Nonlinear periodic flexing in a floating beam

Abstract

This paper considers periodic flexing in a floating beam, in the presence of a small periodic forcing term. The beam is considered as a vibrating beam with the free end boundary condition, in the presence of an additional restoring force due to flotation, which becomes zero as soon as the beam lifts out of the water or constant if the beam becomes partially submerged. The equation is therefore nonlinear. A theorem is proved which shows that in the presence of small periodic forcing terms, both small- and large-amplitude solutions can exist. Numerical evidence is presented.