Mathematical Problems in Engineering
Volume 2005 (2005), Issue 4, Pages 393-410
doi:10.1155/MPE.2005.393
Problems of interaction of vibrating surfaces with
processable materials
Faculty of Mathematics and Mechanics, National University of Dnepropetrovsk, 13 Nauchnaya Street, Dnepropetrovsk 49050, Ukraine
Received 18 June 2004
Copyright © 2005 V. A. Ostapenko. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
Abstract
We consider the mathematical model of interaction of a vibrating surface with
the load placed on it. With the purpose of accounting for
influence on behavior of not only system interaction of a blade
with a load but also internal interaction of particles of a
material, the load is submitted as a finite number of strips with
zero thickness. The carrying blade is represented as a vibrating
membrane. It is supposed that the weight of the material is
comparable to or considerably surpasses the weight of the blade.
Therefore, the model takes into account the inertia of the
material. In the model with joint movement of the blade and the
load, the separation opportunity of the load from the blade is
provided. Therefore, there is a phase of separate movement of the
blade and the load, with their subsequent connection accompanied
with impact. The process of system movement is represented as
alternating sequences of joint and separate movements of the load
and the blade. The modeling of the process of the interaction of
the load and the blade is represented as an initial-boundary value
problem. The method of solution is developed and the exact
solution of the set problem is obtained in a class of generalized
functions.