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Civil-Comp Proceedings
ISSN 1759-3433
CCP: 83
Edited by: B.H.V. Topping, G. Montero and R. Montenegro
Paper 101

Damage Quantification in Smart Beams Using Modal Curvatures: Direct and Inverse Approaches

A. Benjeddou, S. Vijayakumar and I.H. Tawfiq

Laboratory for Engineering of Mechanical Systems and Materials, High Institute of Mechanics at Paris, Saint Ouen, France

Full Bibliographic Reference for this paper
A. Benjeddou, S. Vijayakumar, I.H. Tawfiq, "Damage Quantification in Smart Beams Using Modal Curvatures: Direct and Inverse Approaches", in B.H.V. Topping, G. Montero, R. Montenegro, (Editors), "Proceedings of the Eighth International Conference on Computational Structures Technology", Civil-Comp Press, Stirlingshire, UK, Paper 101, 2006. doi:10.4203/ccp.83.101
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.

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