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

## Palavras-chave:

Wavelets, Finite Element Method, Dynamic Analysis## 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.