Piezoelectric wind energy harvesting device based on the inverted cantilever beam with leaf-inspired extensions

Nowadays, the rapid development of robotic technology and the Internet of Things¹ signifies the increasing prevalence of various sensors and sensor networks. However, the power supply for such sensors has become a critical concern, as the improvement of battery capacity can not keep up with the pace of soaring power consumption of those sensors.² To this end, extracting energy from the ambient environment to recharge or partially replace the batteries has intrigued many researchers. Various energy harvesting devices and underlying mechanisms have been put forward,³ among which the vibration energy harvesting devices based on piezoelectric materials have received the most attention.^4,5

For specific sensor applications with available surrounding fluid flow, flow induced vibrations have been recognized as excellent energy sources and thus employed for energy harvesting.⁶ Some of the devices rely on the vortex induced vibration of flexibly mounted structures, where a prismatic structure, without^7–10 or with^11,12 variable orientation, undergoes vibration in the surrounding cross flow and induced the incorporated piezoelectric structures (usually in the form of patches) into vibration. For some other devices, the direct flutter instability of flexible piezoelectric integrated structures are adopted,^13–15 in which the flag-like composite structure are found to vibration in the presence of axial fluid flow. Some other researchers combined the two mechanisms and introduced the wake galloping based energy harvesting,^16–19 where the piezoelectric integrated structures are placed in the wake of a bluff body in fluid flow and forced into vibration by the alternative wake. Some authors even utilized Helmholtz resonators to harness the flow energy and induce vibration in the piezoelectric structures attached the backplate of the resonator cavity.^20,21 Device configuration design and performance optimization have been the general research focuses.

Here in this contribution, we investigate a novel type of aeroelastic energy harvesting device which is composed of a piezoelectric beam and sector-shaped flexible extensions. The inspiration for the device design is introduced with the resulting device configuration described. Numerical simulations are done to investigate the possible vibration modes. Prototypes are built in order to experimentally investigate the device performance and its dependence upon the extensions. Results of the experiment validate our design and provide some helpful insights into the design and optimization of aeroelastic energy harvesting devices.

We develop the configuration of the piezoelectric energy harvesting device based on the inspiration of plant leaf structure, which is shown in Fig. 1(a). A piece connected to the plant branch is generally composed of the petiole and the lamina. In the presence of wind, the petiole acts like a cantilever beam and bends according to the wind direction, while the lamina is a flexible plate subject to fluttering or torsion. It has been shown that the leaf flutter because of the aeroelastic instability related to torsional galloping.²² Based on this phenomenon, we proposed an aeroelastic energy harvesting device based on a piezoelectric bimorph beam and flexible extensions, which is shown in Fig. 1(b). The piezoelectric bimorph beam is fixed at one end to form a cantilever beam. The other end of the beam is connected to a flexible extension. Here in this schematic diagram, we shown a sector-shaped flexible extension which gains inspiration from the leaves of ginkgo biloba with a bit of modification. The cantilever beam is placed in such a way in the incoming wind that the wind direction is directed from the free end of the beam to the fixed end. This kind of placement is usually called an inverted cantilever beam.²³ 

We have also several other considerations in the design of the proposed aeroelastic energy harvesting device, according to the general dynamic analysis of inverted beams.^23,24 On one hand, unlike the case of a leaf whose petiole is generally considered as a beam with small cross sections, we choose the spanwise dimension of the piezoelectric bimorph beam comparable to that of the flexible extension. In this way, the vibration of the piezoelectric bimorph beam can be tuned by the flexible extension. On the other hand, the equivalent stiffness of flexible extension is much smaller than that of the inverted piezoelectric bimorph beam so that we can achieve energy harvesting at a lower wind velocity. Besides, we make no assumptions about the topology of the flexible extension. It means that apart from the various kinds of leaf shapes existing in the nature, we can choose any other kinds of possible topologies for the flexible extension. As shown in Fig. 2(b) and (c), in this contribution we design two kinds of topologies for the flexible extension: sector-shaped and T-shaped, in contrast to the rectangular one adopted by Zhao et al.²⁵ and the delta wing adopted by Alrowaijeh et al.²⁶ 

The way in which the flexible extensions are attached to the piezoelectric beam is also of interest to us. We consider here two types of attachment: single attachment and dual attachment, as shown in Fig. 2(a). For a single attached flexible extension, only one flexible extension is attached to the upper or lower surface of the piezoelectric beam. For the case of dual attachment, two flexible extensions are attached to the both sides of the piezoelectric beam respectively. As a matter of fact, the stability and coupled dynamics of dual inverted plates have been investigated by Kim et al.²⁷ to indicate that the critical velocity at which the two inverted plates lose stability for the equilibrium of a straight configuration reduces monotonically with respect to the decreasing gap distance between the plates and the increasing aspect ratio of the plates.

Firstly, with COMSOL Multiphysics software, we investigate the fluttering response of the composite beams with sector-shaped or T-shaped flexible extensions. The dimensions of the structures investigated are identical to those shown in Fig. 3 and the assembly is shown in the Fig. 2. As a result, they are not explicitly listed here and we present only the simulation results. It is to be noted that since the gap between the possible two flexible extensions shown in Fig. 2(a) is very small. To simulate the response of the double attachment structures, we therefore have to take into account the collision between the two extensions, which brings about extra computation cost. For the purpose of principle validation, we thus concentrate on the single attachment structures.

Considering the single attachment method, a three-dimensional model is established. Then we change the incoming wind velocity from 0 m/s to 20 m/s, which is the typical range of wind velocity available on earth. Virtually, we use a parallel connection²⁸ of the piezoelectric patches in side the piezoelectric bimorph beam, and an external resistance of 1.2 MΩ is connected to the energy harvesting device. As a result, the magnitudes of the output voltage V_out and that of the output power P_out on the connected resistance are recorded and plotted in Fig. 4.

It is found from the simulation results shown in Fig. 4 no big difference is observed in terms of critical wind velocity for the two kinds of flexible extensions (sector-shaped extension and T-shaped extension). However, the output voltage V_out and harvesting power P_out for the case with sector-shaped extension are much larger than that with T-shaped extension. For an extreme wind velocity of 20 m/s, the output voltage for the piezoelectric bimorph beam with sector-shaped extension is more than 60 V in magnitude, while for the beam with T-shaped extension the output voltage is only of around 20 V in magnitude. When it comes to output power, in the presence of given externally connected resistance of 1.2 MΩ, a maximum magnitude for P_out of more than 1.5 mW is achieved by the beam with sector-shaped extension. In contrast, the beam with T-shaped extension can only generate a maximum magnitude for P_out of around 0.25 mW. A later modal analysis of the beam with the two kinds of flexible extensions shows that the lowest eigenfrequency for the beam with sector-shaped extension is around 76 Hz, compared to the value of 92 Hz of that for the beam with T-shaped extension. The above simulation results amount at least to the conclusion that, the shape of the flexible extension can change the critical wind velocity, the fluttering frequency significantly, and therefore the energy harvesting performance of the device.

For the sake of experimental investigation, we fabricated several prototypes of the proposed energy harvester, as shown in Fig. 5. The piezoelectric bimorph beam is composed of two piezoelectric PZT layers with one aluminum plate in between. They are carefully glued together using epoxy resin adhesive to avoid any pre-stress induced cracking of the piezoelectric elements. After that two electrical wires are soldered to the electrodes covering the piezoelectric elements, acting as output ports. The flexible extension is made of PET polymer material and cut into the desired shapes. They are bolted to the bimorph cantilever beam at the free end according to the attachment method used.

The experiment setup is very simple but proves to be useful, as shown in Fig. 6(a). It consists of a fixed base, some clamping mechanism, the energy harvesting prototype, a wind source and a wind velocity sensor. As the wind source can only provide a fixed output, we managed to change the distance between the wind source and the prototype, and then use a wind velocity sensor to detect the wind velocity at the tip of the prototype. In the experiment, the open-circuit output voltages of the single attachment and dual attachment piezoelectric bimorph beam are recorded using a digital oscilloscope. One of the typical voltage is shown in Fig. 6(b).

We record the amplitude of the output voltage corresponding to four kinds of beam configuration: single attachment T-shaped flexible extension, dual attachment T-shaped flexible extension, single attachment sector-shaped flexible extension, and dual attachment sector-shaped flexible extension. The results are plotted against the measured wind velocity in Fig. 7.

Firstly, for the case of single attachment, the output voltage corresponding to the sector-shaped extension is much larger than that of the T-shaped extension. Though the experiment results are different from the simulation results shown in Fig. 3 quantitatively, we observe that the superiority of sector-shaped is validated qualitatively. The differences lie in the fact that the experiment wind field is not uniform as in the case of numerical simulation. Besides, the externally connected circuit in the simulation contributes partly to the result differences. Secondly, for the case of double attachment, there seems to be no winner in the competition of T-shaped extension and sector-shaped extension. However, we found that, the wind limit for the T-shaped extension is only around 13 m/s, which means that at a wind velocity greater than 13 m/s, the dual flexible extensions will be prone to a divergent mode.²⁷ The limit velocity for the sector-shaped extension is obviously larger. This indicates a wider work range for the sector-shaped extension. Besides, for the dual attachment cases, we don’t obtain a larger voltage output as expected, which can be inferred from the analysis by Kim et al.²⁷ This is probably because that the gap between the dual flexible extensions are too small for them to develop their own dynamics. As a result, they collide and strongly couple with each other. This kind of coupling is to the overall performance of the system, according to the experimental results. The collision and fluid-coupling between the dual flexible extensions are then of great interest to further study of the proposed energy harvesting device.

One point to be noted for the simulation results shown in Fig. 4 and the experiment results shown in Fig. 7 is what happens when the incoming wind velocity U_wind is very high. Indeed, when U_wind is greater than 20 m/s in the simulation or it is greater than 13 m/s in the experiments, the output voltage V_out will decrease instead of continuing to increase. The authors think several factors contribute to the result. Firstly, in both cases, the external electrical circuits do possess a resonant operation point at which the output voltage is maximized. Higher input wind velocity will thus indicate a smaller output voltage if it exceeds the resonant parameter. Secondly, the oscillation mechanism of the inverted cantilever beam in the presence of incoming wind is far more complicated than that assumed in this contribution. When the incoming wind is strong enough, the flexible extension will cease to flutter and instead approaches its divergent operation range. In this case the overall vibration of the piezoelectric element is influenced and may cause the decrease of the output voltage. Thirdly but not the last, there may exist resonance between the fluttering vibration of the flexible extension and the vibration of the piezoelectric cantilever beam. Strong incoming wind will cause the system to operate outside that range and thus decrease the output.

In this paper, based on the inspiration of leaf fluttering in wind, we propose a novel type of wind energy harvesting device composed of a piezoelectric bimorph beam and flexible extensions. Working principle and advantages of the proposed design are discussed with numerical simulations conducted to investigate the influence of extension shape upon the device performance. Prototypes are fabricated and a simple experiment setup is built to investigate the actual device performance. Results show that the shapes of the flexible extension largely affect the device performance with a leaf-inspired sector-shaped flexible extension favorable. The test for the dual attachment case of the flexible extensions shows unexpected results, showing that the interaction and collision between the two flexible extensions are to be further explored. The present research, though at its incipient stage, provides some clues to the improving of the performances of wind energy harvesting devices in the future.

The authors would like to thank the financial support from the National Natural Science Foundation of China (NSFC) under contract number 51705112 and 51805126.