Mathematical Problems in Engineering
Volume 2 (1996), Issue 2, Pages 143-163

Hybrid probabilistic and convex modeling of excitation and response of periodic structures

L. P. Zhu and I. Elishakoff

Department of Mechanical Engineering, Florida Atlantic University, Boca Raton 33431-0991, Florida, USA

Received 8 March 1993

Copyright © 1996 L. P. Zhu and I. Elishakoff. 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.


In this paper, a periodic finite-span beam subjected to the stochastic acoustic pressure with bounded parameters is investigated. Uncertainty parameters exist in this acoustic excitation due to the deviation or imperfection. First, a finite-span beams subjected to the random acoustic pressure field are studied, the exact analytic forms of the cross-spectral density of both the transverse displacement and the bending moment responses of the structure are formulated. The combined probabilistic and convex modeling of acoustic excitation appears to be most suitable, since there is an insufficient information available on the acoustic excitation parameters, to justify the totally probabilitic analysis. Specifically, we postulate that the uncertainty parameters in the acoustic loading belong to a bounded, convex set. In the special case when this convex set is an ellipsoid, closed form solutions are obtained for the most and least favorable mean square responses of both the transverse displacement and bending moment of the structure. Several finite-span beams are exemplified to gain insight into proposal methodology.