Surface instability of orthotropic films under surface van der Waals forces

Surface instability of orthotropic films under surface van der Waals forces We investigate the surface instability of an orthotropic thin elastic film interacting with another flat rigid body through van der Waals forces by means of linear stability analysis. In the obtained dispersion relation, the normalized interaction coefficient can be completely determined by the normalized wavenumber, the normalized surface energy and other two dimensionless material parameters characterizing the orthotropic elasticity of the film. The influence of these two material parameters and surface energy on the critical bifurcation mode and the critical interaction coefficient is probed in detail. The dispersion relation is also obtained for degenerate orthotropic films. An effective method based on transfer matrix is employed to derive the dispersion relations for a multilayered orthotropic elastic film interacting with a rigid contactor and interacting with another multilayered orthotropic elastic film, and also to obtain the critical interaction coefficient for a simply supported mono-layered orthotropic plate attracted by a rigid flat. Some interesting phenomena are observed for a bilayered orthotropic film, for two interacting mono-layered orthotropic films and for an orthotropic plate. http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Zeitschrift für angewandte Mathematik und Physik Springer Journals

Surface instability of orthotropic films under surface van der Waals forces

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Publisher
Springer International Publishing
Copyright
Copyright © 2017 by Springer International Publishing AG
Subject
Engineering; Theoretical and Applied Mechanics; Mathematical Methods in Physics
ISSN
0044-2275
eISSN
1420-9039
D.O.I.
10.1007/s00033-017-0831-7
Publisher site
See Article on Publisher Site

Abstract

We investigate the surface instability of an orthotropic thin elastic film interacting with another flat rigid body through van der Waals forces by means of linear stability analysis. In the obtained dispersion relation, the normalized interaction coefficient can be completely determined by the normalized wavenumber, the normalized surface energy and other two dimensionless material parameters characterizing the orthotropic elasticity of the film. The influence of these two material parameters and surface energy on the critical bifurcation mode and the critical interaction coefficient is probed in detail. The dispersion relation is also obtained for degenerate orthotropic films. An effective method based on transfer matrix is employed to derive the dispersion relations for a multilayered orthotropic elastic film interacting with a rigid contactor and interacting with another multilayered orthotropic elastic film, and also to obtain the critical interaction coefficient for a simply supported mono-layered orthotropic plate attracted by a rigid flat. Some interesting phenomena are observed for a bilayered orthotropic film, for two interacting mono-layered orthotropic films and for an orthotropic plate.

Journal

Zeitschrift für angewandte Mathematik und PhysikSpringer Journals

Published: Jul 11, 2017

References

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