Dynamic analysis of the linear discrete dynamic systems subjected to the initial conditions by using an FFT-based spectral analysis method

In this paper, a fast Fourier transforms (FFT)-based spectral analysis method is introduced for the dynamic analysis of the linear discrete dynamic systems subjected to the non-zero initial conditions. The FFT-based spectral analysis method is developed first for the one degree-of-freedom (dof) system and then extended to the multi-dof systems. To evaluate the accuracy and convergence of the FFT-based spectral analysis method, the forced vibration of a viscously damped 3-dof system is considered as an illustrative problem. The accuracy of the proposed FFT-based spectral analysis method is evaluated by comparing the forced vibration responses obtained by using the FFT-based spectral analysis method with the exact analytical solutions as well as with the numerical results obtained by using the Runge–Kutta method.