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This paper proposes a fast Fourier transforms (FFT)-based spectral analysis method for the dynamic analysis of linear discrete dynamic systems which have non-proportional viscous damping and are subjected to non-zero initial conditions. To evaluate the proposed FFT-based spectral analysis method, the forced vibration of a three degree-of-freedom (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 the present FFT-based spectral analysis method with those obtained by using the well-known Runge-Kutta method and modal analysis method

An FFT-Based Spectral Analysis Method for Linear Discrete Dynamic Systems with Non-Proportional Damping