A theoretical and numerical investigation of large array of cantilever beams in fluids.

Abstract

Over the last decade, several studies have been conducted involving a single cantilever beam oscillating in an unbounded fluid and close to a rigid surface. The purpose of these studies was to understand how the surrounding fluid and a rigid surface influence vibrating beams. In particular, these studies are relevant to applications such as atomic force microscopy (AFM), micro-electromechanical systems (MEMS), and energy harvesting. However, investigations based on multiple beams or a large array of beams in fluids remain unexplored. In addition, applications based on single beams can improve their efficiency by considering the array of beams (for example AFM).

In this work, a two-dimensional boundary integral method (BIM) is employed to investigate the fluid dynamics of a large array of beams, for the first time taking into account the effects of neighbouring and non-neighbouring members.

In order to gain a better understanding of the array dynamics we used a semi-analytical approach involving linearized Navier-Stokes equations. We analyze array sizes from 5 to 25 beams by comparing transverse hydrodynamic force and velocity profiles. An array of beams is studied parametrically by considering various parameters, including the gap between the beams, the height from the rigid surface, the Reynolds number, and the number of beams. BIM is a linearized model which is applicable to small amplitude ratios.

A two-dimensional computational fluid dynamic analysis (CFD) has also been conducted for 3 to 11 beams in the fluid environment for both unbounded and bounded domains, in order to understand the effect of the fluid on a large array at various amplitude ratios and understand the onset, presence and influence of any nonlinearities.

Novel results, directly related to the array configuration or size of the array include an overall increase in hydrodynamic force with an increase in array size, array effects highly coupled to the size of viscous layers, and interesting jump phenomena in hydrodynamic force close to the rigid surface. CFD analysis indicates the dominance of convection-driven nonlinearities. Further, we have compared and validated both the results of BIM and CFD analysis.