Structural resonance and mode of flutter of hummingbird tail feathers

Feathers can produce sound by fluttering in airflow. This flutter is hypothesized to be aeroelastic, arising from the coupling of aerodynamic forces to one or more of the feather's intrinsic structural resonance frequencies. We investigated how mode of flutter varied among a sample of hummingbird tail feathers tested in a wind tunnel. Feather vibration was measured directly at ~100 points across the surface of the feather with a scanning laser Doppler vibrometer (SLDV), as a function of airspeed, Uair. Most feathers exhibited multiple discrete modes of flutter, which we classified into types including tip, trailing vane and torsional modes. Vibratory behavior within a given mode was usually stable, but changes in independent variables such as airspeed or orientation sometimes caused feathers to abruptly 'jump' from one mode to another. We measured structural resonance frequencies and mode shapes directly by measuring the free response of 64 feathers stimulated with a shaker and recorded with the SLDV. As predicted by the aeroelastic flutter hypothesis, the mode shape (spatial distribution) of flutter corresponded to a bending or torsional structural resonance frequency of the feather. However, the match between structural resonance mode and flutter mode was better for tip or torsional mode shapes, and poorer for trailing vane modes. Often, the 3rd bending structural harmonic matched the expressed mode of flutter, rather than the fundamental. We conclude that flutter occurs when airflow excites one or more structural resonance frequencies of a feather, most akin to a vibrating violin string.