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Shock and Vibration
Volume 13, Issue 6, Pages 595-606

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

Jooyong Cho and Usik Lee

Department of Mechanical Engineering, Inha University, 253 Yonghyun-Dong, Nam-Ku, Incheon 402-751, South Korea

Received 26 September 2005; Revised 11 November 2005

Copyright © 2006 Hindawi Publishing Corporation. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


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.