Efficient Natural Frequency-Based Crack Detection Based on a Strain Energy Approach

Accurate and efficient modelling of damage-induced modifications to the vibration response of structures is crucial for the early detection and mitigation of structural degradation. In this paper, a novel analytical method for modelling the effects of arbitrarily oriented cracks on the natural frequencies of plates has been developed. Cracks are represented by equivalent rotational springs, and their influence is incorporated through a compliance-based formulation that quantifies the additional rotation induced at the crack location. This enables a fully analytical estimation of natural frequency shifts for arbitrarily oriented cracks. The relationship between the location and severity of the crack and the degradation in the natural frequencies of the plate was developed using a strain energy approach based on a modified parametric crack-compliance relationship. The developed analytical approach was validated against finite element simulation results, achieving 91% accuracy with a computational time of 0.023 s. The enhanced capability of the proposed compliance-based analytical approach to model the influence of arbitrarily oriented open cracks on vibration response is substantial. The proposed model was demonstrated to work with inverse identification algorithms to infer the location and severity of cracks in plate structures within 50–60 s. The study shows the proposed improved crack compliance-based analytical formulation to have significant computational advantages and a sufficient level of accuracy for modelling and identification of cracks in simple structures.