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.