Investigação numérica sobre a detecção de danos em vigas metálicas pelo método do erro na equação de movimento

Abstract

The main objective of this paper was to develop a numerical investigation regarding the application of Error Method in the Motion Equation in beams. The method tested was developed by Genovese (2000) and basically consists on evaluating the error generated in the equation of motion of a dynamic system in free vibration, when the system's equation of motion are considered as mass and stiffness matrices of the integral system and the eigenvalues and eigenvectors of the damaged system. The method was tested in two beams, the first beam was a simply supported and the second was the cantilever type, which were simulated, individually, two damages in each beam, in two different positions, the first being half of the length and the other near the end. For each damage were assessed two damage intensities, the first had a reduction of 2% and posterior of 40% at the moment of inertia of the cross section. The beams were discretized in 20 elements using the Finite Element Method. A computation implantation was made using the software Scilab, version 5.5.2. Starting from the differences in the residue matrix was possible to locate the position and the intensity of the damages that were being simulated. Thus, with the elaboration of this paper was possible to prove the efficiency of the method of the error in the movement equation, presenting the steps and the foundations.