Rigid-body support motion and post-flutter piezoelectric energy harvesting from a pitch-plunge-flap aerofoil

Abstract

A piezoelectric transducer on a pitch-plunge aerofoil with a finite-mass trailing-edge flap turns the limit cycle that follows flutter into electrical power. The design findings for such a harvester have so far been obtained with the section's suspension reacting against rigid ground, which is what a wind-tunnel mounting provides. Here a 3-dof aerofoil with a transducer is carried by a fuselage mass that is itself free to translate, so that the coupled system is free-free and the wing's plunge is measured relative to a support that moves. The support degree of freedom is destabilising on its own, softening the flutter mode by taking a share of it in antiphase with the wing's plunge, and it acts on the three transducer mountings unequally, amplifying the plunge mounting's destabilisation, leaving the largest pitch-mounted stabilisation untouched while halving it where the electrical time constant meets the flutter frequency, and leaving the flap mounting alone. The optimum coupling and load resistance do not move, so the matching rules of the rigidly supported section carry over unchanged. The harvested power rises with the support mass at a fixed flow speed for every mounting, and that rise is shown to be an artefact of the fixed-speed convention rather than a property of the cycle. Measured instead at a fixed margin above each system's own flutter boundary, which divides out the boundary's motion, the plunge mounting keeps a real gain while the pitch mounting loses power, so the apparent benefit of a soft support to a pitch-mounted harvester is entirely the boundary coming down to meet the flow speed. A harvester result quoted at a fixed speed and read as a property of the limit cycle is therefore wrong by the whole of that difference.