Cell Geometry and Material Property Effects on Membrane and Flow Response

TO OPTIMIZE micro aerial vehicle (MAV) designs for size and speed regimes characteristic of small birds and insects, a growing subset of low-Reynolds-number research groups practice biomimetics to take advantage of nature-optimized designs proven effective within the MAV flight regime [1]. One common feature of many natural flyers is wing flexibility. Engineering models that mimic low-Reynolds-number fliers with fixed-wing flexibility have demonstrated improved aerodynamics compared with conventional rigid airfoils. This improvement is attributed to a combination of passive static and dynamic deformations of the flexible-membrane wings supported by semirigid, fixed-wing frames. Static deformation, of bothmembrane and frame, can advantageously affect airfoil camber and tip washout through inflation and alteration of aerodynamic and geometric twist [2–4]. Dynamic membrane deformations can improvemomentum transfer between the leeside free shear layer and recirculation region of models with rigid leading and trailing edges and a membrane attached in between, thereby, decreasing the extent of flow separation and corresponding wake size, as well as advantageously affecting the aerodynamic forces [5,6]. Similar vibrations also exist for membrane wings with an unattached trailing edge. Hubner and Hicks [7] showed aerodynamic efficiency improvement by scalloping the trailing edge and developed scaling trends with respect to cell geometry. Johnston et al. [8] demonstrated via high-speed imagery that membrane prestrain increased flutter onset velocity while reducing the magnitude of the postflutter limit cycle oscillations. A free trailing-edge wing structure typically includes a flat or cambered frame of moderate or low aspect ratio that is significantly less compliant than the attached membrane. The membrane is attached along the leading edge of the frame and along battens (or ribs) extending from the leading edge. In this Note, it is documented that the initial flutter onset frequency of zero-applied-pretension membranes originates from small-amplitude membrane vibrations at the natural frequency of the membrane. Although applied pretensioning will affect the frequency, cell geometry and material properties are shown to play an important role as well. Spectral data from the membrane and the leeside shear layer via simultaneously sampled hot-wire anemometry and laser vibrometry are presented and discussed in this Note.