Wavelet-based numerical investigation on damage localisation and quantification in beams using static deflections and mode shapes

Abstract

In this paper discrete Wavelet-based analysis (DWT) was applied to recognise, localise and quantify simulated damages in beams. The damages were simulated by reducing the Young's modulus, whose value for the healthy beam is 210 GPa. Damage beams were stepped reduced at 5% from its original value – i.e. 210 GPa – up to 50%. Both analysis, static and modal, were performed through finite elements varying, whenever it is possible, boundary conditions – i.e. double clamped, simply supported or cantilever beams, the load type (concentrated or distributed) and the local of the load and damage application. Further, the Wavelet analysis was performed through Matlab® package and two different indexes were computed: d1index and d2index. The first one was only employed to recognise and localise the damaged element, whereas the second index was invoked to quantify the damage. As the main outcomes from this paper one can cite the successful localisation and quantification of the damage through the indexes. Also, it was worth to mention the robustness of proposed indexes (d1 and d2) which their effectiveness was tested facing several changes imposed to boundary conditions of the beams, load system and the damage severity.