Resonance and Damping in Drop-Cantilever Interactions

The interactions of a drop and a cantilever beam represent an elaborate mechanism that is applicable to many industrial fields and natural phenomena. Previous studies have focused on the positive correlation between the length and damping ratio of an elastic cantilever; however, we observed that around the resonance beam length in which the droplet frequency matches with the beam's natural frequency, this trend is not valid. To investigate this, we tested thin polycarbonate beams of nine varying lengths with a water droplet impact and used high-speed cameras to record the vibrational responses. The damping ratio of the cantilever increases with cantilever lengths shorter than resonance due to the droplet and cantilever being out of phase. For longer cantilevers, the phase of the droplet and cantilever are aligned in momentum and is significantly less than the damping rates for shorter lengths. These beam-droplet interactions can be helpful for future developments in energy-conversion techniques by understanding how droplets interact with elastic surfaces.