Non-linear modal interactions in the oscillations of a liquid drop in a gravitational field

I. Rozhkov, A. F. Vakakis, R. H. Rand

Research output: Contribution to journalArticlepeer-review


Non-linear modal interactions in the dynamics of a vibrating drop are examined. The partial differential equations governing the drop vibrations are formulated assuming potential flow and incompressibility. The solution is expressed in terms of the eigenfunctions of the (linearized) Laplace operator in spherical coordinates. A small parameter ε is introduced to scale the (small) deformation of the drop surface from its position of equilibrium. A 2:1 internal resonance is then imposed between the second and third modes of the resulting discretized system, and the ensuing non-linear modal interactions are studied using the method of multiple scales. A bifurcation in the slow dynamics of the system is detected that leads to amplitude modulations of the drop oscillations. The method employed in this work is general and can be used to study other types of non-linear interactions involving two or more drop modes.

Original languageEnglish (US)
Pages (from-to)803-812
Number of pages10
JournalInternational Journal of Non-Linear Mechanics
Issue number5
StatePublished - Jul 2001

ASJC Scopus subject areas

  • Mechanics of Materials
  • Mechanical Engineering
  • Applied Mathematics


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