Dynamic response with arbitrary initial conditions using the FFT

Purpose: An FFT-based dynamic analysis method is proposed for damped linear discrete dynamic systems subjected to arbitrary nonzero initial conditions. Design/methodology/approach: The DFT theory is used to develop an FFT-based spectral analysis method. The total dynamic response is considered as the sum of the forced vibration response part and the free vibration response part. The forced vibration response part is obtained from the dynamic stiffness matrix and the Fourier components of excitation force based on the concept of Duhamel’s integral, and the free vibration response part is obtained by determining its integral constant to satisfy arbitrary initial conditions in the frequency-domain. Findings: Through some numeral examples, the proposed FFT-based dynamic analysis method is shown to provide very successful solutions which satisfy all arbitrary non-zero initial conditions. Research limitations/implications: (not applicable). Practical implications: (not applicable). Originality/value: The present FFT-based method is unique because it does not use the superposition of corrective free vibration solution or the pseudo-force concept used by other researchers to take into account the non-zero initial conditions.