Detection of Multiple Cracks Using an Energy Method Applied to the Concept of Equivalent Healthy Beam

Abstract

We introduce herein the concept of global stiffness of a damaged beam, and the Equivalent Healthy Beam (EHB) as a damage model. This model simplifies the process of assessing multiple cracks in beams. It consists of a thinner beam with constant cross-section, but with unchanged mass, which stores in each vibration mode identical energy as the damaged beam. Hence, the model has similar frequencies as for the damaged beam. We estimate the amount of the stored energy from the beam deflection under dead mass. Each additional crack provokes a deflection increase, and consequently the beam stores less energy. The resulted EHB becomes therefore thinner. We performed simulations for beams with transversal cracks which are present on the opposite beam faces. By iteratively removing one crack relative to the other, we obtained the values of the deflections and the eigenfrequencies for the first vibration modes. Comparing the separate frequency drop due to cracks with the effect of the concomitantly acting cracks, we demonstrated the superposition principle applies successfully for most locations of the multiple cracks. As an exception, for nearby-located cracks the principle does not apply. In such a case, a bigger frequency drop is noticed.