THE TRIGONOMETRIC WAVELET FINITE ELEMENT METHOD APPLIED TO FREE VIBRATION ANALYSIS OF EULER-BERNOULLI BEAMS

Resumo

Over the past years several numerical methods have been formulated so as to not only find the
numerical solution of a mathematical model that describes a phenomenon, but also to find this solution
in the fastest way, with low computational cost and especially, in the most accurate way. One of the
characteristics of the enriched methods based on the Finite Element Method (FEM) is the possibility of
including new shape functions, which are not necessarily polynomial, in the approximate solution space.
The Wavelet Finite Element Method (WFEM) is an example of an enriched method that seeks to find
numerical solutions to engineering problems using the adaptability that Wavelet functions present. The
WFEM is the combination of FEM and Wavelets. WFEM uses the so-called scaling functions as shape
functions, whose linear combination, using the FEM techniques, will describe the approximate solution
space. In this sense, the objective of this work is to study the use of trigonometric Wavelets as enrichment
functions in WFEM for dynamic analysis of structures, seeking to combine the high convergence rates
of enriched methods with the trigonometric Wavelet properties. In this work the trigonometric WFEM
method is applied to free vibration analysis of Euler Bernoulli beams in order to verify its efficiency in
dynamic analysis. The natural frequencies obtained by the WFEM are compared with those obtained
from analytical solutions and by other numerical methods such as the traditional FEM.