Theoretical and Experimental Study of Damage Identification of Beams and Plates

Structural characteristic deflection shapes (CDS’s) such as mode shapes and operational deflection shapes which contain spatial information of structures are highly sensitive for damage detection and localisation in beam- or plate- type structures. Despite substantial advances in this kind of methods, several issues must be addressed to boost their efficiency and practical applications, including the following: (1) The estimation of CDS’s involves substantial inaccuracies and is mainly affected by operational, environmental, measurement and computational uncertainties. (2) The curvature estimation of CDS’s is much more sensitive to measurement noise. (3) The extraction of damage-caused singularities from CDS’s or their curvatures is difficult when the baseline data of healthy structures is not available. (4) Damage index for multi-damage identification is challenging due to the different damage location sensitivities of each CDS. These problems have been investigated and the objective of this study is to enhance the accuracy and noise robustness of baseline-free damage detection and localisation. The original contributions of this study have been made in several aspects. Firstly, common principal component analysis is proposed to enhance accuracy of mode shape estimation in operational modal analysis, which statistically evaluates the common subspace bases of a set of covariance or power spectral density matrices as the mode shapes. Secondly, without the baseline data of healthy structures, polynomial fitting approaches and low-rank models are investigated for damage localisation, which extract the damage-induced local shape singularities by using only mode shapes or mode shape curvatures of damaged structures. Thirdly, in order to fairly incorporate damage information of several modes, two robust damage indexes are proposed for beam-type structures and plate-type structures, respectively. The above studies focus on linear damage such as open cracks in beam or plate structures without nonsmooth mass and stiffness distribution. Apart from these, the identification of fatigue cracks in stepped beam-type structures is investigated as well. In the theoretical aspect, the relationship between damage and structural characteristic deflection shapes is explained. Then, the finite element models of beams and plates are coded in MATLAB, which are validated by comparing corresponding results with the commercial software ABAQUS. Moreover, the numerical models of beams and plates with multiple damage are used to verify the feasibility and efficiency of the proposed methods in damage identification. Here, the damage is introduced by reducing the depth of beams or thickness of plates. In the experimental aspect, beams and plates with multiple damage are tested to demonstrate the proposed damage detection and localisation methods. In order to acquire the data of a large number of measurement points, the advanced scanning laser Vibrometer is used. It is found that the proposed mode shape estimation approaches are demonstrated to be more accurate and noise robust than the traditional frequency domain decomposition and time domain decomposition methods. Additionally, the noise effects on spatial domain features such as mode shape and mode shape curvatures can be significantly reduced by the polynomial fitting or multi-scale approaches. Furthermore, the developed robust multi-damage indexes for beams and plates are validated to be effective by using numerical simulations and experimental results. Finally, the proposed breathing crack identification approaches are effective in localising the breathing cracks but insensitive to the steps of the beams