Frequency-domain analysis of exponentially damped linear systems

In this paper, frequency-domain analysis of linear exponentially damped systems subjected to arbitrary initial conditions is studied. The standard Discrete Fourier Transform (DFT) procedure combined with Fast Fourier Transform (FFT) algorithms is applied to compute dynamic responses, after transforming the original motion equations subjected to non-zero initial conditions into new ones with completely null initial conditions by using the pseudo-force approach. A multi-degree-of-freedom (MDOF) system and a continuum system with exponential damping are considered as the illustrative problems. The accuracy of the proposed method is evaluated by comparing the results with those obtained from Simulink based on the state-space method.

► Represent the DFT/FFT method for the exponentially damped linear systems in detail.
► Apply the pseudo-force method to deal with non-zero initial conditions.
► The MDOF and the continuum linear systems are studied as the illustrative problems.
► The proposed method is general for the exponential and the other non-viscous damping.
► It has the advantages of extensive applicability, high efficiency and high accuracy