A Comparative Assessment of Methodologies Based on Modal Analysis and B-Spline Interpolation for the Estimation of Stresses In Beams

Abstract

In this work two methodologies for the estimation of stresses on a cantilever beam by sequentially measuring accelerations in nine different locations are compared. The first procedure uses modal analysis, specifically the experimentally determined mode shapes, to predict the stress spectrum and the time response to an impulse excitation based on the signals from the accelerometers. The second methodology is based on B-Spline approximation of the displacement fields method using Least Squares Error Minimization. In both methodologies numerical integration is required to obtain the displacement from the acceleration field. Three different integration techniques, conducted in time and frequency, respectively have been implemented and compared. The signals estimated with both methods are compared with the experimental stresses, measured with a strain gauge placed on the structure. A good prediction of the both the stress spectrum obtained under white noise excitation and the impulse response time signal is obtained with both methods, with the B-Spline method offering a simpler and more straightforward approach. In either case the possibility of reliability measuring stress in a cantilever beam using accelerometers is successfully demonstrated.