Two Dimensional Damage Localization Using the Interpolation Method

Abstract

This paper presents a vibration based procedure for locating reductions of stiffness in two-dimensional structures that can be modeled as plates. This procedure is a generalization to the two-dimensional case of the previously published Interpolation Damage Detection Method (IDDM). The method is based on the definition of a damage sensitive feature in terms of the accuracy of a spline function in interpolating the operational displacement shapes of the structure. These latter are recovered from frequency response functions (FRFs) measured at different locations of the structure during vibrations. At the i-th location, the FRF is calculated through spline interpolation using the FRF’s recorded at the all the instrumented locations but the i-th. For two-dimensional structures a spline surface is defined to interpolate the operational shapes. The accuracy of the spline interpolation is measured by an error function defined as the difference between the measured and interpolated operational mode shapes. At a certain location an increase (statistically meaningful) of the interpolation error, with respect to a reference configuration, points out a localized variation of the operational shapes thus revealing the existence of damage. The two dimensional IDDM algorithm is checked herein through numerical simulations, using the FE model of a plate and modeling local reductions of stiffness through a reduction of the elastic modulus of the material of one or more elements of the model.