Wave propagation in a one-dimensional structure using wavelet spectral finite element
Helio Vitor Cantanhêde da Silva1; José Maria Campos dos Santos1
1 Universidade Estadual de Campinas
doi:10.20906/CPS/COB-2015-2450
Resumo
In the present paper, a study of wave propagation in an elementary rod is made using the wavelet based spectral finite element (WSFE) method. Computing the exact values of the connection coefficients and derivative operators of Daubechies compactly supported wavelets over a finite interval, the wave equation has been transformed from time to the wavelet domain. This reduces the partial differential equation to coupled ordinary differential equations, which are decoupled using eigenvalue analysis. The WSFE technique is very similar to the Fourier based spectral finite element (FSFE) except that it uses compactly supported Daubechies. The wave equations are reduced to ordinary differential equations using Daubechies compactly supported, orthonormal, scaling functions for approximations in time. Unlike FSFE formulation with periodicity assumption, the wavelet-based method allows imposition of initial values and thus is free from wrap around problems. This helps in analysis of finite length undamped structures, where the FSFE method fails to simulate an accurate response. Numerical experiments are performed to extract the wave characteristics, namely the spectrum and dispersion relation for these waveguides, and the results are compared with the ones from the literature.
Palavras-chave: wavelets; spectral finite element; wave propagation; waveguides