Stability and bifurcations in three-dimensional analysis of axially moving beams

Mergen H. Ghayesh, Marco Amabili, Hamed Farokhi

Research output: Chapter in Book/Report/Conference proceedingConference contributionpeer-review

Abstract

The geometrically nonlinear dynamics of a three-dimensional axially moving beam is investigated numerically for both sub and supercritical regimes. Hamilton's principle is employed to derive the equations of motion for in-plane and out-of plane displacements. The Galerkin scheme is applied to the nonlinear partial differential equations of motion yielding a set of second-order nonlinear ordinary differential equations with coupled terms. The pseudo-arclength continuation technique is employed to solve the discretized equations numerically so as to obtain the nonlinear resonant responses; direct time integration is conducted to obtain the bifurcation diagrams of the system. The results are presented in the form of the frequency-response curves, bifurcation diagrams, time histories, phase-plane portraits, and fast Fourier transforms for different sets of system parameters.

Original languageEnglish
Title of host publicationASME 2013 International Mechanical Engineering Congress and Exposition
Subtitle of host publicationDynamics, Vibration and Control
PublisherAmerican Society of Mechanical Engineers(ASME)
Volume4 A
ISBN (Print)9780791856246
DOIs
Publication statusPublished - 15 Nov 2013
EventASME 2013 International Mechanical Engineering Congress and Exposition, IMECE 2013 - San Diego, CA, United States
Duration: 15 Nov 201321 Nov 2013

Conference

ConferenceASME 2013 International Mechanical Engineering Congress and Exposition, IMECE 2013
CountryUnited States
CitySan Diego, CA
Period15/11/1321/11/13

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