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IEEE/ASME TRANSACTIONS ON MECHATRONICS, VOL. 18, NO. 5, OCTOBER 2013 1527

A Piezoelectric Energy Harvester for Rotary MotionApplications: Design and Experiments

Farbod Khameneifar, Siamak Arzanpour, and Mehrdad Moallem

Abstract—This paper investigates the analysis and design of avibration-based energy harvester for rotary motion applications.The energy harvester consists of a cantilever beam with a tipmass and a piezoelectric ceramic attached along the beam thatis mounted on a rotating shaft. Using this system, mechanical vi-bration energy is induced in the flexible beam due to the gravita-tional force applied to the tip mass while the hub is rotating. Thepiezoelectric transducer is used to convert the induced mechan-ical vibration energy into electricity. The equations of motion ofthe flexible structure are utilized along with the physical charac-teristics of the piezoelectric transducer to derive expressions forthe electrical power. Furthermore, expressions for the optimumload resistance and maximum output power are obtained and val-idated experimentally using PVDF and PZT transducers. The re-sults indicate that a maximum power of 6.4 mW at a shaft speedof 138 rad/s can be extracted by using a PZT transducer with di-mensions 50.8 mm × 38.1 mm × 0.13 mm. This amount of poweris sufficient to provide power for typical wireless sensors such asaccelerometers and strain gauges.

Index Terms—Cantilever beam, energy harvesting, piezoelectrictransducers, power optimization, rotational motion.

I. INTRODUCTION

R EAL-TIME condition monitoring of rotating machinesand structures such as turbines and tires is highly desir-

able to achieve improved safety and health monitoring. Withadvancements in wireless technology, modern fault detectionmechanisms for rotary applications can be implemented by in-stalling wireless sensors on the structure to transmit data to ahealth and status monitoring unit. Wireless systems do not havethe drawback of rotating wired systems that require the use ofslip rings to transfer sensory data. However, wireless sensorsand their transmission units need batteries as power sources fortheir operation [1].

Manuscript received June 13, 2011; revised September 26, 2011,January 26, 2012, and May 5, 2012; accepted May 19, 2012. Date of publi-cation July 12, 2012; date of current version July 11, 2013. Recommended byTechnical Editor J. Wang. This work was supported in part by the NaturalSciences and Engineering Research Council of Canada (NSERC) under theDiscovery Grants program, in part by the Simon Fraser University Start-upfund, and in part by the British Columbia NRAS fund.

F. Khameneifar was with the Department of Mechatronic Systems Engi-neering, School of Engineering Science, Simon Fraser University, Surrey, BCV3T 0A3, Canada. He is now with the Department of Mechanical Engineer-ing, University of British Columbia, Vancouver, BC V6T 1Z4, Canada (e-mail:[email protected]).

S. Arzanpour and M. Moallem are with the Department of MechatronicSystems Engineering, School of Engineering Science, Simon Fraser University,Surrey, BC V3T 0A3, Canada (e-mails: [email protected]; [email protected]).

Color versions of one or more of the figures in this paper are available onlineat http://ieeexplore.ieee.org.

Digital Object Identifier 10.1109/TMECH.2012.2205266

A major shortcoming of using batteries is the requirement torecharge or replace them on a regular basis [2]. Since stoppingthe systems to replace the batteries may not be practical, anapparatus such as an energy harvester that can locally scavengeor harvest energy to recharge the batteries is highly advanta-geous. Several energy harvesting mechanisms have been devel-oped for transforming ambient energy (in this case, mechanicalvibrations) into electricity. Among them, electrostatic, electro-magnetic, and piezoelectric harvesters have been proposed [3].Electrostatic generators require an additional power source tooperate, whereas electromagnetic transducers generate low out-put voltages. Roundy et al. [4] compared the aforementionedenergy harvesting techniques and concluded that piezoelectrictransducers are good candidates for converting vibration energyinto electricity. As noted in [5], the energy density of piezoelec-tric transducers is three times higher when compared to electro-static and electromagnetic transducers. A piezoelectric energyharvester is usually comprised of a cantilever beam on which apiezoceramic layer and a tip mass are mounted. Sodano et al.[6] tested three types of piezoelectric devices, i.e., the mono-lithic piezoceramic material Lead–Zirconate–Titanate (PZT),the Quick Pack (QP), and the macrofiber composite (MFC), andcompared their capability to charge a battery. Their investiga-tion indicated that MFC is not well suited for energy harvesting,whereas QP and PZT are both capable of efficiently rechargingbatteries. Different models have been utilized to describe theelectromechanical behavior of piezoelectric energy harvesters.Sodano et al. [7] used the Rayleigh–Ritz solution for modelinga piezoelectric energy harvester beam without a tip mass. Erturkand Inman [8] concluded that a lumped model may yield inac-curate results for predicting the motion of cantilever beams andproposed a coupled distributed solution [9], [10]. The placementof PZT electrodes to achieve efficient energy harvesting was in-vestigated by Erturk et al. [11] through a study of the strain nodesof a cantilever harvester. Wickenheiser et al. [12] studied the ef-fects of electromechanical coupling of a cantilever harvester onthe dynamics of charging a storage capacitor. Other interest-ing applications of piezoelectric energy harvesting include theworks by Almouahed et al. [13], and Platt et al. [14], [15], whoused piezoelectric energy harvesters to provide power for in vivoknee implants.

Most energy harvesters that have been reported so far in theliterature rely on the vibrations induced from a base excita-tion. In the energy harvester discussed in this paper, a novelmethod has been used to excite the beam vibration. We utilizethe gravitational force on the tip mass to generate continuousoscillations in a cantilever beam during its rotating motion. InSection II, a simplified single-degree-of-freedom model of the

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1528 IEEE/ASME TRANSACTIONS ON MECHATRONICS, VOL. 18, NO. 5, OCTOBER 2013

Fig. 1. Schematic view of the energy harvester mounted on a rotating hub.

piezoelectric energy harvesting system is presented. Hence, thedynamic equations describing the interaction of the piezoelectrictransducer and flexible beam are obtained. Expressions describ-ing the electrical output voltage and power of the combinedpiezoelectric energy harvesting system are presented includingthe optimal value of load resistance connected to the energyharvester. Furthermore, an upper bound for the output poweris obtained through impedance matching for the proposed de-sign. In Section III, details of the test bed used and experimen-tal results are presented. The results indicate close agreementbetween theory and experiments including system dynamics,generated output voltage of the harvester, and the optimal loadfor maximizing the output power.

II. ROTATING HARVESTER DESIGN AND MATHEMATICAL

MODEL

The proposed energy harvester consists of a cantilever beamwith a piezoelectric layer carrying a tip mass with the wholesystem mounted on a rotating hub. A schematic diagram of themechanism is shown in Fig. 1. The dimensions of the beamstructure in Fig. 1 are provided in Table III. As shown in thefigure, the hub is rotating about the “Z” axis and gravity is actingalong the negative “Y” axis.

The main source of vibration input to the harvester is thealternating gravitational force on the cantilever beam. The con-cept is shown in Fig. 2 for one cycle of rotation of one of thefour cantilever beams. When the beam is in position (a), thegravitation force on the tip mass applies a bending momenton the cantilever beam in the negative Z direction. As the beamreaches position (b), the bending moment on the cantilever beamis zero. At position (c), the bending moment due to the tip massis in the positive Z direction. Position (d) is identical to (b),where the effect of the tip-mass gravitational force is zero. As a

Fig. 2. Orientation of the beam and gravitational force in one cycle of rotationand the material mode orientation.

result, a 360◦ rotation of the hub results in the application of analternating force on the harvester. The frequency of this forceis as same as the hub rotational frequency. Thus, the inducedvibration generates a harmonic voltage on the piezoelectric ele-ment that is a function of the strain applied to this element. Thematerial mode orientation of the PZT transducer is also shownin Fig. 2(a), where “X” and “Y” axes correspond to dimensions1 and 3, respectively.

Detailed modeling of the dynamics of the rotating energyharvester with tip mass is presented in [16]. In the following, weprovide a brief overview of the derivation of dynamic equationsusing a single mode analysis.

A. Vibration Model of the Rotating Beam With a PiezoelectricElement

Let us consider the Euler–Bernoulli beam equation that de-scribes the vibration behavior of a cantilever beam as follows(see e.g., [10]):

EI∂4w(ξ, t)

∂ξ4 + ρAL4 ∂2w(ξ, t)∂t2

= 0 (1)

where the deflection of the beam relative to its base is denotedby w(ξ, t), ξ = x/L is the normalized position x along the beamwith length L, E is Young’s modulus, I is the area moment ofinertia, ρ is the mass density, and A is the cross-sectional areaof the beam. Here, E, I, ρ, and A are not functions of ξ due tothe uniform distribution of the piezoelectric layers. Moreover,placing the piezoelectric layers on a part of the beam would notbe appropriate if the device is to be used as an energy harvesteras the goal is to extract maximum power. The solution of (1)

KHAMENEIFAR et al.: PIEZOELECTRIC ENERGY HARVESTER FOR ROTARY MOTION APPLICATIONS: DESIGN AND EXPERIMENTS 1529

can be obtained by using the separation of variables as follows:

w(ξ, t) = ϕ(ξ).δ(t) (2)

where ϕ(ξ) is the shape eigenfunction and δ(t) is the modalmechanical response. Next, we utilize the Lagrangian formula-tion to derive a mathematical model that describes the systemdynamics, including the piezoelectric beam, tip mass, and therotating hub. The kinetic and potential energies of the system,T and U, are respectively given as follows:

T =12Jb θ

2 +12

∫beam

(w2 + 2wxθ)dm +12Jh θ2

+12JL

(θ +

∂w(L, t)∂x

)2

+12ML (θ2w(L, t)2

+ (w(L, t) + Lθ)2) (3)

U =∫ L

0

EI

2

(∂2w

∂x2

)2

dx + gρA

×∫ L

0

( w

cos θ+ (x − w tan θ) sin θ

)dx

+ MLg

(w|ξ=1

cos θ+ (L − w|ξ=1 tan θ) sin θ

)(4)

where ML and JL are the load mass and inertia, and Jb and Jh

are beam and hub inertia, respectively. Let us define the vectorof generalized coordinates as q = [ θ δ ]T with the vector ofgeneralized force defined as F = [ τ FP ]T , where θ is theangular displacement of the hub [16], τ is the applied torqueto the hub, and FP is the moment induced by the piezoceramiclayer. The dynamic equations of the flexible beam can then beobtained by using the Lagrangian formulation as follows:

M(δ, t)[

θ

δ

]+ C(δ, θ, δ, θ, t)

[θ

δ

]+ G(δ, θ, t)

+[

0

Kδ(t)

]=

[τ(t)

FP (t)

](5)

where M2×2 is the symmetric inertia matrix and C2×2 is thevector of Coriolis and centrifugal forces. The induced momentFP (t) is given by [17]

FP (t) = kv(t)[ϕ′(0) − ϕ′(1)]. (6)

The elements of the matrices M and C are given by the fol-lowing terms:

m11 = Jh + Jb + JL + MLL2 + ML (ϕeδ)2 (7)

m12 = m21 = MLLϕe + JLϕ′e + σ (8)

m22 = mbϕ2e + MLϕ2

e + JLϕ′2e (9)

c11 = MLϕ2e δδ (10)

c12 = −c21 = MLϕ2e δθ (11)

c22 = 0 (12)

where subscript “e” denotes that the parameter is evaluated atthe tip of the beam. The elements of the vector G(δ, θ, t) are as

follows:

g11 =[gρA(− sin θ)

∫ 1

0ϕdξ + MLg(− sin θ)ϕe

]δ

+ gρAL2

2cos θ + MLgL cos θ (13)

g21 = g cos θ

[ρA

∫ 1

0ϕdξ + ML ϕe

](14)

where mb is the beam mass, subscript e denotes the end of thebeam, and σ is a function of the integral of mode shape givenby σ = ρAL2

∫ 10 ϕ(ξ)dξ.

Furthermore, the equivalent spring constant K in (5) is givenby

K =(

EI

∫ 1

0ϕ′′2dξ

)(15)

where κ is the backward coupling term. The coupling term is afunction of geometric parameters of the system, the piezoelectricconstant, and the modulus of elasticity of the piezoelectric layerand the flexible beam. Since the objective of this study is toharvest energy at the steady-state speed of a rotary system,the angular acceleration is set to zero in (5), i.e., θ = 0. Theeffect of damping can be added to the Euler–Bernoulli equationby incorporating internal strain rate damping and viscous airdamping.

Therefore, the modal damping coefficient ζ1can be expressed

by 2ζ1ω1 = Cs ω 21

E + Ca

m , where the first term represents the ef-fect of the strain-rate damping and the second term representsair damping. Other parameters represent the damping coeffi-cients Cs , and Ca , and the natural frequency of the first modeω1 respectively [16]. Incorporating all the terms in (5) results in

δ(t) + 2ζ1ω1 δ(t) + ω21 δ(t) +

X

Bv(t) = −A

Bcos θ t (16)

where X, A, and B are given by

X = κϕ′e (17)

A =[ρA

∫ 1

0ϕdξ + MLϕe

]g (18)

B = (MLϕ2e + JLϕ′2

e + mbϕ2e ). (19)

The natural frequency of the first mode ω1 in (16) is√

C/Bwhere C is given by

C = (K − MLθ2ϕ2e ). (20)

B. Piezoelectric Transducer Electrical Model

A piezoelectric element under excitation can be modeled asa current source in parallel with an internal capacitance [18].Fig. 3 shows the circuit representation of a piezoelectric elementconnected across a purely resistive load, which represents theeffect of an energy storage, or energy consuming load.

The electrical circuit equation of the system, considering thefirst mode of vibrations, can be obtained by using Kirchhoff’s


Fig. 3. Electrical circuit symbolizing the resistive load connected to the singlepiezoelectric layer.

laws as follows [17]:

CP v(t) +v(t)Rl

= − d31

SE11

hpnbϕ′e δ(t) (21)

where Rl is the load resistance; Cp = εs33bL/hp is the inter-

nal capacitance of piezoelectric layer; γ = − d3 1S E

1 1hpnbϕ′

e is the

forward coupling term; εs33 is the permittivity constant; b, L,

and hp are the width, length, and thickness of the piezoceramiclayer, respectively; hpn is the distance between the neutral axisand the center of piezoceramic layer; d31 is the piezoelectricconstant; and SE

11 is the elastic compliance at a constant electricfield. The right-hand side of (21) represents ip (t). Referring toFig. 2(a), there are two operating modes, d31 and d33 , throughwhich the piezoelectric transducer can generate electricity. Inthe d33-mode, both the mechanical stress and output voltage actalong dimension 3. In the d31-mode, the mechanical stress actsalong dimension 1, while the voltage acts along dimension 3. Asdiscussed in previous works (e.g., [19], [20]), a thin piezoelec-tric layer bonded to a substrate cantilever beam that operatesin the d31-mode can produce larger strains with smaller inputforces.

C. Closed-Form Solution of the Electrical Output Power

The amplitude of the vibration δ can be obtained from (16)and (21) to yield the amplitude of output voltage given by

∣∣∣V (θ)∣∣∣ =

2θRlγA√D2

1 + D22

(22)

where the D1 and D2 terms are given by

D1 =

(B + 2RlCP B

(2ζ

√C

B

)+ MLϕ2

e

)θ2 − K (23)

D2 = 2RlCP (B + MLϕ2e )θ

3

−(

2Rl(γX + CP K) + 2Bζ

√C

B

)θ. (24)

Using (22), the average harvested electrical power ispresented by

|P | =|V |2

Rl=

4θ2Rlγ2A2

(D21 + D2

2 ). (25)

Differentiating (25) with respect to Rl (resistive load), an op-timal load to maximize the amplitude of harvested power can beobtained. An important issue that should be noted here is the ef-fect of damping on the optimal resistive load. By differentiatingthe expression for the optimal resistance in terms of the dampingratio, it can be concluded that an increase in the damping termwill result in an increase in the value of the optimal resistance.

Fig. 4. Experimental setup used for validating the analytical model.

TABLE IGEOMETRIC AND PHYSICAL PARAMETERS OF THE PVDF ENERGY HARVESTER

III. EXPERIMENTAL VALIDATION

A. Experimental Setup for Vibration Energy Harvesting Froma Rotating Hub

The experimental setup for generating electric voltage froma rotating hub is shown in Fig. 4. Two different energy har-vesters were utilized in our tests, i.e., a PZT manufactured byMIDE Inc., and a PVDF film manufactured by Images SI, Inc.(PZ-03). The harvesters are attached to a flexible cantileverbeam using Loctite glue (Model No. 330). A tip mass is also at-tached to the cantilever beam (48 and 65 g) for tuning the naturalfrequency of the structure. The geometric, physical, and mate-rial properties of the piezoelectric layer and substructure aregiven for the PVDF and PZT harvesters in Tables I and II, andTables III and IV, respectively. The cross hub has room for fourharvesters; however, for proof of concept demonstration onlyone is utilized. The output power can increase by using the fullcapacity of the system and employing a suitable power man-agement unit. The shaft is driven by a dc motor from MaxonMotors (A-max 32 Model No. 236669) equipped with a shaftencoder with 500 Counts per (HEDL 5540 Model No. 110514).The maximum power in this harvester occurs at its natural fre-quency with an optimal load. To identify the natural frequencythe hub velocity is gradually increase from 0 to 150 rad/s and theoutput voltage is measured for an arbitrary resistive load (100 Ω).The angular velocity at which the maximum voltage is achievedrepresents the natural frequency of the beam. The optimal re-sistive load was then identified by maintaining the hub angular


TABLE IIMATERIAL PARAMETERS OF THE PVDF ENERGY HARVESTER

TABLE IIIGEOMETRIC AND PHYSICAL PARAMETERS OF THE PZT ENERGY HARVESTER

TABLE IVMATERIAL PARAMETERS OF THE PZT ENERGY HARVESTER

velocity at the harvester natural frequency and varying the loadresistance until a maximum in the power was achieved. Theresults for the power versus resistive load are shown in Figs. 5and 6 for different tip masses. Figs. 7 and 8 illustrate the outputvoltage of the harvester at the optimal load for different hubvelocities.

Fig. 5. Output power versus resistive load for 48-g tip mass: PVDF experi-mental data (blue dotted line) and theoretical data (red line).

Fig. 6. Output power versus resistive load for 65-g tip mass for PVDF: exper-imental data (blue dotted line) and theoretical data (red line).

Fig. 7. Output voltage for 48-g tip mass and R = 600 kΩ: experimental data(blue dotted line) and theoretical data (red line).

B. Validation of the Single-Mode Closed Form Expressions forthe Output Electric Voltage

The mathematical model in (22) and (25) are used to calcu-late the output voltage, optimal resistive load, and maximumpower. The strain rate damping in those equations is obtainedexperimentally using the exponential decay of the response ofthe beam in an impact hammer test. The damping term due to airflow was not considered in our simulations. The output voltage


Fig. 8. Output voltage for 65-g tip mass and R = 600 kΩ: experimental data(blue dotted line) and theoretical data (red line).

of the harvester with a 600-kΩ resistive load was simulated forthe 48 and 65 g tip masses at different hub angular velocities asdepicted in Figs. 7 and 8, respectively. The results indicate closeagreement between the theory and experiments. There existsa small discrepancy between the experimental and simulationresults, i.e., 8.6% for voltage response of the PVDF harvesterwith a 48-g tip mass, and 5.8% for a 65-g tip mass. Also, thesimulated optimal resistive load of the harvester for the 48 and65-g tip masses were 560 and 540 kΩ, respectively, i.e., cor-responding to 6.7% and 10% errors, respectively. Figs. 5 and6 illustrate the experimental and simulation results of the har-vested power versus different resistive loads. The largest erroroccurs close to the natural frequency where the beam vibrationand consequently the air damping effect is maximum.

To verify the effect of imbalance of the shaft on the outputvoltage, we performed measurements when the setup was ori-ented in the vertical position where the gravity cannot act as thesource of beam excitation. The output voltage that was mainlydue to the shaft imbalance induced vibrations was less than 2%of the horizontal configuration. This experiment indicates thatthe effect of imbalance can be neglected.

The experimental and simulation results indicate that the ef-fect of tip mass on the optimum load resistance is negligible.Although the changes in the tip mass intuitively alter the damp-ing ratio ζ the value of viscous damping coefficient remainsthe same. The experimental output power extracted from thisdevice using the 65-g tip mass at the optimal resistive load was30.8 μW at 85 rad/s (natural frequency).

Similar experiments were conducted for measuring the outputvoltage and calculating the optimal resistive load using the PZTlayer. It should be noted that the PZT has a higher modulus ofelasticity and thus a higher natural frequency. In the setup used inthis study, the angular velocity of the hub cannot reach velocitiesbeyond 200 rad/s due to the limitation on the maximum speedof the dc motor. To reduce the natural frequency of the beam a105-g tip mass was used. The natural frequency of the har-vester beam with this tip-mass is 138 rad/s. A simulation wasconducted on the PZT harvester with the specifications sum-marized in Tables III and IV. The same approach used for thePVDF was used here.

Fig. 9. Output voltage of PZT for 105-g tip mass and R = 40 kΩ: experimentaldata (blue dotted line) and theoretical data (red line).

Fig. 10. Output power versus load resistance for PZT for a 105-g tip mass:experimental data (blue dotted line) and theoretical data (red line).

Fig. 9 shows the experimental and theoretical results for thevoltage output of the PZT energy harvester for an optimal loadof 40 kΩ, which was obtained from the power versus load re-sistance plot. The maximum error of voltage at the resonancefrequency is 10.3% for the PZT harvester.

The output power versus resistive load is plotted for the PZTharvester as shown in Fig. 10. Based on the experimental results,the maximum extracted power of PZT energy harvester occurredwhen the load resistance is 40 kΩ. This number matches withthe resistive load calculated from the mathematical model. Theexperimentally measured maximum output power from the PZTenergy harvester is 6.4 mW, which is very close to the valuecalculated from (25).

To be able to compare the extracted power from the PVDFharvester and the PZT harvester, one should consider similarphysical conditions in terms of the tip mass and length of thebeam. For the PVDF harvester with a 105-g tip mass, a maxi-mum output power of 147 μW was obtained when the harvesterwas connected to the optimal resistance. Comparing the re-sults of the two harvesters investigated in this study, it may beconcluded that the PVDF transducer has a larger optimal resis-tive load than the PZT transducer (600 kΩ in comparison with40 kΩ). The results indicate that the amplitude of generatedpower from the PZT harvester is about 44 times higher than thecase for PVDF (6.4 mW compared with 147 μW, when usingthe same lengths and tip masses). This result is in agreement


with previous studies indicating that the optimal load resistanceis higher for PVDF case due to the low piezoelectric constantof these materials [21]. The amount of power obtained fromthe PZT harvester beam (6.4 mW) with a tip mass of 105 g isenough for supplying a typical wireless sensor [22]. The powerharvested using the PVDF with the same dimensions and a tipmass of 105 g was 147 μW, which can only be used to powera wireless sensor in the sleeping state which requires a typicalpower in the range 10−3 to 10−1 mW [22]. The output powerfrom the PVDF harvester beam with lower tip masses of 48 and65 g, were 10.4 and 30.8 μW, respectively. These power levelsare not suitable for powering a wireless sensor in the sleepingstate. The PZT energy harvester may thus be a better candidatewhen compared to the PVDF harvester due to its higher outputpower. However, in applications where variation of the mechan-ical torque to the rotating hub is large, the risk of failure in thePZT harvester is higher than that of the PVDF since PZT is brit-tle and PVDF is highly flexible. Further studies involving theutilization of impedance concept for power optimization havebeen reported by Liang et al. [23].

IV. CONCLUSION

A novel piezoelectric energy harvester for rotary motion ap-plications was presented in this study. The piezoelectric en-ergy harvester consists of a cantilever beam and a tip massmounted on a rotating hub. When the hub rotates with a con-stant angular velocity, the gravity force on the tip mass causesthe mass-beam system to vibrate. The steady-state closed-formelectromechanical expressions were used to find the maximumharvested power for the optimal load resistance. Experimentalstudies confirm analytical predictions in terms of vibration re-sponse, output voltage, optimal load of the harvester, and outputpower extracted from the energy harvester. Two different energyharvesters were tested; one using a PVDF film and another us-ing a PZT transducer. The results indicate that the output power,when a PZT transducer is used, is about 44 times higher than thecase when a PVDF film is used. As a result, the PZT harvesteris a good candidate to be utilized as a local miniaturized powergenerator for wireless sensors in applications involving rotarymotion condition monitoring. Using more than one harvesteron the hub would contribute to the generation of more power;however, further experimental studies need to be conducted toevaluate power generation capability of the system.

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[22] D. Steingart, “Power sources for wireless sensor networks,” in EnergyHarvesting Technologies. Berlin, Germany: Springer, 2008, ch. 9.

[23] J. Liang and W. Liao, “Impedance modeling and analysis for piezoelectricenergy harvesting systems,” IEEE/ASME Trans. Mechatronics, to bepublished.

Farbod Khameneifar received the B.Sc. degree inmechanical engineering from the University ofTehran, Tehran, Iran, in 2008, and the M.Sc. degreein mechatronic systems engineering from SimonFraser University, Surrey, BC, Canada, in 2011.He is currently working toward the Ph.D. degree inmechanical engineering at the University of BritishColumbia, Vancouver, BC, Canada.

His current research interests include computer-aided design, manufacturing and inspection(CAD/CAM/CAI), computational geometry, geo-

metric and dynamic modeling, and design and optimization of mechatronicsystems.


Siamak Arzanpour received the B.Sc. degree fromthe University of Tehran, Tehran, Iran, in 1998,the M.Sc. degree from the University of Toronto,Toronto, ON, Canada, in 2003, and the Ph.D. de-gree from the University of Waterloo, Waterloo, ON,Canada, all in mechanical engineering.

He is currently an Assistant Professor at SimonFraser University, Surrey, BC, Canada. His currentresearch interests include a wide range of topics, in-cluding smart materials, vibration, haptic systems,pattern and material recognition using vibration sig-

natures of biomaterials, and energy harvesting from mechanical vibrations forremote sensors.

Mehrdad Moallem received the B.Sc. degree fromShiraz University, Shiraz, Iran, in 1986, the M.Sc. de-gree from Sharif University of Technology, Tehran,Iran, in 1988, both in electrical and electronic engi-neering, and the Ph.D. degree in electrical and com-puter engineering from Concordia University, Mon-treal, QC, Canada, in 1997.

From 1998 to 1999, he was a Research and Devel-opment Engineer at Duke University, Durham, NC.From 1999 to 2007, he was an Assistant, and then anAssociate Professor in the Department of Electrical

and Computer Engineering, The University of Western Ontario, London, ON,Canada. Since 2007, he has been with the Mechatronics Systems EngineeringProgram, School of Engineering Science, Simon Fraser University, Surrey, BC,Canada, where he is currently a Professor in the Faculty of Applied Sciences.His current research interests include control applications, in particular, vibra-tion control, power electronic control for energy conversion, smart sensors andactuators, and embedded real-time computing. He has authored or coauthoredextensively in the aforementioned areas and is the coauthor of four technicalbooks on vibration control using piezoelectric transducers, control of flexiblerobots, medical robotics, and wind energy conversion.

Dr. Moallem has served on the Editorial Boards of several conferencesand journals including the American Control Conference and the IEEE/ASMETRANSACTIONS ON MECHATRONICS.

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