Numerical Fourier Transform in Random Vibration

by Jann-Nan Yang,
Masanobu Shinozuka,

Serial Information: Journal of the Engineering Mechanics Division, 1969, Vol. 95, Issue 3, Pg. 731-746

Document Type: Journal Paper


The stochastic structural dynamic analysis for complex structures demands an analytical treatment involving nonstationary stochastic processes, under nonstationary gusty winds or earthquake accelerations. It is emphasized that the frequency domain analysis of such nonstationary problems with the aid of the Fourier transform technique is of vital importance in evaluating the mean value and the covariance function of the response, which are closely related to structural safety. An efficient method of numerical single and double Fourier transform and inversion with the aid of the complex Fourier series technique coupled with the Cooley-Tukey algorithm for evaluation of the Fourier coefficients is presented. Numerical examples indicate that the numerical inversion can be performed within a reasonable time on an IBM 7094.

Subject Headings: Dynamic structural analysis | Fourier analysis | Numerical methods | Vibration | Structural safety | Structural dynamics | Stationary processes | Wind gusts

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