A multi-directional and multi-modal galloping piezoelectric energy harvester with tri-section beam

A traditional wind energy harvester based on galloping can only harvest wind energy from one specific direction, which fails to work efficiently in a natural erratic environment. In this study, we propose a galloping-based piezoelectric energy harvester that can collect energy from wind flow in a wide range of incident directions with multiple vibrational modes being excited. The proposed harvester is composed of a tri-section beam with bonded piezoelectric transducers and a square bluff body with splitters. Finite element analysis of the tri-section beam structure is first performed and confirms the clustered natural frequencies that ease the excitation of different modes. Then, the aerodynamic characteristics of various bluff bodies is conducted through computational fluid dynamics to compare the capability of galloping. Finally, the wind tunnel experiment is carried out to test the wind energy harvesting performance by utilizing the harvester’s multi-modal characteristics. The results of this study demonstrate that the proposed harvester can harvest wind energy in multiple directions with the capability of galloping in multiple vibrational modes, and superior performance is achieved when the second bending mode is triggered. The novel design of the harvester from this work provides a viable solution for harvesting wind energy in a natural environment with varying wind conditions.


Introduction
Over the past decades, the energy crisis has motivated researchers to consider harvesting renewable energies from various ambient sources, such as waste heat, solar energy, wave and tide, and wind flow [1].Immense efforts have been devoted to developing energy harvesting techniques from various aspects, including new transduction materials, power management electronics, and efficient energy storage techniques [2,3].These energy harvesting techniques encompass a wide range of applications, particularly in low-power microelectromechanical systems [4], structural health monitoring and remote sensing [5].Enabled by energy harvesting, high maintenance costs associated with battery replacement can be avoided for traditional battery-powered sensors.
As one of the most common renewable energy sources, wind has been widely converted to vibrations for energy harvesting based on different aeroelastic instability mechanisms, such as galloping [6,7], vortex-induced vibration (VIV) [8,9], wake galloping [10,11], and flutter [12,13].Among them, VIV and galloping based energy harvesting has been extensively studied.It is noticeable that the VIV-based energy harvester can work efficiently if the vortex shedding frequency is equal to the natural frequency of the harvester structure [14], which means that it only performs well in the lock-in wind speed range.In the natural environment, the direction and speed of the wind is generally time-varying.Although the cylinder bluff body can induce VIV from all directions thanks to its geometric characteristics, the classical VIV-based harvester with a straight beam as the supporting structure has restrict the direction adaptivity [15,16].To widen the operational direction range and enhance the output performance, Wang et al [17] and Shi et al [18] proposed the cross-coupled dual-beam VIV energy harvester design in which a cylindrical bluff body was supported by two series-connected beams with bending directions perpendicular to each other, and it can work in two incident wind directions.Su and Lin [19] established a VIV-based wind energy harvester with a U-shape supporter that can widen the incident wind direction range.The experimental result demonstrated the capability of collecting wind energy in two orthogonal directions with the U-shaped supporter.Li et al [20] successively developed a VIV piezoelectric wind energy harvester with a cylinder shell, which could adapt to omnidirectional incident wind due to its geometric characteristic.Gong et al [21] proposed a direction-adaptive VIV-based energy harvester with a guide wing to capture flow energy.The experiment demonstrated that the prototype had an extended range of incident wind directions.Zhang et al [22] and Meng et al [23] established a novel spherical bluff body to scavenge the wind energy from multiple directions based on VIV.Although the above mentioned VIV-based harvesters could work in different directions, they only performed effectively in a narrow wind speed range (lock-in region), restricting their efficiencies and outputs.Apart from VIV, other researchers focused on the galloping based wind energy harvesters, which has the attractive property that the oscillation amplitude of the harvester continues increasing with the wind speed, thus providing useful output in a wide speed range [24].The bluff body plays a critical role to enhance the galloping piezoelectric energy harvester performance.Xing et al [25] explored the potential effect of implementing different bluff body surface protrusions, and the experiment and simulation showed that elliptical protrusions provided the greatest potential to enhance the galloping energy harvesting performance.Wang et al [26,27] found that the isosceles triangle sectioned bluff bodies with Y-shaped attachments could significantly enhance the performance of the piezoelectric galloping energy harvester.However, the galloping performance of bluff bodies were sensitive to incident wind direction, which was not paid much attention in the literature.Further, the normal straight beam also limits the operational range of incident wind directions of the galloping-based harvesters, similar to the VIV-based harvesters.Some researchers focused on designing the galloping-based wind energy harvester to cater to varying incident wind direction.Xin et al [28] and Lu et al [29] utilized the piezoelectric composite cantilever and different shaped bluff body to scavenge multi-directional wind energy through galloping.Lim et al [30] designed a self-tuneable gallopingbased wind energy harvester with a rotating base and vane to scavenge energy from multiple incident directions, but the results indicated that the rotating base configuration caused a higher cut-in speed, which was possibly due to the dampening effect during the angular movement of the base and adversely affected the energy harvesting potential.A similar structural configuration with extra accessories can be found in Tang et al [31], which introduced a wind vane and PVDF film in the harvester to harvest the multi-directional wind energy and an impact stick was utilized to amplify the output performance.
Despite the existing approaches and systems for galloping energy harvesting in multiple incident wind directions, it should be noted that there is little research on such harvesters that can execute multi-directional energy harvesting with multi-modal vibrations.This paper proposes a galloping piezoelectric energy harvester with tri-section beam to fully utilize multiple vibration modes to harness wind energy from a wide range of incident directions.The rest of this paper is organized as follows: in section 2, the finite element method (FEM) is first utilized to explore the modal characteristics of different supporting beams and choose the suitable one with the potential of galloping in multiple vibration modes.The aeroelastic characteristics of different bluff bodies is also studied via computational fluid dynamics (CFD) software.Section 3 presents the physical prototype design and experimental setup for wind tunnel test.In section 4, the simulation and experimental results are compared to confirm the desired modes and natural frequencies being achieved.The performances of the harvester with the tri-section beam and bluff body with splitters, and the counterparts are discussed in detail to show the superior multi-directional and multi-modal performance of the proposed design.Section 5 summarizes the main findings from this work.

FEM and CFD modeling
Only the fundamental mode can be triggered for energy harvesting for a conventional galloping-based energy harvester with a straight beam [32].The frequencies much higher than that of the fundamental mode are the potential reason for not being able to trigger galloping in higher modes.From the perspective of structural dynamics, by tailoring the beam structure, it is possible to cluster a number of lower modes to a relatively low-frequency range so that different modes might be activated under different wind flow conditions.From the aerodynamics perspective, inspired by some existing literature, decorating the bluff body with various surface structures can enhance galloping capability [33,34].Our hypothesis is that by clustering the vibration modes through beam structure design and enhancing galloping capability through bluff body improvement, we can achieve multi-directional and multimodal galloping behavior, which is more suitable for realistic wind energy harvesting.This work proposes a tri-section beam and bluff body with splitters.In this section, FEM is first performed for modal analysis to understand the modal characteristics of straight, bi-section and tri-section beams, and then select the optimal one.CFD model is built for two types of bluff bodies with plain square cross section and square crosssection with splitters, and compare their aerodynamic characteristics to enhance galloping capability.

Modal characteristics
Figure 1 illustrates the schematics of the galloping piezoelectric energy harvester with various bluff bodies and beams.In this configuration, square bluff bodies with and without splitters are considered to explore their different tendencies to trigger galloping.
For the bluff body with splitters, the splitters are attached at the middle of the four side facets of the bluff body.Three different beams have the same total length of 180 mm.The bi-section beam has two sections, each with a length of L 2 = 90 mm and a crease angle α, and the tri-section beam has three sections, each with a length of L 3 = 60 mm and a crease angle β.These beams with bluff bodies will be compared in terms of vibration modes and natural frequencies by finite element modal analysis.When conducting FEM simulation analysis, the cantilever beam and the bluff bodies are modeled as uniform media but have different apparent densities since when they were 3D-printed with Polylactic Acid (PLA), different infill percentages were chosen.Each beam is clamped at one end and the bluff body is attached at the free end.Two piezoelectric transducers (Macro Fiber Composite (MFC), Smart Material Corp.) are bonded on the beam section close to the clamped end, due to the higher strain compared with the other beam sections (which can be confirmed by FEM but not shown here for the sake of brevity).The detailed geometric and material properties of the proposed harvester are listed in table 1.
To analyze the dynamic characteristics of the harvester, FEM is utilized to obtain the vibration modes and corresponding natural frequencies with ANSYS and the results are elaborated in table 2. The bluff body with splitters and multisection beams with different crease angles α and β (90 • , 105 • , 120 • , 135 • and 150 • ) are considered in the FEM analysis.For the bi-section beam, it is noted that with the increase of the crease angle α, the fundamental natural frequency decreases while all the higher natural frequencies increase.For the trisection beam, with the increase of the crease angle β, the trend is generally similar to that of the bi-section beam except for the highest natural frequency at β = 90 • .Besides, except for β = 90 • , the tri-section beam has a slightly higher fundamental natural frequency but lower natural frequencies of higher order modes, as compared to the bi-section beam.Though the straight beam has the lowest fundamental natural frequency (3.82 Hz), its 3rd and 4th natural frequencies are much higher than the multi-section beams (e.g.65.03 Hz of the 4th natural frequency is about 17 times higher than the fundamental one, which brings the difficulty to utilize these higher modes for galloping energy harvesting).This initial comparison indicates that the tri-section beam with β = 105 • and 120 • have very clustered first four natural frequencies worth being investigated for multi-modal energy harvesting.In addition, by comparing the results of the tri-section beam with β = 105 • and 120 • , though the 4th natural frequency for β = 120 • is slightly larger than that for β = 105 • , the first two natural frequencies, which is equivalently essential for the triggering of galloping behavior of the harvester.Hence, taking into account both the clustered modes and lower natural frequencies at lower modes, we choose the tri-section beam with 120 • for further numerical investigation and experimental study.
The mode shapes of the tri-section beam with β = 120 • are further analyzed in figure 2. The first four vibration modes of the harvester with tri-section beam and square bluff body with splitters are as follows: first-order bending mode with the natural frequency of 4.82 Hz; first-order torsional mode with the natural frequency of 7.29 Hz; second-order torsional mode with the natural frequency of 15.48 Hz, and secondorder bending mode with the natural frequency of 17.17 Hz.To harness wind energy in those torsional modes, two MFCs were bonded in parallel along beam width direction near the clamped end of the tri-section beam.In this way, the electrical outputs can be harvested separately, which otherwise will be cancelled out for a single double-sized piece of piezoelectric transducer.

Aerodynamic characteristics
To understand the aerodynamic characteristics of the bluff bodies with and without splitters, CFD simulation is performed.For the bluff body with splitters subjected to the steady wind flow with incident velocity V (figure 3(a)), the aerodynamic force can be expressed as where F L = 1/2ρV 2 rel AC L and F D = 1/2ρV 2 rel AC D are the lift and drag forces, respectively.δ is the wind attack angle, ρ is the air density, A is the windward area, C L is the lift force coefficient, and C D is the drag force coefficient.
To achieve a convergent and accurate solution within a reasonable computational time, the near-wall grid space is selected to produce a dimensionless wall distance, and the boundary layer is shown in figure 3(b).The square bluff body with splitters holds a more significant grid density than the plain square due to the multi-edge corner, and the grid numbers of each section are 182 208 and 97 112, respectively.The transverse force coefficient can be defined as follows: ( According to the quasi-steady theory [35,36], C L and C D , during oscillation, are the same at each wind attack angle δ as the values calculated at the corresponding steady attack angle δ in the wind tunnel tests.CFD software holds the high calculation accuracy and low cost in calculating the aerodynamic coefficients compared with wind tunnel tests, thus, the C L and C D , simulated in the CFD software, are utilized to calculate the transverse force coefficient C Fy .According to the well-known Den Hartog criterion [37][38][39][40], if the first-order derivative of the transverse aerodynamic force coefficient (i.e. the slope of the curve C Fy vs. wind attack angle δ = 0 • ) is positive, galloping instability will occur The transverse force coefficients (C Fy ) of the square bluff body with and without splitters as a function of wind attack angle (δ) at V = 5 m s −1 are elaborated in figure 4(a).It is noted that C Fy increases with δ, peaks at a certain angle δ P and then decreases.The slope of the two curves at zero attack angle is positive.Once the aerodynamical damping is larger than the structural damping, the system total damping is negative causing the galloping to occur.More importantly, the square bluff body with splitters shows a higher peak C Fy = 0.33 and larger attack angle δ when C Fy = 0 (δ 2 ) that those of the square bluff body without splitters.C Fy = 0 is essentially associated with the maximum velocity of transverse oscillation due to the fact that δ is approximately equivalent to ẏ/ V in the quasi-steady theory and the larger peak value reflects a larger aerodynamic transverse force [25,41,42].In addition, the fifth-order polynomial fitting, i.e.C Fy = C 1 δ + C 3 δ 3 + C 5 δ 5 (figure 4(b)) also clearly shows that the bluff body with splitters has a much larger C Fy .Hence, based on C Fy versus δ, it can be deduced that the square bluff body with splitters can provide an enhanced galloping response.

Experiment
The prototyped wind energy harvester consists of a tri-section beam bonded with MFCs, a square cross-sectioned bluff body with splitters and a harvester holder.The tri-section beam and bluff body 3D models were built in the computer-aided design software Inventor and 3D-printed with Polylactic Acid (PLA).A harvester holder was utilized to clamp the harvester beam and position the harvester at an appropriate location in the wind tunnel.An angle adaptor and its scale were created by laser cutting to track the incident wind direction.
With the prototyped harvester properly setup, aerodynamic testing is performed in a small open loop wind tunnel with the cross-section dimensions of the test section being 30.3 cm × 45.5 cm, as shown in figure 5(a) (item ( 6)).The incoming wind flow is generated through a draft fan.A pitotstatic tube is utilized to measure the real-time wind speed and appears on the digital manometer, and the speed controller is used to adjust the incident wind speed.The wind flow direction incident to the harvester is adjusted through the angle adaptor (figure 5(b), item (5)), which is located on the top of the test section of the wind tunnel.Data acquisition (DAQ) module (NI 9229, National Instrument) is utilized to acquire the electrical signal and process it on the computer.
For electrical output measurement, the open circuit voltage and power output on the load resistance R L are of concerned.The internal impedance of the piezoelectric transducer (≈1/(2πfC)) varies under different vibration frequency.For example, at 5.24 Hz of the first-order bending mode for the trisection beam harvester, the internal impedance of the piezoelectric transducer with C = 15 nF is 2.02 MΩ.Similarly, during the second-order bending mode at 17.35 Hz, the internal impedance of the energy harvester is 0.61 MΩ.Hence, the DAQ module with the internal impedance of R DAQ = 1 MΩ cannot measure open circuit voltage V OC of the piezoelectric transducer properly.With a serially connected large resistor R = 20 MΩ (as shown in figure 6(a)), the V OC can be estimated by the voltage divider rule where V DAQ is the voltage red from the DAQ module.
To evaluate the maximum power output, a varying resistance R L should be connected to the piezoelectric transducer.As shown in figure 6(b), the DAQ module measures the voltage V 0 across a small resistor R 0 = 50 Ω, and the total resistance of R DAQ and R 0 , which can be approximated to be R 0 , is further connected in series with a varying R v .R v is composed of multiple varying resistors, each varying between (1 kΩ to 999 kΩ).Thus, the voltage across the effective resistance load and the average power output on R L can be estimated by where V Lrms is the root mean square (RMS) value of V L .
The tuning of R v to achieve optimal P ave will be discussed in section 4.3.

Results and discussion
In this section, the output voltage and power output performance of the proposed wind energy harvester are discussed in detail.The activation range of incident wind direction is compared between three different harvesters (1.Tri-section beam and square bluff body with splitters, 2. Straight beam and square bluff body with splitters, and 3. Straight beam and plain square bluff body).To eliminate the electrical cancellation in torsional vibration, two MFCs are bonded on the tri-section beam at upper and lower positions close to the clamped end, as shown in figure 7(a), and the output root mean square (RMS) voltages are compared.The activation of galloping and the output performance of MFCs are studied under different incident wind directions and multiple vibration modes.Finally, the power output with varying load resistance is carried out to investigate the optimal performance.

Activation range of incident wind direction
The configurations of three wind energy harvesters and their activation ranges of incident wind directions are shown in figure 7. The original position, i.e. zero incident angle, is defined as along the diagonal axis of the square cross-section of the bluff body, as shown in figure 7(a).In figure 7(b), the blue and green shaded areas represent the galloping deactivated and activated ranges for wind energy harvesting.To ascertain the activation ranges of galloping, in the wind tunnel test, the wind energy harvester prototype was tuned from −180 • to 180 • with a 5 • interval, and fine tuning with a smaller interval of 1 • was used around the boundary between activation and inactivation.Galloping is considered to be triggered when the measured voltage signal is a steady harmonic output.The harvester with a straight beam and plain square bluff body can only be triggered for galloping and scavenge wind energy at four specific windward directions −30

Mode activation
For different incident wind directions with galloping activated, different modes are excited with different response amplitudes and electrical outputs.Figure 8 shows the RMS V OC when various harvesters are subject to different incident wind directions with varying wind speed.For the harvester with a straight beam, only the fundamental mode (first-order bending mode) is excited at a few specific incident wind directions.
In general, the galloping response and electrical output of the harvesters with the straight beam increase with the increase of wind speed.Two typical cases of −30 • and −40 • for bluff body without and with splitters, marked as 'S1' and 'S2' will be further analyzed later.
As shown in figure 8(c), the harvester formed by a trisection beam and square bluff body with splitters has a wide activation range of incident wind directions.This is attributed to the effective utilization of the multiple vibration modes of the tri-section beam, together with the enhanced aerodynamic response by the bluff body with splitters.In general, when the incident wind direction is close to perpendicular to the bluff body square edge, the harvester undergoes galloping in bending vibrational mode for harvesting wind energy.To be more specific, when the wind flow is incident from −49 • to −40 • , the first-order bending mode can be triggered.When the wind  'a', 'b', 'c', 'd', 'e' and 'f' are selected for further analysis in the later sections.
As aforementioned, to avoid the charge cancellation in torsional modes, two MFCs are used and their open circuit voltages are compared.Figure 9 compares the outputs from MFCs bonded on the straight beam with different bluff bodies.In general, the two MFCs provide similar outputs.For example, for the harvester with straight beam and the plain square bluff body at the wind speed of 10 m s −1 , the RMS V OC of lower MFC (19.04 V) is slightly larger than the upper MFC (17.69 V).For the harvester with straight beam and square bluff body with splitters at a wind speed of 8.3 m s −1 , the RMS V OC of the lower and upper MFCs are 6.85 V and 6.46 V, respectively.The similar outputs from two MFCs are due to the fact that only the first-order bending mode is activated for the wind energy harvesters based on the straight beam and the strains at the positions of the upper and lower MFCs are similar.The minor discrepancies could be attributed to various factors, such as the slightly different parameters of two MFCs and bonding epoxy layers, etc.
Figure 10 illustrates the RMS V OC of the harvester with trisection beam and square bluff body with splitters under different incident wind directions and vibrational modes.When the incident wind directions are −40  second-order bending mode in the wind speed range between 5.2 m s −1 and 7.2 m s −1 , and the outputs of the upper and lower MFCs are almost identical.At the same incident wind direction, the first-and second-order coupled torsional modes are triggered in the wind speed range between 7.3 m s −1 and 10.5 m s −1 and the RMS V OC of the upper and lower MFCs are 4.88 V and 6.14 V with obvious difference in the amplitude and phase.This is similar to the different outputs noted in figures 10(b) and (c) due to the coupled torsional modes.Overall, when the harvester undergoes the bending modes, the RMS V OC outputs from the upper and lower MFCs are similar.However, in the coupled torsional modes, there is an obvious difference in the RMS V OC outputs.
According to the previous analysis, the lower MFC has a larger voltage output.Thus, in the following analysis, only the experimental results of the lower MFC will be provided to demonstrate the performance of the harvester.To assess the vibration frequency experimentally, the Data Acquisition (DAQ) module (NI 9229, National Instruments) was utilized to capture voltage time-domain signals and the frequency of different vibration modes are directly determined using the Fast Fourier Transform function in the DAQ software.The simulation and experimental results of the three different harvesters' vibration modes and corresponding frequencies are tabulated in table 3. It can be seen that, in general, the oscillation frequencies of the triggered modes of three harvesters are consistent with the predicted natural frequencies from FEM.For example, the errors for the four natural frequencies of the harvester with tri-section beams are −8.71%,1.92%, 7.95%, and −1.05%, respectively.In the experiment, the harvester with tri-section beam can take advantage and utilize the multiple vibration modes to harvest the wind energy in an efficient way, while for the harvesters with straight beam, only the first-order bending mode can be triggered.
Figure 11 shows the V OC and the frequency spectrum of the harvesters with straight beam and square bluff body with and without splitters subjected to varying wind speed, which indicates the first-order bending mode is triggered and the corresponding frequency.In general, the output increases with the wind speed and the frequency does not change.
The output V OC and frequency spectra of the harvester with tri-section beam at different incident wind directions are shown in figure 12.When the incident wind directions are −40 • (figure 12      6.56 V can be obtained at the wind speed of 7.9 m s −1 .The output declines during the transition to the second-order bending mode.The output increases once the harvester is transitioned to the second-order bending mode (17.35 Hz) and reaches 37.0 V at the wind speed of 12 m s −1 .Overall, the output in the second-order bending mode is much higher than that in the first-order bending mode.

Power output
Figure 13 illustrates the power outputs and RMS V OC of various wind energy harvesters with varying load resistance.The wind speed is set to be around 10 m s −1 except for the straight beam and tri-section beam with splitters since MFC is found susceptible to damage in the first-order bending mode due to large deformation in the test.
In figures 13(a) and (b), the harvesters with straight beams can harness the wind energy under the first-order bending mode with 4.61 Hz and 4.05 Hz for the square bluff body without splitters and with splitters under the wind speed of 10 m s −1 and 8.5 m s −1 .The internal impedances of the energy harvester (≈1/(2πfC)) are 2.30 MΩ and 2.62 MΩ, respectively.With the optimal load resistances 2.21 MΩ and 2.52 MΩ, the peak power outputs are 98.53 µW and 46.99 µW, respectively.For the harvester with a tri-section beam, four vibration modes at frequencies of 5.24 Hz, 7.15 Hz, 14.25 Hz, and 17.35 Hz can all be triggered, and the internal impedances of the piezoelectric transducers in different vibrational modes are 2.02 MΩ, 1.48 MΩ, 0.74 MΩ, and 0.61 MΩ, respectively.In the second-order bending mode with the incident wind direction of 35 • and at the wind speed of 10.5 m s −1 (figure 13(d)), the harvester can harness wind energy in a significantly efficient way.The maximum output power of 538.22 µW is obtained at R L = 0.57 MΩ.In the first-order bending mode with the incident wind direction of −40 • and at the wind speed of 6 m s −1 (figure 13(c)), the maximum output power of 84.22 µW is obtained at the load resistance of 2.06 MΩ.In the first-order and second-order coupled torsional modes with the incident wind direction of −25 • and wind speed of 10 m s −1 (figure 13(e)), the harvester can obtain powers of 19.12 µW and 20.26 µW at the optimal load resistances of 1.44 MΩ and 0.71 MΩ, respectively.Overall, the harvester with the tri-section beam and square bluff body with splitters can efficiently harness wind energy in the secondorder bending mode (17.35 Hz) with the highest power output of 538.22 µW, which is five times larger than the harvester with the straight beam and square bluff body without splitters (98.53 µW), and 11 times larger than the harvester of straight beam and square bluff body with splitters (46.99 µW).These results demonstrate that the proposed harvester can not only harvest energy from a broad range of incident wind directions but also achieve outstanding power output performance.

Conclusions
This paper has comprehensively investigated the effects of a tri-section beam and bluff body with splitters on wind energy harvesting in multiple vibration modes and from different incident wind directions.Finite element analysis firstly predicts the clustered natural frequencies of the first four modes of the tri-section beam with confirmation from the measured outputs.The CFD simulation also indicates the greater potential of the square bluff body with splitters for triggering galloping behavior compared to the counterpart without splitters.
Wind tunnel tests then comprehensively analyze the output performance of the proposed galloping piezoelectric energy harvester and the ability of incident wind direction adaptation.The results show that the proposed harvester can experience galloping in multiple ranges of incident wind directions from −49 • to −40 • , −30 • to 5 • and 15 • to 43 • , while the galloping is only triggered for the first-order bending mode and in a few specific incident directions nearly perpendicular to the bluff body square edge for the straight beam configurations.The detailed analysis of the electrical outputs from the piezoelectric transducers and the spectra designates that different modes are triggered when the proposed harvester is subjected to wind flows in different incident wind directions and wind speed ranges, including two bending modes and the coupled torsional modes.In some ranges of incident wind directions, only bending modes or coupled torsional modes are activated.In other ranges of incident wind directions, the mode transition is observed depending on the wind speed range.In general, we can draw the following conclusions.
• The proposed harvester can achieve an outstanding performance when the galloping is triggered in the 2nd bending mode compared to the first bending mode or coupled torsional modes.• Apart from the dip during the transition of modes in the same incident wind direction, the electrical output increases overall with the increasing wind speed.• The upper and lower MFCs produce close RMS V OC outputs in a bending mode but different outputs when the coupled torsional modes are triggered.• The lower piezoelectric transducer from the proposed harvester can produce 538.22 µW at the incident wind direction of 35 • and wind speed of 10.5 m s −1 with the galloping triggered in the second-order bending mode.In comparison, the straight beam with splitters at the direction of −35 • and wind speed of 8.5 m s −1 can only provide 46.99 µW with galloping triggered in the first-order bending mode.
The proposed harvester clearly demonstrates the feasibility of wind-direction adaptive energy harvesting through innovative beam design and bluff body improvement.It unveils the potential of multi-modal galloping-based energy harvesting from varying wind conditions in the natural environment.

Figure 1 .
Figure 1.Beam and bluff body configurations of the galloping piezoelectric energy harvester: (a) straight beam, (b) bi-section beam with crease angle α, (c) tri-section beam with crease angle β, (d) square bluff body without splitters, and (e) square bluff body with splitters.

Figure 2 .
Figure 2. Modes of the harvester with tri-section beam from FEM: (a) first-order bending mode, (b) first-order torsional mode, (c) second-order torsional mode, (d) second-order bending mode.

Figure 3 .
Figure 3. (a) Definitions of wind attack angle (δ) and transverse galloping force (Fy) and (b) Computational mesh for a bluff body with splitters in the wind flow.

Figure 4 .
Figure 4. Transverse force coefficients (C Fy ) of square bluff bodies with and without splitters as a function of wind attack angle δ.(a) CFD simulation, (b) the fifth-order polynomial fitting.

Figure 5 .
Figure 5. Prototype of the proposed galloping piezoelectric energy harvester and experimental setup for wind tunnel test: (a) experimental setup and (b) control and data flow chart.

Figure 6 .
Figure 6. Circuit connections for (a) open circuit voltage measurement and (b) power measurement with varying load resistance.

, − 25 •
, 35 • and 40 • .The harvester with a straight beam and square bluff body with splitters has a widened activation range (−40 • to −35 • , −1 • , 10 • , and 45 • to 48 • ).This is due to the more significant aerodynamic response compared with the plain square bluff body, which has been confirmed in section 2.2.As for the proposed harvester with tri-section beam and bluff body with splitters, galloping behavior in different vibration modes can be activated in the widest range of incident wind directions (i.e., −49 • to −40 • , −30 • to 5 • , 15 • to 43 • , and 90 • ) among the three different configurations.

Figure 7 .
Figure 7.Comparison of activation ranges of incident wind directions for different wind energy harvesters.(a) Proposed design in this work, (b) activation range comparison of different wind energy harvesters: (i) tri-section beam and square bluff body with splitters, (ii) straight beam and square bluff body with splitters, (iii) straight beam and plain square bluff body.

Figure 8 .
Figure 8. RMS open circuit voltages of different wind energy harvesters subject to different incident wind directions and varying wind speed: (a) straight beam and plain square bluff body, (b) straight beam and square bluff body with splitters, (c) tri-section beam and square bluff body with splitters.
• and 40 • (figures 10(a) and (f)), the harvester can scavenge wind energy with the first-and second-order bending modes, respectively, and the RMS V OC outputs from the upper and lower MFCs are close to each other.For example, the RMS V OC outputs for the upper and lower MFCs at the wind speed of 10 m s −1 and incident wind direction of −40 • are 21.28 V and 21.67 V, respectively.The wind flow from the incident direction of −25 • activates coupled torsional modes (figure 10(b)).As a result, the two MFC outputs are out of phase with different values.For example, at the wind speed of 12 m s −1 , the RMS V OC outputs of the upper and lower MFCs are 11.25 V and 13.27 V, respectively.Multiple modes can be triggered in different wind speed ranges for other incident directions of −5 • , 3 • and 35 • (figures 10(c)-(e)).When the harvester experiences the bending vibrational modes, the upper and lower MFCs have a close V OC output in phase.For example, at the incident wind direction of 3 • (figure 10(d)), the harvester can trigger

Figure 9 .
Figure 9. RMS V OC of wind energy harvesters with: (a) straight beam and plain square bluff body at the incident wind direction of −30 • , (b) straight beam and square bluff body with splitters at the incident windward direction of −40 • .
(a)) and 40 • (figure 12(f)), only one bending mode is activated, which is evident in the frequency spectra.The V OC outputs increase with the increasing wind speed.At the incident wind direction of −40 • , the first-order bending mode is triggered with a frequency of 5.24 Hz, while at the incident wind direction of 40 • , the second-order bending mode is triggered with a frequency of 17.35 Hz.When the incident wind direction is −25 • (figure 12(b)), the firstorder and second-order coupled torsional modes are triggered with frequencies of 7.15 Hz and 14.25 Hz in the whole wind speed range, which is indicated in the frequency spectrum.The V OC output increases with the increasing wind speed.At other incident wind directions of −5 • , 3 • and 35 • (figures 12(c)-(e)), the frequency spectra clearly indicate the transition of vibration modes in different wind speed ranges for harvester with the tri-section beam.At the incident wind direction of −5 • (figure 12(c)), the harvester can harness wind energy between 3.0 m s −1 to 7.4 m s −1 in the first-order bending mode with the frequency of 5.24 Hz and reach a peak RMS V OC of 4.21 V at the wind speed of 6.3 m s −1 .The output then declines during the transition and increases with the wind speed increasing from 7.5 m s −1 to 12 m s −1 once the first-and second-order coupled torsional modes (7.15 Hz and 14.25 Hz) are triggered.At the incident wind direction of 3 • (figure 12(d)), a trend similar to that at the incident wind direction of −5 • is observed except that the second-order bending mode with the frequency of 17.35 Hz is triggered in the low wind speed range (under 6.1 m s −1 ).At the incident wind direction of 35 • (figure 12(e)), two bending modes are triggered for different wind speed ranges.In the low speed increase (6.7-9.8 m s −1 ), the harvester harnesses the wind energy in the first-order bending mode (5.24 Hz) and the peak RMS V OC of

Figure 11 .
Figure 11.V OC and frequency spectra of wind energy harvesters with: (a) straight beam and plain square bluff body at the incident wind direction of −40 • and (b) straight beam and square bluff body with splitters at the incident wind direction of −25 • .

Figure 13 .
Figure 13.RMS voltages and power outputs with varying R L from different harvesters in different vibration modes: (a) straight beam with plain square bluff body in first-order bending mode (incident wind direction of −30 • , wind speed of 10 m s −1 ); (b) straight beam with square bluff body with splitters in the first-order bending mode (incident wind direction of −35 • , wind speed of 8.5 m s −1 ); tri-section beam with square bluff body with splitters in (c) the first-order bending mode (incident wind direction of −40 • , wind speed of 6 m s −1 ), (d) second-order bending mode (incident wind direction of 35 • , wind speed of 10.5 m s −1 ), and (e) the first-and second-order coupled torsional modes (incident wind direction of −25 • , wind speed of 10 m s −1 ).

Table 1 .
Geometric and material properties of the proposed harvester.

Table 2 .
Comparison of the first four natural frequencies (in Hz) of various harvesters with straight beam and multi-section beams with different crease angles from FEM.

Table 3 .
Comparison of frequencies (in Hz) of various harvesters with different beams in different modes from FEM and experiment.