Mathematical analysis of some new Reynolds-rod elastohydrodynamic models

✍ Scribed by G. Bayada; B. Cid; C. Vázquez

• Publisher: John Wiley and Sons
• Year: 2001
• Tongue: English
• Weight: 162 KB
• Volume: 24
• Category: Article
• ISSN: 0170-4214
• DOI: 10.1002/mma.267

✦ Synopsis

Abstract

In this paper, some new elastohydrodynamic Reynolds‐rod models are posed to obtain the existence of solution (the lubricant pressure and the elastic rod displacement). More precisely, a sign restriction on fluid pressure for cavitation modelling and different unilateral conditions on the rod displacement associated with a rigid structure coating are formulated in terms of coupled variational inequalities. The particular hinged or clamped boundary conditions on the rod displacement require different techniques to prove the existence of solution. Besides nearly linear coupled problems, two non‐linear rod problems including curvature effects are analysed. Mainly, regularity results and L^∞^ estimates for the solution of variational inequalities and fixed‐point theorems lead to the existence results for the various coupled models. Copyright © 2001 John Wiley & Sons, Ltd.