Modelling of Nonlinear Dynamic Linked Elastic Structures

Mary Ann Horn Vanderbilt University

In recent years, the tools required to study elastic systems have been sufficiently developed to allow researchers to focus on linked elastic structures. For example, linear models of plate-beam configurations which involve geometric junction conditions are known to be wellposed and controllable. Extensions to nonlinear plate-beam systems are motivated by issues arising from large-amplitude periodic oscillations, but such systems have not been seen in the literature. A model comprised of a nonlinear von Kármán plate coupled with a nonlinear beam equation is developed. Dynamic junction conditions are imposed at the interface. Wellposedness is established by first considering a corresponding linear problem, then applying a perturbation theorem for nonlinear semigroups. Proof of regularity takes advantage of elliptic theory, as well as the regularity of the Airy’s stress function.