Introdução ao método dos elementos espectrais

Abstract

In order to overcome the current limitations in the dynamic analysis of structures, methods have been developed using the finite element method, since it shows imprecision in systems with high frequencies. Thus, the study of the method of spectral elements is shown as relevant, since it presents advantages such as the high frequency precision and the low computational cost during the solution of the problem. For the present work the Finite Element Method will be presented initially, because this way it is possible to explain the Method of the Spectral Elements in a simpler way. The studies were carried out in the form of a comparison between the presented methods, applying them in a periodic bar, structure studied in a doctoral thesis in which experimental results were obtained. Then, the validation of the method is performed by comparing the actual and simulated data. Initially, a detailed study of the equations governed the method was necessary, so that it would generate a script in Scilab to obtain the spectral matrix, so that it would be possible to find the transmissibility graphs of the structure. The simulated results were similar to the experimental results. The study in obtaining the FRFs is important because the variation in the natural frequencies can indicate cracks and faults in the structure.