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2 Journal of Achievements in Materials and Manufacturing Engineering

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FFT-based spectral dynamic analysis for linear discrete dynamic systems

Lee U., Cho J.

Journal of Achievements in Materials and Manufacturing Engineering

2007

Vol. 25, nr 1

95-102

Purpose: An FFT-based spectral dynamic analysis method is developed for the viscously damped, linear discrete dynamic systems subjected to nonzero initial conditions. Design/methodology/approach: The discrete Fourier transform (DFT) theory is used to develop a spectral dynamic analysis method. The dynamic response of a linear system is assumed as the sum of the forced and free vibration response parts. The forced vibration response part is obtained by convolving the dynamic stiffness matrix and Fourier components of excitation force through the Duhamel's integral, and the free vibration response part is obtained by determining its integral constants so as to satisfy initial conditions in frequency-domain. Findings: It is shown through some numeral examples that the proposed FFT-based spectral dynamic analysis method provides the solutions which accurately satisfy all initial conditions. Practical implications: This analysis method is applicable to viscously damped, linear discrete dynamic systems subjected to nonzero arbitrary initial conditions. In this study, two types of viscous damping are considered: proportional damping and non-proportional damping. Originality/value: The FFT-based spectral dynamic analysis method proposed in this paper is unique because the pseudo-force concept or the superposition of corrective free vibration solution used by other researchers is not used to take into account non-zero initial conditions.

Dynamic response with arbitrary initial conditions using the FFT

Lee U., Cho J.

Journal of Achievements in Materials and Manufacturing Engineering

2006

Vol. 18, nr 1-2

299--302

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.