On vibrodynamics of pendulum and submerged solid

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15 Citations (Scopus)

Abstract

The paper is devoted to the studying of a dynamical system 'solid + fluid' in the presence of vibrations using the Van-der-Pol-Krylov-Bogoliubov (VPKB) averaging method. The main result of the paper is the discovery of a close similarity between a classical pendulum and a system of 'inhomogeneous solid + fluid' in the presence of vibrations. First, we consider the celebrated example of the Stephenson-Kapitza pendulum using the least action formulation of the VPKB averaging method. The method directly exploits the least action principle, in which an averaging procedure appears most naturally and conservation laws follow automatically. Its main advantage is a substantial decrease of the required amount of analytical calculations, which are typically cumbersome for the VPKB averaging method. Then, we consider the dynamics of a rigid sphere in an inviscid incompressible fluid, which fills a vibrating vessel of an arbitrary shape. The sphere can be either homogeneous or inhomogeneous in density. The results provide a full model for the averaged (or 'slow') motions, which includes the 'slow Lagrangians', the 'slow potential energy', and the 'vibrogenic' force, exerted by a surrounding fluid on a solid. We outline our calculations, present results in general forms, and briefly discuss related examples, properties, and conjectures.

Original languageEnglish
JournalJournal of Mathematical Fluid Mechanics
Volume7
Issue number3 SUPPL.
DOIs
Publication statusPublished - Aug 2005

Keywords

  • Averaging method
  • Fluids
  • Solids
  • Vibrations

ASJC Scopus subject areas

  • Mathematical Physics
  • Condensed Matter Physics
  • Computational Mathematics
  • Applied Mathematics

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