Theoretical and experimental investigation of the nonlinear vibration of a buckled beam to a subharmonic resonance

Samir A. Emam, Ali H. Nayfeh

Research output: Contribution to journalConference articlepeer-review

1 Citation (Scopus)


We investigate the nonlinear vibrations of a clamped-clamped buckled beam to a subharmonic resonance of order one-half of its first vibration mode. We use a multi-mode Galerkin discretization to reduce the governing nonlinear partial-differential equation in space and time into a set of nonlinearly coupled ordinary-differential equations in time only. We solve the discretized equations using the method of multiple scales to obtain a second-order approximation, including the modulation equations governing its amplitude and phase. To investigate the local and global dynamics, we numerically integrate the discretized equations using a shooting method to compute periodic orbits and use Floquet theory to investigate their stability and bifurcations. We obtain interesting dynamics, such as a phase-locked motion, resulting from a Hopf bifurcation, snapthrough motions, and a sequence of period-doubling bifurcations leading to chaos. It is important to note that by using a single-mode Galerkin discretization, one cannot predict some of these nonlinear phenomena. We carry out an experiment and obtain results that are in good qualitative agreement with the theoretical results.

Original languageEnglish
Pages (from-to)2771-2780
Number of pages10
JournalCollection of Technical Papers - AIAA/ASME/ASCE/AHS/ASC Structures, Structural Dynamics and Materials Conference
Publication statusPublished - 2003
Externally publishedYes
Event44th AIAA/ASME/ASCE/AHS/ASC Structures, Structural Dynamics, and Materials Conference - Norfolk, VA, United States
Duration: Apr 7 2003Apr 10 2003

ASJC Scopus subject areas

  • Architecture
  • General Materials Science
  • Aerospace Engineering
  • Mechanics of Materials
  • Mechanical Engineering


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