Spectral Element Analysis of the Continuum Systems with Arbitrary Initial Conditions

In this paper, an FFT-based spectral element method (SEM) is introduced for the linear continuum dynamic systems subjected to arbitrary, non-zero 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-forces 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 a good agreement with the analytical solutions obtained by using the mode superposition method. I