Projects per year
Abstract
The paper is devoted to the studying of a dynamical system ‘solid + fluid’ in the presence of vibrations using the VanderPol–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 language  English 

Pages (fromto)  S397S412 
Journal  Journal of Mathematical Fluid Mechanics 
Volume  7 
Issue number  Supplement 3 
DOIs  
Publication status  Published  Aug 2005 
Projects
 1 Finished

Stability of Inviscid flows through a given domain
1/03/06 → 29/02/08
Project: Research project (funded) › Research