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Title: A simple method for exponentially modulated random excitation
Author(s): Leung, Andrew Yee Tak 
Issue Date: 1987
Publisher: Elsevier
Journal: Journal of Sound and Vibration 
Volume: 112
Issue: 2
Start page: 273
End page: 282
The spectral method in stationary random process is extended to exponentially modulated stationary and non-stationary random processes in a straightforward manner by replacing the frequency parameter iω by α=β+iω where exp (βt) is the modulating function. Therefore, the transfer function is now H(α) instead of H(iω), and the formulation follows the conventional method. Integration formulae for the response spectra for the root mean square (r.m.s.) response, velocity and acceleration are presented. The results are compared to approximate formulae, for resonance conditions. For the case of a constant modulating function (β=0), the usual approximate formula for the r.m.s. displacement is more accurate when the natural frequency ω1 is less than that, ω0, at the peak of the excitation spectral density curve. For the approximation, the behaviour of the acceleration is just the reverse of that of the displacement, and the influence of the damping is not as significant as that of ω0−ω1, as is usually the case. The method is suitable for applications in earthquake engineering and blasting analysis.
DOI: 10.1016/S0022-460X(87)80195-5
CIHE Affiliated Publication: No
Appears in Collections:CIS Publication

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