On flat thin elastic rods with rapidly varying periodic characteristics

A thin elastic rod in a plane is considered. The free form of the rod is described by a periodic curve. It is shown that, under constant loads, its equilibrium form tends to the equilibrium form of a thin rectilinear rod when the frequency of the function describing the free form increases infinitely. The problem under study is solved on the basis of modeling the spatial annular DNA molecules by a thin rectilinear elastic rod.