Enhancement of damage indicators in wavelet and curvature analysis

Damage in a structural element induces a small perturbation in its static or dynamic displacement profile which can be captured by Wavelet analysis. The paper presents the wavelet analysis of damaged linear structural elements using DB4 or BIOR6.8 family of wavelets. An expression is developed for computing the natural frequencies of a damaged beam using first order perturbation theory. Starting with a localized reduction of EI at the mid-span of a simply supported beam, damage modelling is done for a typical steel beam element. Wavelet analysis is performed for this damage model for displacement, rotation and curvature mode shapes as well as static displacement profiles. Damage indicators like displacement, slope and curvature are magnified under higher modes. Instantaneous step-wise linearity is assumed for all the nonlinear elements. A localization scheme with arbitrararily located curvature nodes within a pseudo span is developed for steady state dynamic loads, such that curvature response and damages are maximized and the scheme is numerically tested and proved.