Nonprobabilistic, convex-theoretic modeling of scatter in material properties

Nonprobabilistic, convex modeling of uncertain material properties for viscoelastic structures is developed in this paper. In particular, the problem of forced vibrations of viscoelastic beams is studied. First the analytic solution by Inman is generalized for a deterministic set of variables, describing material properties. Next, these variables are treated as varying in a solid ball in the four-dimensional space, thus modeling the scatter in material properties. The least favorable response needed for the design of the structure is determined.