<p>A beam-like model is proposed to address the nonlinear dynamic response of an annular thin pipe, under the action of a resonant transverse load. The mechanical model consists in an underlying Timoshenko beam enriched with further kinematic and dynamic variables, which consistently describe extension and bending plus local effects, namely ovalization and warping of the cross-section. The nonlinear equations of motions are derived via a variational approach and are then expanded retaining up to cubic order nonlinearities. They are then&nbsp;discretized via the Galerkin approach and a perturbation scheme based on the multiple scale method is adopted to&nbsp;study the dynamic behavior. Depending on the length of the beam-like system, different internal resonances may be achieved.&nbsp;In particular, for the case here analyzed, the geometry is set in order to give rise to a&nbsp;1&nbsp;:&nbsp;2 as well as 1 : 3&nbsp;internal resonances that take place&nbsp;between the global and local modes, triggered by the external harmonic excitation. As expected from the literature numerical results, the aymptotic solution allows to predict a&nbsp;softening behavior for the&nbsp;beam-like structure that is&nbsp; induced by the local deformation. Indeed, the effect is stronger when the&nbsp;1 : 2 internal resonance is predominat, migrating towards a hardening behavior when resonance is lost.&nbsp;&nbsp;</p>

Dynamic Response to Transverse Loading of a Beam-Like Pipe via a Perturbation Approach

Paper Proceedings: https://asmedigitalcollection.asme.org/IDETC-CIE/IDETC-CIE2021/volume/85369

ASME 2021 International Design Engineering Technical Conferences & Computers and Information in Engineering Conference (IDETC/CIE2021)

Supporting the need among researchers worldwide for additional online and multimedia content, ASME now offers the ASME Conference Video Collection. This platform will collect and provide long-term access to conference presentation videos, encompassing all technology areas within ASME's technical conference and events program. About 30,000-40,000 engineers across all mechanical engineering and related disciplines participate in ASME conferences each year. This includes authors of approximately 6,000 to 8,000 technical papers published by ASME, the majority of whom also submit video presentations for our virtual conferences. The video collection will be available as an add-on to existing product packages or as a separate subscription.