HYBRID PROBABILITIC AND CONVEX MODELING OF EXCITATION AND RESPONSE OFPERIODIC STRUCTURES

In this paper, a periodic finite-span beam subjected to the stochastic acoustic pressure with bounded parameters is investigated. Uncertaint y parameters exist in this acoustic excitation due to the deviation or imperfection. First, a finite-span beams subjected to the random acou stic 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 probabi listic and convex modeling of acoustic excitation appears to be most s uitable, since there is an insufficient information available on the a coustic excitation parameters, to justify the totally probabilitic ana lysis. Specifically, we postulate that the uncertainty parameters in t he acoustic loading belong to a bounded, convex set. In the special ca se when this convex set is an ellipsoid, closed form solutions are obt ained for the most and least favorable mean square responses of both t he transverse displacement and bending moment of the structure. Severa l finite-span beams are exemplified to gain insight into proposal meth odology.