Nonlinear response of a buckled beam to a three-to-one internal resonance

Samir A. Emam, Ali H. Nayfeh

Research output: Contribution to conferencePaperpeer-review

Abstract

We investigate the nonlinear response of a clamped-clamped buckled beam to a three-to-one internal resonance between the first and third modes when one of them is externally excited. To examine whether the first and third modes are nonlinearly coupled, we use the method of multiple scales to directly attack the partial-differential equation and associated boundary conditions and obtain the equations governing the modulation of their amplitudes and phases. We find that the two modes are nonlinearry coupled. To investigate the large-amplitude dynamics, we use a multi-mode Galerkin discretization to obtain a reduced-order model of the problem. We use a shooting method to compute periodic orbits of the discretized equations and Floquet theory to investigate the stability and bifurcations of these periodic orbits. We note an energy transfer from the first mode, which is externally excited by a primary resonance, to the third mode. We obtain preliminary experimental results of the energy exchange between the first and third modes as a result of a three-to-one internal resonance. More experimental results are being generated.

Original languageEnglish
Pages2491-2499
Number of pages9
DOIs
Publication statusPublished - 2003
Externally publishedYes
Event2003 ASME Design Engineering Technical Conferences and Computers and Information in Engineering Conference - Chicago, IL, United States
Duration: Sep 2 2003Sep 6 2003

Other

Other2003 ASME Design Engineering Technical Conferences and Computers and Information in Engineering Conference
Country/TerritoryUnited States
CityChicago, IL
Period9/2/039/6/03

ASJC Scopus subject areas

  • Engineering(all)

Fingerprint

Dive into the research topics of 'Nonlinear response of a buckled beam to a three-to-one internal resonance'. Together they form a unique fingerprint.

Cite this