SupersonicFlutterUtilizationforEffective Energy ...downloads.hindawi.com/journals/smr/2012/181645.pdf · Energy-harvesting (power-generation or power-scaveng-ing) is a process by

Hindawi Publishing CorporationSmart Materials ResearchVolume 2012, Article ID 181645, 10 pagesdoi:10.1155/2012/181645

Research Article

Supersonic Flutter Utilization for EffectiveEnergy-Harvesting Based on Piezoelectric Switching Control

Kanjuro Makihara1 and Shigeru Shimose2

1 Department of Aerospace Engineering, Tohoku University, 6-6-01 Aramaki-Aza-Aoba, Aoba-ward, Sendai 980-8579, Japan2 Japan Aerospace Exploration Agency (JAXA), Institute of Space and Astronautical Science (ISAS), 3-1-1 Yoshinodai,Chuo-ward, Sagamihara, Kanagawa 252-5210, Japan

Correspondence should be addressed to Kanjuro Makihara, [email protected]

Received 4 January 2012; Revised 9 March 2012; Accepted 10 March 2012

Academic Editor: Osama J. Aldraihem

Copyright © 2012 K. Makihara and S. Shimose. This is an open access article distributed under the Creative Commons AttributionLicense, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properlycited.

The harvesting of electrical energy generated from the flutter phenomenon of a plate wing is studied using the quasi-steadyaerodynamic theory and the finite element method. The example of supersonic flutter structure comes from sounding rockets’wings. Electrical energy is harvested from supersonic flutter by using piezoelectric patches and switching devices. In order toevaluate the harvesting performance, we simulate flutter dynamics of the plate wing to which piezoelectric patches are attached. Wedemonstrate that our harvesting system can generate much more electrical energy from wing flutter than conventional harvestingsystems can. This flutter utilization changes our perception to a useful one in various fruitful applications from a destructivephenomenon.

1. Introduction

Flutter is caused by the interaction between the structuralmotion of a wing and the aerodynamic load exerted on thewing. It is a typical self-excited aeroelastic phenomenon thatoccurs in wings, thin walls, and so on. Dowell [1] occursmost frequently within a high-speed, that is, transonic,supersonic, and hypersonic flow. Lottati [2] investigated theeffects of structural and aerodynamic damping on the speedof flutter of a composite plate wing. Tang and Dowell [3] haveanalyzed the nonlinear behavior of a flexible rotor blade dueto structural free-play and aerodynamic stall nonlinearities.The analytical results were compared with experimentalobservations. Various studies have been conducted on flutterdynamics, such as prediction of flutter and robust structuraloptimization of wings [4]. The use of sophisticated smartmaterials such as piezoelectric materials, shape memoryalloys, and magnetostrictive materials in aerospace engineer-ing can lead to the development of new design concepts. Anew design concept is to alter structural dynamics by exertionof force or deformation. Moon and Hwang [5] used thelinear quadratic regulator theory to suppress nonlinear panel

flutter. Han et al. [6] designed a mu-synthesis controller toenhance flutter suppression performance despite parametricuncertainties. Raja et al. [7] used multilayer piezoelectricactuators and piezoelectric sensors for constructing a linearquadratic Gaussian controller to suppress the flutter ofa composite plate. Agneni et al. [8] applied this passivemethod to flutter suppression and demonstrated satisfactorysuppression performance. However, flutter suppression per-formance achieved by adopting this passive method is poorerwhen the electrical resonance frequency is slightly differentfrom the frequency of the structure. Hence, the passivemethod provides limited robustness against model errorsand is unsuitable for systems whose structural frequenciescan shift because of aerodynamic influence.

Energy-harvesting (power-generation or power-scaveng-ing) is a process by which energy is extracted from varioussources and stored for future use, such as solar energy, tidalenergy, piezoelectricity, thermoelectricity, and kinematicenergy [9, 10]. Energy-harvesting techniques are expectedto be of vital importance in the future when fossil fuelreserves will exhaust completely. Among the various sourcesmentioned above, this study focuses on harvesting energy

2 Smart Materials Research

from vibrating structures using piezoelectricity. Cornwell etal. [11] developed an approach to improve energy output byusing a tuned auxiliary structure.

Owing to the interest in the use of wind in harvestingenergy, various studies and investigations were conductedby researchers. Robbins et al. [12] discussed vortex-inducedoscillations of piezoelectric cantilevers located behind bluffbodies. Kwon [13] conducted an investigation of a simple T-shaped cantilever design with a mass flow controller (MFC)at a low air flow speed.

Thus far, wing flutter has been considered as a phe-nomenon that should be avoided, especially in aerospaceengineering. However, adding electromotor or piezoelectrictransducers to wings under aeroelastic vibrations is a fea-sible method for harvesting energy, as Isogai et al. [14]verified in simulation and experiments. This research usedthe conventional rectified harvester composed of a diode-bridge. Bryant and Garcia [15] proposed a piezoelectricharvester using a conventional rectified harvester based onthe impedance matching method. De Marqui et al. [16,17] proposed an electromechanically coupled finite elementmodel that was combined with an unsteady aerodynamicmodel. They also developed a piezoelastic model for airflow excitation of cantilevered plates using doublet-latticemethod. Dunnmon et al. [18] presented an aeroelastic energyharvester that was exploited for piezoelectric power gen-eration from aerodynamic flows, especially nonlinear limitcycle oscillations. Sousa et al. [19] presented modeling andexperiments of aeroelastic energy harvesting using piezo-electric transduction with a focus on exploiting combinednonlinearities. Erturk et al. [20] investigated the conceptof piezoaeroelasticity for energy harvesting and focused onmathematical modeling and experimental validations of theproblem of generating electricity at the flutter boundary ofa piezoaeroelastic airfoil. Although these previous studiesshowed the possibility of energy-harvesting from flutterphenomenon, they used only a simple rectified harvesterand their flutter performances were not high. Therefore,in order to enhance the flutter harvesting performance, weintroduce an energy-harvesting system that extracts electricalenergy from wing flutter using a switching control witha piezoelectric material. Furthermore, we modified theswitching control to adopt to flutter systems that are subjectto the change in natural frequency. This paper clearly showsthe difference between the conventional flutter harvester andour new harvester, by explaining both energy-harvestingmechanisms in detail. The effective use of wing flutterchanges our perception of it—from being a destructivephenomenon as it was formerly known to be to being usefulin various applications.

2. Aerodynamic Pressure of TailWing of Sounding Rocket

2.1. Sounding Rocket. In this study, we focus on harvest-ing energy from the wing flutter of a sounding rocket[21]. Institute of Space and Astronautical Science (ISAS),Japan Aerospace Exploration Agency (JAXA), has developed

Figure 1: Sounding rocket having its four titanium tail wings.

a sounding rocket S-310 (Figure 1), which we consider as anexample in our study. The outline of this rocket is explainedin brief here to highlight its characteristics. The S-310 isa single-stage rocket, 310 mm in diameter; it can reach analtitude of 150 km. The rocket attains approximately Mach4.6 in 23 seconds, which indicates that it flies at a supersonicspeed during most of its flight. The sounding rocket has fourtail wings (fins) made of a solid titanium plate.

2.2. Aerodynamic Pressure of Tail Wing for Flutter Interaction.A titanium plate simulates the wings of a sounding rocketflying at a supersonic speed, as Figure 2 depicts. Thus, theplate can be subject to supersonic flutter during the flight ofthe sounding rocket. We include a cantilevered-plate wing inthe study to investigate the harvesting of energy from wingflutter. Piezoelectric patches are attached to the wing surfaceto generate electrical energy from the motion of the wing. Inreality, patches attached to the wing surface may adverselyaffect fluid dynamics because they cause discontinuity ofthe wing surface. Furthermore, the patches may be adverselyaffected by the heat generated by aerodynamic interference.However, in this study, we do not consider these issues.Nevertheless, we need to develop piezoelectric actuators suchas piezoelectric fibers embedded in composite plate wings.

Aerodynamic pressure at a high supersonic speed isdescribed by a quasi-steady first-order piston theory [22].The pressure exerted on the wing plate of a rocket flying ata speed U is given by

p − p∞ = ρ∞U2√M2 − 1

[∂u

∂y+M2 − 2M2 − 1

1U

∂u

∂t

], (1)

where

M ≡ U

a∞. (2)

Smart Materials Research 3

Sou

ndi

ng

rock

et

x

Wind (U)

Piezoelectric patch

Tail wing

z

y

Aerodynamic

pressure

Figure 2: Tail wing subject to flutter and piezoelectric patchesattached to the wing.

Assuming that the pressure is exerted on both sides ofthe wing, we can express the resultant pressure, pa(x, y, t),exerted on the wing as

pa(x, y, t

) ≡ −2ρ∞U2√M2 − 1

[∂u

∂y+M2 − 2M2 − 1

1U

∂u

∂t

]. (3)

3. Harvesting Scheme for Wingwith Piezoelectric Patches

3.1. Equation of Motion with Aerodynamic. Piezoelectricpatches shown in Figure 2 are assumed to be polarized inthe thickness direction (z-direction) and isotropic in thein-plane direction (x-y plane). Hence, their constitutiveequations [23] are given by

σp = cDp εp − hDz, Ez = −hTεp + βSzzDz, (4)

where

σp ≡⎧⎪⎨⎪⎩σxσyτxy

⎫⎪⎬⎪⎭, εp ≡

⎧⎪⎨⎪⎩εxεyγxy

⎫⎪⎬⎪⎭, h ≡

⎧⎪⎨⎪⎩hxzhxz0

⎫⎪⎬⎪⎭,

cDp ≡cDp

1− ν2p

⎡⎢⎢⎣

1 νp 0νp 1 0

0 01− νp

2

⎤⎥⎥⎦.

(5)

The stress-strain relation of a wing is written as

σw = cwεw, (6)

where

cw ≡ cw1− ν2

w

⎡⎢⎢⎣

1 νw 0νw 1 0

0 01− νw

2

⎤⎥⎥⎦. (7)

The linear strain-displacement relation based on the Kirch-hoff-Love assumption is

ε = −z

[∂2

∂x2,∂2

∂y2, 2

∂2

∂x∂y

]T

u(x, y, t

). (8)

On the surface of the wing, np pieces of piezoelectric patchesare attached, and the jth patch (1 ≤ j ≤ np) is attachedat positions x1 j ≤ x ≤ x2 j , y1 j ≤ y ≤ y2 j , and z1 j ≤ z ≤z2 j . To ensure the generality of this theoretical analysis, amultiple-input-multiple-output system is considered. UsingHamilton’s principle, we can construct

∫ t2

t1

⎡⎣δTw − δUw +

np∑j=1

(δTp j − δUp j

)+ δW

⎤⎦dt = 0, (9)

where

Tw ≡∫V

12ρw

(∂u

∂t

)2

dV , Uw ≡ 12

∫V

σTwεwdV ,

Tp j ≡∫Vpj

12ρp j

(∂u

∂t

)2

gj(x, y, z

)dV ,

Upj ≡ 12

∫Vpj

(σTp εp + EzDz

)dV ,

gj(x, y, z

) ≡ [H(x − x1 j

)−H

(x − x2 j

)]

×[H(y − y1 j

)−H

(y − y2 j

)]

×[H(z − z1 j

)−H

(z − z2 j

)].

(10)

Virtual work, δW , can be written as

δW ≡∫Sδu[f(x, y, t

)+ pa

(x, y, t

)]dS

+np∑j=1

Vj

∫Sp j

δDz jg j(x, y, z

)dS.

(11)

Here, f (x, y, t) is the external force normal to the wing andVj is the voltage applied to the jth piezoelectric patch as ageneralized external force.

The finite element method (FEM) element proposedby Zienkiewicz and Taylor (known as the ACM element)[24], which is a four-node nonconforming plate element,is employed to discretize the partial derivative equationsof motion. From (3)–(11), the equation of motion forthe cantilevered wing with multiple piezoelectric patchesattached to it can be expressed as

Mx + Kx + μAx = BQ + f , (12)

where

M≡∑ele

∫V+Vp

ρNTF NF dV , K≡

∑ele

∫V+Vp

z2BTF cBFdV ,

A ≡∑ele

∫S

NTF∂NF

∂ydS, B ≡

∑ele

∫Vp

(z

Sele

)BTF hdV ,

BF ≡[∂2NF

∂x2,∂2NF

∂y2, 2∂2NF

∂x∂y

]T

, μ ≡ 2ρ∞U2√M2 − 1

.

(13)


A vector-matrix form equation for piezoelectric voltage is de-scribed as

V = −BTx + C−1Q, (14)

where

C−1 ≡∑ele

∫(zβSzzSele

)dz. (15)

We perform the transformation x = Φη and introduce themodal damping ratio in (12) as

η + Ξη +(Ω + μΦTAΦ

)η = ΦTBQ + ΦT f , (16)

where

Φ ≡ [φ1,φ2, . . . ,φn], Ω ≡ diagonal

[ω2k

],

Ξ ≡ diagonal[2ζωk].(17)

This eigenvalue problem is solved for the homogenous partof (12) without aerodynamics (i.e., μ = 0).

3.2. Piezoelectric Switching Control for Energy-Harvesting. Aconventional energy-harvesting device that employs piezo-electric materials to generate energy includes a vibratingpiezoelectric structure and an energy storage system [9, 10].The energy generator is composed of piezoelectric materials,which are attached to the structure, and a harvesting circuit.Circuit I shown in Figure 3 is a conventional harvestingcircuit consisting of a diode bridge of four diodes. The diodebridge is connected to the piezoelectric materials and itprovides a mechanism for current rectification. When thepiezoelectric voltage Vp is positive, electric current starts toflow in one loop (from A, B, D, F, C, E, and to G), and Vs

instantly becomes equal to Vp. When Vp is negative, electriccurrent starts to flow in one loop (from G, E, D, F, C, B, and toA), and Vs instantly becomes equal to −Vp. This harvestingsystem is used in many vibration systems; however, it doesnot satisfactorily harvest electrical energy.

To enhance the energy-harvesting performance, we usethe energy-recycling semiactive approach [25] as an effectiveenergy-harvesting mechanism. This approach involves theuse of Circuit II, which is connected to the piezoelectricmaterial, as shown in Figure 4. The circuit has only twodiodes and a selector switch. The selector switch is connectedto point 1 or 2 to control the current flow. Accordingto our previous study [25], the advanced energy-recyclingapproach can simultaneously manage multiple circuits andpiezoelectric patches. The harvesting system is assumed toconsist of circuits and np pieces of piezoelectric patches.One switching strategy of managing vibration semiactivelyinvolves controlling the jth switch (1 ≤ j ≤ np) so that Qj

has the same polarity as QT j and the absolute value of Qj

is maximum. Here, QT j is the active feedback input that isdetermined by an active control scheme. The switching logic[25] is

when QT j < 0, turn jth switch to point 1,

when QT j > 0, turn jth switch to point 2.(18)

Piezoelectric patchDiode

bridge

C

F

A

D

B

E

G

Vs

Vp

Cs

Figure 3: Circuit I—conventional harvesting circuit.

L

Piezoelectric patch

D

C

AB

H

V s

E

G

F

Point 1Point 2

Vp

Cs

Figure 4: Circuit II—efficient harvesting circuit with energy-recycling mechanism.

Because our semiactive method just changes the switch con-nection to point 1 or 2, it never increases the vibrationenergy by its switching action. Hence, we can infer that oursemiactive approach is safer than other active approachesthat usually involve a risk of instability such as spillover.

As will be seen later, in flutter problems, modal fre-quencies can shift according to dynamic pressure. Therefore,sophisticated controls based on modal decomposition areimpractical. One way of implementing switching controlswithout modal information is to adopt an approach based onthe direct velocity feedback method [26], that is, describingQT j as

QT j ≡ −εp j , (19)

where εp j is the strain at the position of the jth piezoelectricpatch.

3.3. Energy-Harvesting Mechanism. This study focuses onthe energy harvested from wing flutter via piezoelectric


V

τ

τ

Vs

u

t1 t2 t3

t

t

Vp

Figure 5: Illustration of energy-harvesting mechanism with switch-ing control.

patches. We here explain the harvesting mechanism shownin Circuit II (Figure 4) using a single-degree-of-freedom(SDOF) system, as this system is comprehensible. Figure 5shows a schematic of the single-mode vibration in energy-harvesting. When the velocity Vp is negative, the switch isconnected to point 2, whereas when Vp is positive, the switchis connected to point 1. When the displacement reaches apeak and when Vp is positive (e.g., t = t1 in Figure 5), thepolarity of Vp is expected to change from positive to negative.When the selector switch is connected to point 1 from point2, electric current starts to flow in one loop (from A, E, F,G, L, and to H). Because of this current flow, the polarity ofVp reverses to negative. After Vp reaches the minimum peak,the diode between points E and F prevents electric currentfrom flowing in the opposite direction, and Vp retains theminimum negative value. This current flow is responsible forthe voltage reversal mechanism. After the completion of thisprocess and while −Vp is lesser than Vs, no electric currentflows in any branch circuit. During this time, Vp decreasesaccording to the structural motion because of the effect ofpiezoelectric materials. As soon as −Vp reaches Vs (e.g.,t = t2 in Figure 5), electric current starts to flow in one loop(from H, L, G, F, C, B, and to A), and some electric chargeis stored in the capacitor. This current flow is responsible forthe energy-harvesting mechanism.

To summarize the above discussion, once the connectionpoint of the selector switch is changed, the voltage-reversaland energy-harvesting processes automatically proceed inthe circuit.

4. Numerical Simulation

We carried out a numerical simulation of the energy-har-vesting on the plate wing (Figure 2). The wing had an area of0.37 × 0.49 m and a thickness of 6.75 mm. It was made of atitanium alloy (Ti-6Al-4V). This configuration is essentiallya simpler model of the S-310’s tail wing for explaining the

Table 1: Parameters of titanium wing and piezoelectric patch.

UnitPiezoelectric

patchTitanium

wing

Piezoelectric coefficient 108 V/m 4.67 NA

Dielectric coefficient 107 Vm/C 1.95 NA

Density 103 kg/m3 8.10 4.47

Young’s modulus 1010 N/m2 6.40 11.3

Poisson’s ratio NA 0.32 0.31

harvesting performance on which we focus in this study.The wing was rigidly supported on one of its boundaries,that is, x = 0. A piezoelectric patch (ceramic type, 154 ×175 × 0.5 mm) was attached at 0 ≤ x ≤ 0.154 and 0.28 ≤y ≤ 0.455 on the wing. The total resistance in the circuitwas 30Ω, and the piezoelectric capacitance Cp was 1.17 ×10−6 F. Without considering the aerodynamic influence, thefirst and second mode frequencies of the open circuit (i.e.,constant charge) were 43.0 Hz and 84.5 Hz, respectively. Thesimulation parameters are listed in Table 1. These parameterswere determined on the basis of the materials used in theinvestigation to carry out realistic simulations.

4.1. Eigenvalue Analysis of Flutter. Equation (12) can bereduced into an eigenvalue problem:

det[−λM + K + μA

] = 0, (20)

where λ is a complex eigenvalue. Because the eigen analysis isperformed on a no-control system, the control input and theexternal disturbance are neglected. Figure 6 plots eigenvaluesas a function of the dynamic pressure parameter μ. Thecurves of the two values of the real part approach each otheras μ increases. When μ = 2.86 × 106, the two values ofthe real part can be combined as Re [λ] = 1.86 × 103.At this critical value of μ the wing experiences a flutterphenomenon. This figure shows the loci of only the first andsecond modes. Since this critical value indicates the smallestdynamic pressure among all critical values, we focus on therelation between only two vibration modes.

4.2. Simulations of Harvesting Performance. We simulatedflutter dynamics in the case that a white noise force wasexerted on the wing surface. The power spectral density(PSD) per unit frequency of the random force (white noise)had a constant value of 0.1 N2/Hz in the range of 30 to 100 Hzand a value of 0 in the rest of the frequency range. Therefore,the frequency range of the nonzero PSD covered the first andsecond modes.

The history of wing dynamics at a critical dynamic pres-sure (i.e., μ = 2.86 × 106) is shown in Figure 7. Thishistory shows the dynamics in the case of the switchingcontrol with Circuit II for the purpose of energy-harvesting.Piezoelectric voltage, storage voltage, electric charge, tipdisplacement at the wing corner, and input random forceare shown. The tip displacement increases due to the flutterphenomenon, and accordingly, both voltages and charge alsoincrease. The storage capacitor has a storage capacitance,


0.5

1

1.5

2

2.5

3×106

×106

Re

(λ)

1.5 2 2.5 3

k

First modeSecond mode

(a)

−3

0

3

×104

Im(λ

)

1.5 2 2.5 3

k ×106

First modeSecond mode

(b)

Figure 6: Eigenvalues as a function of dynamic pressure.

Cs, of 1.17 × 10−6 F. At t = 0.2 s, the tip displacementreached 4.1 × 10−3 m. Because of the piezoelectric effect atthis point, the wing experienced a flutter phenomenon; thecorresponding piezoelectric voltage was 79.1 V.

Figure 8 shows history of flutter harvesting with CircuitII for a zoomed time scale of Figure 7. Due to the energy-recycling mechanism, the piezoelectric voltage alternativelytakes positive and negative values. The relation betweenpiezoelectric and stored voltages is clearly depicted. Thestored voltage increases only if the absolute value of piezo-electric voltage reaches the value of stored voltage, and,after then, both are equal. This equality indicates that theelectrical energy is transferred to the stored capacitor. We canconfirm that electric charge is constant while energy is nottransferred, whereas the amount of electric charge decreaseswhile energy is transferred. These behaviors of both voltagesagree with the explanation of energy-harvesting in Figure 5.

Figure 9 shows history of flutter harvesting with CircuitI for a zoomed time scale. The piezoelectric voltage is quitedifferent from that of history of energy-harvester with CircuitII (Figure 8), and is a sine wave based on the piezoelectriceffect of structural vibration. Compared with Figures 8 and 9,the energy-recycling mechanism enables the stored voltage tobe larger, which means that Circuit II is much more effectivefor flutter-harvester than the conventional system.

Further, the storage capacitor and diode bridge wereconnected to the harvesting circuit. The storage capacitanceis expressed with a capacitance ratio as κ ≡ Cs/Cp. Figure 10shows the voltage in the two harvesting systems with CircuitI and Circuit II for κ = 1.0. The line for the harvesting systemwith Circuit I indicates the conventional method, whereasthat with Circuit II indicates the new harvesting method.Clearly, the harvesting system with Circuit II performsbetter in harvesting energy from wing flutter. The voltagein the harvesting device, Vs, is shown to have a step-likecurve, which is characteristic of harvesting systems that usediode bridges. Stored electrical energy can be described as

(1/2) CsV 2s . Our harvesting system with Circuit II generates

6.7 × 10−2 J at t = 0.25 s, whereas the system with CircuitI generates 5.2 × 10−3 J. Therefore, our flutter harvestingsystem can generate 10 times more electrical energy thanthe conventional system. The generation ratio, that is, 10times, is quite a striking and attractive number as a powerfulenergy harvester. Our harvesting system shows potential andis effective because it takes advantage of the wing flutter thathas thus far been considered as destructive.

To extensively assess the harvesting performance, wecarried out further simulations with various values of storagecapacitance Cs. The time-averaged electrical power wascalculated with each capacitance ratio κ between 0 s and0.3 s. Figure 11 shows the electrical power as a function of κ.Interestingly, the harvesting system with Circuit I harvestedthe maximum power with approximately κ = 31.6, whereasthe system with Circuit II harvested the maximum powerwith approximately κ = 5.62. The result indicates that theoptimum storage capacitance that harvests the maximumpower should be incorporated into the harvesting system.

5. Discussion on Supersonic FlutterUtilization for Energy-Harvesting

This section contains a discussion on the utilization of su-personic flutter for energy-harvesting.

Firstly, so far we have looked at rocket wings as anexample feasibility study of harvesting the energy producedby supersonic flutter. However, any structure, as long asthe flutter phenomenon occurs, can be used for flutterharvesting. Possible examples are harvesting flutter withinthin flag-type structures using flexible piezoelectric film,and harvesting panel flutter in fuselages using ceramic-type piezoelectric patches, in addition to the wing flutterdiscussed here.


0

60

0 0.05 0.1 0.15 0.2

Time (s)

Vol

tage

(V

)

−60

(a)

0

5

0 0.05 0.1 0.15 0.2

Time (s)

−5

×10−5

Ch

arge

(C

)

(b)

0

0.003

Piezoelectric voltageStorage voltage

0 0.05 0.1 0.15 0.2

Time (s)

−0.003

u at

win

g ti

p (m

)

(c)

0

4

0 0.05 0.1 0.15 0.2

Time (s)

−4

Inpu

t fo

rce

(N/m

2)


(d)

Figure 7: Timeline of the tail wing at critical dynamic pressure with energy-harvesting (Circuit II).

0.17 0.175 0.18 0.185 0.19 0.195 0.2

Time (s)

0

60


−60Vol

tage

(V

)

(a)

0

5

0.17 0.175 0.18 0.185 0.19 0.195 0.2

Time (s)

−5

×10−5

Ch

arge

(C

)


(b)

Figure 8: Magnified view of timeline of the tail wing with energy-harvesting (Circuit II).

0.17 0.175 0.18 0.185 0.19 0.195 0.2

Time (s)

0

20


−20Vol

tage

(V

)

(a)

0

1

0.17 0.175 0.18 0.185 0.19 0.195 0.2

Time (s)

×10−6

Ch

arge

(C

)

−1


(b)

Figure 9: Magnified view of timeline of the tail wing with energy-harvesting (Circuit I).


0.1

1

10

100

0 0.05 0.1 0.15 0.2 0.25

Conventional harvestingNew harvesting

Stor

age

volt

age

(V)

Time (s)

Figure 10: Comparison of stored voltages in the harvesting systemswith conventional and new methods (κ = 1.0).

0

0.1

0.2

0.3

0.4

0 25 50 75 100

Conventional harvestingNew harvesting

Har

vest

ed e

lect

rica

l pow

er (

W)

Capacitance ratio κ

Figure 11: Harvested electrical power as a function of capacitanceratio κ with conventional and new methods.

Secondly, although linear analysis indicates that flut-ter can often be expected to increase without limitation,nonlinear analysis of fluttering structures and aerodynamictheory suggest that the flutter phenomenon can lapse intolimit cycle oscillation (LCO) [27–29]. Accordingly, if devicesdesigned to work with intentional flutter are well built, fluttermagnitude may not increase to infinity and cause criticalfailure. From this viewpoint, despite the conventional viewof flutter as a destructive phenomenon, energy-harvestingbased on the flutter phenomenon is quite a feasible conceptwith significant potential as a target for future research.

Lastly, we summarize the advantage and contribution ofour harvesting method. These days, ecogeneration and eco-friendly inventions strongly attract more and more attention.Efficiency of energy harvesting is one of the most importantissues for moving vehicles in aerospace engineering, such asairplanes and space vehicles. It is because oil fuel is quitecostly and low-emission is requested by modern society.Our switching harvesting system through wing flutter cangenerate 10 times more electrical energy than a conventionalharvesting system that is composed of a simple diode-bridge.This increase in harvested energy is a noteworthy number forthe future development of power generation. This paper canprovide a great potential of flutter harvesting and also changeour notion against wing flutter from a harmful phenomenonto a profitable energy source.

6. Conclusions

We proposed a harvesting system that extracts electricalenergy by effectively using wing flutter. This study employedthe quasi-steady aerodynamic theory and the FEM forsimulating the dynamics of a cantilevered-plate wing. Theuse of electric circuits and piezoelectric patches led toeffective harvesting from supersonic flutter. We evaluated ourswitching approach using piezoelectric patches in supersonicflutter. Our proposed harvesting system via wing flutter cangenerate 10 times more electrical energy than conventionalharvesting systems. We expect that our proposed techniquewill be applicable to various energy-harvesting systems, andwe anticipate that it will be the basis for further studiesin this field. More experimental validation is essential forassessing the harvesting performances, and an experiment iscurrently being carried out for this purpose. The effectiveutilization of flutter changes our perception of it—frombeing a destructive phenomenon to being useful in variousapplications.

Nomenclature

a∞: Speed of sound in airc: Young’s modulusDz,Ez: z-directional electric displacement and

electric fieldf : External disturbance vectorF: Feedback matrixhxz: Piezoelectric coefficientnp: Number of piezoelectric patchesNF : Shape function of FEM elementp: Pressure exerted on the platep∞: Air pressureQ: Electric charge vector of piezoelectric

patchesTw: Kinetic energy of wingTp j : Kinetic energy of jth piezoelectric patchu(x, y, t): z-directional displacement of wingU : Flight speedUw: Strain energy of wing


Upj : Mechanical and electrical energy of jthpiezoelectric patch

Vs: Storage voltage in storage capacitorV: Voltage vector of piezoelectric patchesx: Assembled displacement vector at FEM

nodesβSzz: z-directional dielectric coefficient at

constant strainε, σ : Strain and stress vectorsη: Modal displacement vectorρ, ν: Density and Poisson’s ratioρ∞: Air densityζ : Modal damping ratioγ: Ratio of storage capacitance to

piezoelectric capacitance.

Superscript

D: Constant electric displacementS: Constant strainT: Transpose.

Subscript

p: Piezoelectric patchp j: jth piezoelectric patchw: Wing structure without piezoelectric

patches.

References

[1] E. H. Dowell, “Nonlinear oscillations of a fluttering plate,”AIAA Journal, vol. 4, no. 7, pp. 1267–1275, 1966.

[2] I. Lottati, “The role of structural and aerodynamic dampingon the aeroelastic behavior of wings,” Journal of Aircraft, vol.23, no. 7, pp. 606–608, 1986.

[3] D. M. Tang and E. H. Dowell, “Experimental and theoreticalstudy for nonlinear aeroelastic behavior of a flexible rotorblade,” AIAA Journal, vol. 31, no. 6, pp. 1133–1142, 1993.

[4] Y. Odaka and H. Furuya, “Robust structural optimizationof plate wing corresponding to bifurcation in higher modeflutter,” Structural and Multidisciplinary Optimization, vol. 30,no. 6, pp. 437–446, 2005.

[5] S. H. Moon and J. S. Hwang, “Panel flutter suppression withan optimal controller based on the nonlinear model using pi-ezoelectric materials,” Composite Structures, vol. 68, no. 3, pp.371–379, 2005.

[6] J. H. Han, J. Tani, and J. Qiu, “Active flutter suppression ofa lifting surface using piezoelectric actuation and moderncontrol theory,” Journal of Sound and Vibration, vol. 291, no.3–5, pp. 706–722, 2006.

[7] S. Raja, A. A. Pashilkar, R. Sreedeep, and J. V. Kamesh, “Fluttercontrol of a composite plate with piezoelectric multilayeredactuators,” Aerospace Science and Technology, vol. 10, no. 5, pp.435–441, 2006.

[8] A. Agneni, F. Mastroddi, and G. M. Polli, “Shunted piezoelec-tric patches in elastic and aeroelastic vibrations,” Computersand Structures, vol. 81, no. 2, pp. 91–105, 2003.

[9] S. Beeby and N. White, Energy Harvesting for AutonomousSystems (Smart Materials, Structures, and Systems), ArtechHouse, 2010.

[10] T. J. Kazmierski and S. Beeby, Energy Harvesting Systems:Principles, Modeling and Applications, Springer, 2010.

[11] P. J. Cornwell, J. Goethal, J. Kowko, and M. Damianakis, “En-hancing power harvesting using a tuned auxiliary structure,”Journal of Intelligent Material Systems and Structures, vol. 16,no. 10, pp. 825–834, 2005.

[12] W. P. Robbins, D. Morris, I. Marusic, and T. O. Novak, “Wind-generated electrical energy using flexible piezoelectric mate-rials,” in Proceedings of the ASME International MechanicalEngineering Congress and Exposition (IMECE ’06), November2006.

[13] S. D. Kwon, “A T-shaped piezoelectric cantilever for fluid en-ergy harvesting,” Applied Physics Letters, vol. 97, no. 16, ArticleID 164102, 2010.

[14] K. Isogai, M. Yamasaki, and T. Asaoka, “Application of CFD todesign study of flutter-power-generation,” Special Publicationof National Aerospace Laboratory, vol. 57, pp. 106–111, 2003(Japanese).

[15] M. Bryant and E. Garcia, “Modeling and testing of a novelaeroelastic flutter energy harvester,” Journal of Vibration andAcoustics, Transactions of the ASME, vol. 133, no. 1, Article ID011010, 2011.

[16] C. De Marqui, A. Erturk, and D. J. Inman, “Piezoaeroelasticmodeling and analysis of a generator wing with continuousand segmented electrodes,” Journal of Intelligent MaterialSystems and Structures, vol. 21, no. 10, pp. 983–993, 2010.

[17] C. De Marqui Jr., W. G. R. Vieira, A. Erturk, and D. J. Inman,“Modeling and analysis of piezoelectric energy harvestingfrom aeroelastic vibrations using the doublet-lattice method,”Journal of Vibration and Acoustics, Transactions of the ASME,vol. 133, no. 1, Article ID 011003, 2011.

[18] J. A. Dunnmon, S. C. Stanton, B. P. Mann, and E. H. Dowell,“Power extraction from aeroelastic limit cycle oscillations,”Journal of Fluids and Structures, vol. 27, no. 8, pp. 1182–1198,2011.

[19] V. C. Sousa, M. De Anicezio, C. De. Marqui, and A. Erturk,“Enhanced aeroelastic energy harvesting by exploiting com-bined nonlinearities: theory and experiment,” Smart Materialsand Structures, vol. 20, no. 9, article 094007, 2011.

[20] A. Erturk, W. G. R. Vieira, C. De Marqui, and D. J. Inman, “Onthe energy harvesting potential of piezoaeroelastic systems,”Applied Physics Letters, vol. 96, no. 18, Article ID 184103, 2010.

[21] National Research Council Board, Sounding Rockets; Their Rolein Space Research, General Books LLC, National Academy ofSciences, 2009.

[22] H. Ashley and G. Zartarian, “Piston theory—a new aerody-namic tool for the aeroelastician,” Journal of the AeronauticalSciences, vol. 23, pp. 1109–1118, 1956.

[23] B. Jaffe, W. R. Cook, and H. Jaffe, Piezoelectric Ceramics,Academic Press, London, UK, 1971.

[24] O. C. Zienkiewicz and R. L. Taylor, The Finite Element Method,Mcgraw-Hill, Berkshire, UK, 1985.

[25] J. Onoda, K. Makihara, and K. Minesugi, “Energy-recyclingsemi-active method for vibration suppression with piezoelec-tric transducers,” AIAA Journal, vol. 41, no. 4, pp. 711–719,2003.

[26] M. J. Balas, “Direct velocity feedback control of large spacestructures,” Journal of Guidance, Control, and Dynamics, vol.2, no. 3, pp. 252–253, 1979.

[27] J. E. Cooper and T. T. Noll, “Technical evaluation report on the1995 specialists’ meeting on advanced aeroservoelastic testing


and data analysis,” in Proceedings of the Conference ProceedingsCP-566 (AGARD ’95), 1995.

[28] M. J. Patil, D. H. Hodges, and C. E. S. Cesnik, “Nonlinearaeroelasticity and flight dynamics of high-altitude long-endurance aircraft,” in Proceedings of the 40th Structures, Struc-tural Dynamics and Materials Conference, AIAA-1999-1470,Saint Louis, Mo, USA, 1999.

[29] J. P. Mayuresh, H. H. Dewey, and E. S. C. Carlos, “Limit cycleoscillations of a complete aircraft,” in Proceedings of the 41stAIAA/ASME/ASCE/AHS/ASC Structures, Structural Dynam-ics, and Materials Conference, AIAA-2000-1395, Atlanta, Ga,USA, 2000.

Submit your manuscripts athttp://www.hindawi.com

ScientificaHindawi Publishing Corporationhttp://www.hindawi.com Volume 2014

CorrosionInternational Journal of

Hindawi Publishing Corporationhttp://www.hindawi.com Volume 2014

Polymer ScienceInternational Journal of



CeramicsJournal of


CompositesJournal of

NanoparticlesJournal of



International Journal of

Biomaterials


NanoscienceJournal of

TextilesHindawi Publishing Corporation http://www.hindawi.com Volume 2014

Journal of

NanotechnologyHindawi Publishing Corporationhttp://www.hindawi.com Volume 2014

Journal of

CrystallographyJournal of


The Scientific World JournalHindawi Publishing Corporation http://www.hindawi.com Volume 2014


CoatingsJournal of

Advances in

Materials Science and EngineeringHindawi Publishing Corporationhttp://www.hindawi.com Volume 2014

Smart Materials Research



MetallurgyJournal of


BioMed Research International

MaterialsJournal of


Nano

materials


Journal ofNanomaterials

Documents

SupersonicFlutterUtilizationforEffective Energy ...downloads.hindawi.com/journals/smr/2012/181645.pdf · Energy-harvesting (power-generation or power-scaveng-ing) is a process by