Combining viscoelastic damping and nonlinearities to widen the operational speed range of flutter energy harvesting

We propose to use viscoelastic damping with combined hardening and free-play structural nonlinearities to increase the harvesting performance and control the vibration of a pitch and plunge airfoil with piezoelectric transduction. The numerical simulations are performed by direct integration of the equation of motion in the time domain for an unsteady aerodynamic load. Moreover, a fractional derivative model accounts for the viscoelastic material behavior in an efficient way. The effect of each structural nonlinearity is discussed and a good condition for harvesting in terms of cut-in speed and operational speed range is determined. From this condition, it is found that the the viscoelastic damper in pitch can further reduce the cut-in speed in $13$~\%, slightly increase the harvested power and help to reduce the dynamical complexity of the system response. In turn, the viscoelastic damper in plunge can be tuned to control the vibration amplitude at post-critical flow speeds, increasing the operational speed range up to $28$~\% and the power up to two orders of magnitude in some cases. It is shown that the viscoelastic damping conserves a favorable condition for harvesting for temperature variations from $10^{\circ}$C to $35^{\circ}$C.