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Design of piezoaeroelastic energy harvesters

机译：压电弹性弹性能量收集器的设计

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We design a piezoaeroelastic energy harvester consisting of a rigid airfoil that is constrained to pitch and plunge and supported by linear and nonlinear torsional and flexural springs with a piezoelectric coupling attached to the plunge degree of freedom. We choose the linear springs to produce the minimum flutter speed and then implement a linear velocity feedback to reduce the flutter speed to any desired value and hence produce limit-cycle oscillations at low wind speeds. Then, we use the center-manifold theorem to derive the normal form of the Hopf bifurcation near the flutter onset, which, in turn, is used to choose the nonlinear spring coefficients that produce supercritical Hopf bifurcations and increase the amplitudes of the ensuing limit cycles and hence the harvested power. For given gains and hence reduced flutter speeds, the harvested power is observed to increase, achieve a maximum, and then decrease as the wind speed increases. Furthermore, the response undergoes a secondary supercritical Hopf bifurcation, resulting in either a quasiperiodic motion or a periodic motion with a large period. As the wind speed is increased further, the response becomes eventually chaotic. These complex responses may result in a reduction in the generated power. To overcome this adverse effect, we propose to adjust the gains to increase the flutter speed and hence push the secondary Hopf bifurcation to higher wind speeds.
机译：我们设计了一种压电气动弹性能量收集器，该能量收集器由刚性翼型组成，该刚性翼型被限制为俯仰和插入，并由线性和非线性扭力和挠性弹簧支撑，压电弹簧耦合到插入自由度上。我们选择线性弹簧以产生最小的颤振速度，然后执行线性速度反馈以将颤振速度减小至任何所需值，从而在低风速下产生极限循环振荡。然后，我们使用中心流形定理推导颤振起始点附近的Hopf分支的范式，然后使用该范式选择产生超临界Hopf分支的非线性弹簧系数，并增加随后极限环的幅度。因此收获的力量。对于给定的增益并因此降低了颤振速度，观察到的收获功率会增加，达到最大值，然后随风速的增加而降低。此外，响应经历次级超临界Hopf分叉，从而导致准周期运动或大周期的周期性运动。随着风速进一步增加，响应最终变得混乱。这些复杂的响应可能导致所产生的功率降低。为了克服这种不利影响，我们建议调整增益以增加颤振速度，从而将次级Hopf分叉推向更高的风速。

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