Surface instability of orthotropic films under surface van der Waals forces. (English) Zbl 1386.74092
Summary: 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.
MSC:
| 74K35 | Thin films |
| 74G60 | Bifurcation and buckling |
| 39A28 | Bifurcation theory for difference equations |
| 39A30 | Stability theory for difference equations |
| 65L10 | Numerical solution of boundary value problems involving ordinary differential equations |
Keywords:
surface instability; orthotropic film; linear stability analysis; dispersion relation; degenerate material; transfer matrix; multilayerReferences:
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