Improvement on modal curvatures methods for multiple damage identification in beams

PurposeThe purpose of this paper is to present a study on the application of four damage factors to several single and multiple damage scenarios of aluminium beams. Each one of these damage factors is defined by the information given by modal curvatures of the beams.Design/methodology/approachThe methodology consisted of a first experimental stage in which the modal rotations were measured with shearography and a subsequent numerical analysis in order to obtain the modal curvatures. To this end, three finite difference formulae were applied. The modal curvatures were then used to calculate the damage factors.FindingsIt was found that the profile of the damage factors varies according to the finite difference formula used. In view of the findings, the differences among the damage factors analysed are highlighted and some final recommendations to improve damage identifications via modal curvature-based are presented.Originality/valueTo the best of the authors’ knowledge, the application and comparison of several finite difference formulae and corresponding optimal sampling has not been carried out before. With the proposed approach, it is possible to identify multiple damages, which is still a great challenge. The post-processing of shearography measurements with a numerical method, which is inherently a multidisciplinary approach, is also a substantial improvement upon other type of approaches found in the literature.

Damage Detection in Glass/Epoxy Laminated Composite Plates Using Modal Curvature for Structural Health Monitoring Applications

This paper deals with detection of macro-level crack type damage in rectangular E-Glass fiber/Epoxy resin (LY556) laminated composite plates using modal analysis. Composite plate-like structures are widely found in aerospace and automotive structural applications which are susceptible to damages. The formation of cracks in a structure that undergoes vibration may lead to catastrophic events such as structural failure, thus detection of such occurrences is considered necessary. In this research, a novel technique called as node-releasing technique in Finite Element Analysis (FEA), which was not attempted by the earlier researchers, is used to model the perpendicular cracks (the type of damage mostly considered in all the pioneering research works) and also slant cracks (a new type of damage considered in the present work) of various depths and lengths for Unidirectional Laminate (UDL) ([0]S and [45]S) composite layered configurations using commercial FE code Ansys, thus simulating the actual damage scenario. Another novelty of the present work is that the crack is modeled with partial depth along the thickness of the plate, instead of the through the thickness crack which has been of major focus in the literature so far, in order to include the possibility of existence of the crack up to certain layers in the laminated composite structures. The experimental modal analysis is carried out to validate the numerical model. Using central difference approximation method, the modal curvature is determined from the displacement mode shapes which are obtained via finite element analysis. The damage indicators investigated in this paper are Normalized Curvature Damage Factor (NCDF) and modal strain energy-based methods such as Strain Energy Difference (SED) and Damage Index (DI). It is concluded that, all the three damage detection algorithms detect the transverse crack clearly. In addition, the damage indicator NCDF seems to be more effective than the other two, particularly when the detection is for damage inclined to the longitudinal axis of the plate. The proposed method will provide the base data for implementing online structural health monitoring of structures using technologies such as Machine Learning, Artificial Intelligence, etc.

Damage Identification Method of Beam Structure Based on Modal Curvature Utility Information Entropy

Generally, the damage of the structure will lead to the discontinuity of the local mode shape, which can be well reflected by the modal curvature of the structure, and the local information entropy of the beam structure will also change with the discontinuity of the mode. In this paper, based on the information entropy theory and combining the advantages of modal curvature index in damage identification of beam structure, the modal curvature utility information entropy index is proposed. The modal curvature curves of nondestructive structures were obtained by fitting the modal curvature curves of damage structures with the gapped smoothing technique to avoid dependence on the baseline data of nondestructive structures. The index comprehensively reflects the damage state of the structure by calculating mutual weight change matrix and the weight-probability coefficient. The performance of the new index was verified by the finite element simulation and model test of simply supported beam, respectively. The results show that the modal curvature utility information entropy index takes advantage of the modal curvature index which is sensitive to damage and can overcome its shortcomings effectively. The index proposed can identify the damage location and damage degree accurately and has certain noise immunity, which provides an effective damage identification indicator for beam structures.

Mode shape curvature of multiple cracked beam and its use for crack identification in beam-like structures

The problem of using the modal curvature for crack detection is discussed in this paper based on an exact expression of mode shape and its curvature. Using the obtained herein exact expression for the mode shape and its curvature, it is demonstrated that the mode shape curvature is really more sensitive to crack than mode shape itself. Nevertheless, crack-induced change in the approximate curvature calculated from the exact mode shape by the central finite difference technique (Laplacian) is much greater in comparison with both the mode shape and curvature. It is produced by the fact, shown in this study, that miscalculation of the approximate curvature is straightforwardly dependent upon crack magnitude and resolution step of the finite difference approximation. Therefore, it can be confidently recommended to use the approximate curvature for multiple crack detection in beam by properly choosing the approximation mesh. The theoretical development has been illustrated by numerical results.