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FFT‐based spectral element analysis for the linear continuum dynamic systems subjected to arbitrary initial conditions by using the pseudo‐force method
Author(s) -
Lee Usik,
Cho Jooyong
Publication year - 2007
Publication title -
international journal for numerical methods in engineering
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.421
H-Index - 168
eISSN - 1097-0207
pISSN - 0029-5981
DOI - 10.1002/nme.2171
Subject(s) - fast fourier transform , finite element method , superposition principle , mathematics , equations of motion , spectral element method , mathematical analysis , fourier transform , fourier series , algorithm , classical mechanics , physics , structural engineering , extended finite element method , engineering
In this paper, a fast Fourier transform (FFT)‐based spectral element method (SEM) is developed for the linear continuum dynamic systems subjected to arbitrary, non‐null initial conditions. In the FFT‐based SEM, the original equations of motion subjected to arbitrary initial conditions are transformed into a new set of equations of motion subjected to completely null initial conditions by using the pseudo‐force method so that the conventional spectral element analysis can be applied to obtain desired dynamic responses. A simply supported beam and a cantilevered beam are considered as the illustrative problems to evaluate the FFT‐based SEM. The dynamic responses obtained by using the FFT‐based SEM are shown to be in good agreement with the analytical solutions obtained by using the mode superposition method. Copyright © 2007 John Wiley & Sons, Ltd.