Surface Instability of an Elastic Thin Film Interacting With a Suspended Elastic Plate

Abstract

This paper studies surface instability of a compliant elastic thin film on a rigid substrate interacting with a suspended elastic plate through van der Waals forces. The analysis is based on a novel method which permits a simple rational expression for the interaction coefficient as a function of the wave number of instability mode. The critical value of the interaction coefficient and the instability mode of the film-plate system can be determined easily by identifying the minimum of the interaction coefficient within an admissible range. When the stability strength of the plate is lower than the film even for the shortest plate-lengths, the interaction coefficient is found to be an increasing function of the wave number, and thus the film-plate system exhibits a long-wave instability mode determined by the suspended plate. In all other cases, the interaction coefficient admits an internal local minimum representing the short-wave mode of the film, and the critical value and instability mode of the film-plate system are determined by the internal local minimum for shorter plates, or by the long-wave mode of the plate for longer plates. Some numerical examples are given to illustrate the results.