB-FE Toolbox; whereas, the ANN architecture is constructed using the MATLAB-Neural Networks Toolbox. The results obtained confirm the authors previous results using static curvature; i.e., the direct approach allows the detection but partial quantification (location and length) only of the simulated (material removal) damage, while the inverse (non parametric) ANN-based method allows its detection and full quantification (location, length and depth) within 6.75% of maximum absolute error for all BC and the considered first four modes.

1

S.W. Doebling, C.R. Farrar, M.B. Prime, "A summary review of vibration-based damage identification methods", The Shock and Vibration Digest, 30(2), 91-105, 1998. doi:10.1177/058310249803000201

2

Y. Zou, L. Tong, G.P. Steven, "Vibration-based model-dependent damage (delamination) identification and health monitoring for composites structures - a review", Journal of Sound and Vibration, 230(2), 357-378, 2000. doi:10.1006/jsvi.1999.2624

3

C.C. Chang, T.Y.P. Chang, Y.G. Xu, "Structural damage detection using an iterative neural network", Journal of Intelligent Material Systems and Structures, 11(1), 32-42, 2000. doi:10.1106/XU88-UW1T-A6AM-X7EA

4

J.-M. Ndambi, J. Vantomme, K. Harri, "Damage assessment in reinforced concrete beams using eigen frequencies and mode shape derivatives", Engineering Structures, 24, 501-515, 2002. doi:10.1016/S0141-0296(01)00117-1

5

J.-T. Kim, Y.-S. Ryu, H.-M. Cho, N. Stubbs, "Damage identification in beam-type structures: frequency-based method vs. mode-shape-based method", Engineering Structures, 25, 57-67, 2003. doi:10.1016/S0141-0296(02)00118-9

6

H.P. Zhou, Y.L. Xu, "Damage detection of mono-coupled periodic structures based on sensitivity analysis of modal parameters", Journal of Sound and Vibration, 285, 365-390, 2005. doi:10.1016/j.jsv.2004.08.012

7

E. Sazonov, P. Klinkhachorn, "Optimal spatial sampling interval for damage detection by curvature or strain energy mode shapes", Journal of Sound and Vibration, 285, 783-801, 2005. doi:10.1016/j.jsv.2004.08.021

8

W. Lestari, P. Qiao, "Damage detection of fiber-reinforced polymer honeycomb sandwich beams", Composite Structures, 67, 365-373, 2005. doi:10.1016/j.compstruct.2004.01.023

9

A. Benjeddou, S. Vijayakumar, I. Tawfiq, "Damage identification in laminated composite beams using piezoceramic materials and static signatures", in Proceedings of the First International Congress on Design and Modelling of Mechanical Systems, Hammamet (Tunisia), March 23-25, 2005.

10

S. Vijayakumar, A. Benjeddou, I. Tawfiq, "Damage quantification in smart laminated beams using neural networks and static signatures", in C.A. Mota Soares et al. (Eds.), Proceedings of II ECCOMAS Thematic Conference on Smart Structures and Materials, Lisbon (Portugal), July 18-21, 2005.

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