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Structures are usually designed to undergo some yielding, cracking and damage during any catastrophic events like earthquakes. It is necessary to identify these damage locations to avoid the failure of the structure. In this study, a novel method of damage localization for a linear one-dimensional mathematical model of Euler-Bernoulli beam is developed. The damage is modeled as a normalized box-car function. The first-order perturbation in the form of a small change in the stiffness is introduced to the structure. This study employed an effective boxcar filtration technique in damage localization. The proposed formulation shows a distinct peak at the damage location. Further, a two-point roving technique is employed on the experimental model of an overhanging beam under impact loading to check the effectiveness of the proposed localization procedure under real measurement conditions. For its entirety, the finite element model for different end conditions through numerical simulations is also briefly addressed. It is observed that the results obtained from the experimental investigation and the simulation studies are in agreement with the proposed formulation. The proposed methodology does not consider the effect of noise, which can be addressed as the future scope of the present study.

Perturbation approach for damage localization in beam-type structures: analytical, experimental and numerical exposition