Large-Amplitude Oscillations of Geometrically Nonlinear Elastic Beams Subjected to Hydrodynamic Excitation

Abstract

The dynamic response of slender pipes to cyclic flexural excitations could be significantly influenced by the “membrane” stiffness of a beam axially restrained at the ends, where the magnitude of the exciting force is such as to induce large lateral deflections. This typical nonlinearity of structural mechanics is generally approached adopting semi-analytical procedures for simple configurations, and more often using numerical solutions as well as finite element techniques for more realistic configurations. This paper deals with: the mathematical formulation of large-amplitude oscillations of geometrically nonlinear beams; and numerical models for nonlinear response of beams under harmonic and random excitations. Two applications are reported: analysis of the effect of the initially deflected shape on dynamic response under regular vortex shedding; analysis of the dynamic stiffening due to axial restraint on lock-in range.