Uniform attractor of shallow arch motion under moving points load

Abstract

We study the long time behavior of arches and membrane-like structures in the strong damping case. Our main goal is to incorporate moving points load, and to establish the existence of a non-empty, compact, uniform attractor for the associated semi-flows. The existence of such an attractor is established for almost periodic forcing terms. The method employs Kuratowski's measure of non-compactness. The presentation is mostly self-contained. Examples simulating a vehicular traffic across a long bridge are considered.