Damage quantification in beam-type structures using modal curvature ratio

Modal curvature ratio approach for the localization and quantification of damage in beam-type structures is proposed, demonstrating capability across both dense and sparse measurement grids. This method directly utilizes modal properties (i.e., mode shape) without the requirement of a complete structural model of the structure. This study involves the mathematical derivation of the proposed algorithm, which relies on establishing correlations between modal parameters derived from fundamental theoretical formulations for both pristine and damaged beams. The method’s efficiency and universality are confirmed through numerical case studies that identify and measure damage under various predefined scenarios. Numerical modal analysis is conducted using MATLAB for both damaged and pristine beams. The proposed approach demonstrates a high degree of accuracy in localizing and quantifying the damage. Notably, the approach exhibits a remarkable capability to identify and measure damage with a stiffness loss, as low as 5%. The investigation extends to multiple damage scenarios and considers the influence of noise. The methodology proves effective in discerning the severity of damage, showcasing improvements over prior results. Eventually, an integrated model-free approach for damage locating and quantification is presented for proposal based on the mathematical and numerical method. Considering the versatility of beams as structural elements, the proposed method provides a potential instrument for real-world damage detection in the field of structural health monitoring.