Aerodynamic damping of sidewall bounded oscillating cantilevers

Abstract As a result of their simplicity, low power consumption, and relative ease of implementation, oscillating cantilevers have been investigated for use in multiple applications. However, the in situ operation in many cases, requires oscillating near one or more solid walls. When the separation distance between the vibrating cantilever and the solid wall becomes small, damping from the surrounding fluid is increased, which in turn can increase the power required to maintain certain operational performance characteristics (e.g., vibration amplitude). This increase in damping is a well-studied phenomenon for certain configurations (e.g., microcantilevers in Atomic Force Microscopy, or AFM), but is largely unexplored for a cantilever sweeping across a solid wall, which has direct impact for many macro-based applications including electronics cooling and propulsion. In this paper, we experimentally investigate the aerodynamic damping as a function of the gap between two sidewalls parallel to the oscillating motion of the cantilever. Multiple voltage and frequency inputs are considered in addition to the magnitude of the wall to cantilever gap. Experiments performed across a range of operating conditions reveal that decreasing the distance between the walls and the oscillating cantilever can increase the aerodynamic damping as much as 5 times that of the isolated (i.e., without sidewalls) operation. The resonance frequency is also shown to decrease when the gap spacing is extremely small, suggesting the added mass of the fluid is also sensitive to this variable. However, this change is much smaller (~0.5%) compared to the change typically observed in damping. The findings in the paper help to quantify the overall effect of solid enclosure walls on the performance of an oscillating cantilever, which will better enable the designer to achieve the maximum operational effectiveness. The experimental findings also suggest viscous damping with sidewalls could be predicted from first principles in a similar manner to well accepted analytical models of a cantilever vibrating above a solid surface.

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