Dynamic response to transverse loading of a single-layered tubular beam via a perturbation approach

A beam-like model is proposed to address nonlinear dynamic response of a thin pipe, under the action of a resonant transverse load. The mechanical model consists of a Timoshenko beam enriched with further kinematic and dynamic variables which, besides extension and bending, consistently describe local effects, related to ovalization and warping of the cross-section. The nonlinear equations of motions are derived via the principle of virtual work, and internal resonance between the global and local modes is addressed by the multiple scale method, after a Galerkin projection of the equations on the first significant modes. The softening behavior induced by the local deformation remarkably affects the asymptotic solution, which turns out to be in good agreement with that provided by numerical integration.