Periodic excitation of a buckled beam using a higher order semianalytic approach
type: Item
instance of: scholarly article
title: Periodic excitation of a buckled beam using a higher order semianalytic approach
zbMATH Open document ID: 1193.74063
author: N. E. Zubov
published in: Nonlinear Dynamics
publication date: 2009-09-22T00:00:00Z
review text: This paper considers the steady-state behavior of a transversally excited, buckled pinned-pinned beam, which is free to move axially on one side. This research focuses on higher order single-mode as well as multimode Galerkin discretizations of the beam's partial differential equation. The convergence of the static load-paths and eigenfrequencies (of the linearized system) of the various higher-order Taylor approximations is investigated. In the steady-state analyses of the semianalytic models, amplitude-frequency plots are presented based on 7th order approximations for the strains. These plots are obtained by solving two-point boundary value problems and by applying a path-following technique. Local stability and bifurcation analysis is carried out using Floquet theory. Dynamically interesting areas (bifurcation points, routes to chaos, snapthrough regions) are analyzed using phase space plots and Poincaré plots. In addition, parameter variation studies are carried out. The accuracy of some semianalytic results is verified by Finite Element analyses. It is shown that the described semianalytic higher order approach is very useful for fast and accurate evaluation of the nonlinear dynamics of the buckled beam system.
Mathematics Subject Classification ID: 74H60
Mathematics Subject Classification ID: 74K10
Mathematics Subject Classification ID: 74S05
Mathematics Subject Classification ID: 74H65
zbMATH DE Number: 5605866
zbMATH Keywords: buckled beams
zbMATH Keywords: Galerkin discretization
zbMATH Keywords: nonlinear dynamics
zbMATH Keywords: FEM
zbMATH Keywords: parameter variation
MaRDI profile type: Publication
full work available at URL: s11071-006-9161-6
OpenAlex ID: W2163131138
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DOI: 10.1007/S11071-006-9161-6
description: scientific article; zbMATH DE number 5605866