Subharmonic travelling waves in a geometrically non-linear circular plate

Tariq A. Nayfeh, Alexander F. Vakakis

Research output: Contribution to journalArticle

Abstract

The subhannonic motions of thin, axisymmetric, geometrically non-linear circular plates are analyzed. It is well known that such cyclic systems possess pairs of degenerate modes in "1-1" internal resonance, i.e. modes having equal linearized natural frequencies. The non-linear interaction of such a pair of modes is examined by discretizing the non-linear partial differential equations of motion and then investigating the resulting set of non-linear ordinary differential equations analytically and numerically. Two types of forced subhannonic motions are detected, namely subharmonic standing waves (SSW) and subharmonic travelling waves (STW). Moreover, it is found that for sufficiently large values of frequency detuning of the forcing function the STW lose stability in a Hopf bifurcation, leading to quasi-periodic motions of the plate, i.e. to oscillations on a two-torus. The analytical results are confirmed by numerical integrations of the equations of motion and by numerical Poincare maps. The results reported in this work are expected to have applicability on the dynamic analysis and design ofthin, flexible disks, of the type used for data storage in the computer industry.

Original languageEnglish (US)
Pages (from-to)233-245
Number of pages13
JournalInternational Journal of Non-Linear Mechanics
Volume29
Issue number2
DOIs
StatePublished - 1994
Externally publishedYes

Fingerprint

circular plates
Circular Plate
Subharmonics
traveling waves
Traveling Wave
Equations of motion
Equations of Motion
equations of motion
Quasi-periodic Motion
Internal Resonance
Hopf bifurcation
Motion
Poincaré Map
Nonlinear Interaction
Standing Wave
Data Storage
Nonlinear Ordinary Differential Equations
data storage
Natural Frequency
numerical integration

ASJC Scopus subject areas

  • Mechanical Engineering
  • Statistical and Nonlinear Physics

Cite this

Subharmonic travelling waves in a geometrically non-linear circular plate. / Nayfeh, Tariq A.; Vakakis, Alexander F.

In: International Journal of Non-Linear Mechanics, Vol. 29, No. 2, 1994, p. 233-245.

Research output: Contribution to journalArticle

Nayfeh, Tariq A. ; Vakakis, Alexander F. / Subharmonic travelling waves in a geometrically non-linear circular plate. In: International Journal of Non-Linear Mechanics. 1994 ; Vol. 29, No. 2. pp. 233-245.
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