Research ArticleMultifrequency Piezoelectric Energy Harvester Based onPolygon-Shaped Cantilever Array

Dalius MaDeika ,1 Andrius Heponis ,1 and Ying Yang2

1Vilnius Gediminas Technical University, Sauletekio Avn. 11, LT-10223 Vilnius, Lithuania2Nanjing University of Aeronautics and Astronautics, 29 Yudao Street, P.O. Box 359, Nanjing, Jiangsu 210016, China

Correspondence should be addressed to Dalius Mazeika; dalius.mazeika@vgtu.lt

Received 25 August 2017; Revised 3 December 2017; Accepted 11 January 2018; Published 8 March 2018

Academic Editor: Michele Magno

Copyright © 2018 DaliusMazeika et al.This is an open access article distributed under the Creative Commons Attribution License,which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

This paper focuses on numerical and experimental investigations of a novel design piezoelectric energy harvester. Investigatedharvester is based on polygon-shaped cantilever array and employs multifrequency operating principle. It consists of eightcantilevers with irregular design of cross-sectional area. Cantilevers are connected to each other by specific angle to form polygon-shaped structure. Moreover, seven seismic masses with additional lever arms are added in order to create additional rotationmoment. Numerical investigation showed that piezoelectric polygon-shaped energy harvester has five natural frequencies inthe frequency range from 10Hz to 240Hz, where the first and the second bending modes of the cantilevers are dominating.Maximum output voltage density and energy density equal to 50.03mV/mm3 and 604 𝜇J/mm3, respectively, were obtained duringnumerical simulation. Prototype of piezoelectric harvester was made and experimental investigation was performed. Experimentalmeasurements of the electrical characteristics showed that maximum output voltage density, energy density, and output power are37.5mV/mm3, 815.16 𝜇J/mm3, and 65.24 𝜇W, respectively.

1. Introduction

Modern electronic and mechatronic systems have highdemand on wireless sensors, low-power electronic devices,and wireless data transfer systems. In general, such devicesare used to control numerous physical parameters to storeand transfer data wirelessly [1, 2]. Usually electric powerfor the aforementioned electronic devices is delivered byelectrochemical batteries that have numerous disadvantagessuch as short lifetime, high costs of maintenance, and beingunfriendly for the environment. Therefore, novel powersupply technologies must be applied to the wireless and low-power electronic systems [3, 4].

Nowadays, energy harvesting technologies can be suc-cessfully used as an alternative solution to the electrochemicalbatteries. However, a proper energy harvesting technologymust be chosen to obtain the highest efficiency of alternativepower supply [5, 6]. Therefore electromagnetic, electrostatic,and triboelectric harvesters were developed. However, all ofthese harvesters have low-power density, are expensive, andhave complex structures. Moreover, external power supply is

needed for operation of electrostatic harvesters. Therefore,practical application of these energy harvesting technologiesis complicated or economically unacceptable [7, 8]. Onthe other hand, piezoelectric energy harvesters are able toprovide such features as high power density, long lifetime,and low costs of production andmaintenance. Usually, designof piezoelectric energy harvesters is based on conventionalcantilevers. Such type of the harvesters operates at theresonant frequency; as a result, the highest output power isachieved when natural frequency of the harvester matcheswith the vibration frequency of the host. It means that theoutput power of piezoelectric harvester depends on vibrationfrequency of the host; therefore operation bandwidth of theharvester must be increased to avoid this problem [9–11].Twomajor principles are used to broaden frequency responserange of the piezoelectric energy harvester, that is, nonlinearoperation principle and multifrequency principle. Nonlinearbehavior of piezoelectric energy harvester can be achievedby several active and passive techniques like stiffness tuning,axial preload, and magnetic coupling operation [12–15].

HindawiShock and VibrationVolume 2018, Article ID 5037187, 11 pageshttps://doi.org/10.1155/2018/5037187

2 Shock and Vibration

Wang et al. proposed magnetically coupled piezoelectricenergy harvester with an elastic magnifier. Goal of theinvestigations was to overcome potential well barriers andto obtain much large-amplitude bistable motion. Numericaland experimental investigation confirmed that proposedenergy harvesting system provides high output power, whilemass/stiffness ratio of the harvester has the highest value.The maximum measured output power was 6.76mW whenresistance load of 100 kΩ was applied at excitation frequencyof 17.6Hz. It is 26 times higher output power value comparedto conventional energy harvester [16].

Jiang et al. analyzed a multistep piezoelectric buckledbeam energy harvester. Magnetic forces generated by perma-nent magnets were used for excitation. Multistep mechanismwas employed to increase bandwidth and power density ofthe piezoelectric energy harvesting system. Authors showedthat proposed buckled beam system is able to provide high-voltage output at broadband excitation frequencies; thatis, open-circuit voltage generated by energy harvester was±5.5 V, while the maximum voltage of ±9.3 V was achievedat 4.4Hz. Moreover, output power of the harvester reached5.0 𝜇Wwhen the load resistance was 3.3MΩ [17].

Upadrashta and Yang introduced a new design of nonlin-ear piezomagnetoelastic energy harvester [18]. Nonlinearitywas obtained by magnetic interaction between embeddedmagnet in the tip of each cantilever and the rigidly fixedmagnet. Array of monostable cantilevers ensured 100𝜇Woutput power at bandwidth of 3.3Hz.

Piezoelectric energy harvesters based on multifrequencyoperation principle can be used for wide bandwidth energyharvesting as well. Usually multifrequency energy harvestersconsist of several cantilevers that can operate at differentresonant frequencies. This type of the harvesters has simpledesign and usually has linear-type vibrations.

Zhou et al. investigated energy harvester based on multi-mode dynamic magnifier [19]. Investigation was focused onenergy harvester which consisted of multimodal magnifierand simple cantilever with the seismic mass. Results ofinvestigation revealed that proposed harvester is able toacquire 25.5 times larger amount of energy compared tothe conventional cantilever in frequency range from 3Hzto 300Hz. Moreover, authors showed that this particulardevice can harvest from 100 till 1000 timesmore energy whileoperating near the first three natural frequencies of the energyharvesting system.

Lee et al. designed and investigated a segmented-typeharvester that employs multiple modes of harvester vibra-tions [20]. Results of investigation showed that the proposedharvester has two suitable resonant modes and the differencebetween resonant frequencies is relatively small. Moreover,authors claimed that electrical characteristics of the deviceare suitable to ensure power supply for industrial wirelesstemperature sensors used for building monitoring systems.

Qi et al. investigated a clamped-clamped type piezoelec-tric energy harvester with side mounted cantilevers [21].Numerical and experimental investigations revealed thatinvestigated system has five natural frequencies that werelocated at the narrow frequency range. Authors claimed thatproposed harvester is able to exhibit broadband frequency

response. Also, authors concluded that obtained summationof the modal strains improved efficiency of the harvester atwide frequency range and ensured true broadband energyharvesting.

Rezaeisaray et al. published results of investigation aboutpiezoelectric micro energy harvester with multiple degreesof freedom [22]. Based on results of investigation, it wasshown that proposed design of the harvester has threenatural frequencies at frequency range from 71Hz to 189Hz.Authors claimed that maximum open-circuit voltage andoutput power reached 1V and 136 nW, respectively, whenload resistance was 2MΩ. These electrical characteristicswere obtained when excitation amplitude was 0.2 g, whileexcitation frequency was 97Hz.

Toyabur et al. investigated a multimodal vibration energyharvester withmultiple piezoelectric elements [23]. Proposeddesign of the harvester consists of four piezoelectric modulesand has four natural frequencies at frequency region from10Hz to 20Hz. Based on results of investigation, authorsclaimed that one module is able to provide 249.78𝜇W peakpower under 0.4 g of base acceleration. Authors concludedthat parallel connection of themodules can ensure four timeshigher output power and generate much higher power atevery vibration mode.

Dhote et al. designed and investigated amultimode piezo-electric energy harvester based on a trileg compliant ortho-planar spring with multiple masses [24]. Random excitationof the harvester revealed that it has three natural frequencieswith values lower than 150Hz. Also, the authors claimedthat proposed device is able to harvest energy under randomvibrations. Authors concluded that analyzed harvester hasnonlinear multimode vibrations and is able to harvest energyfrom random environmental vibrations.

A new polygon-shaped multifrequency piezoelectricenergy harvester is proposed in this paper. Special design ofthe harvester ensures modal strain summation and multi-frequency energy harvesting. Irregular design of the cross-sectional areas of the cantilevers and special design of theseismic masses improve strain distribution characteristicalong the cantilevers length. Strain summation and advanceddesign of the proposed piezoelectric harvester allow increas-ing electrical output power of the energy harvesting systemsignificantly.

2. Design of Polygon-Shaped Energy Harvester

Design of polygon-shaped cantilever array consists ofeight piezoelectric cantilevers with irregular cross-sectionaldesign, seven seismic masses, and a clamping system (Fig-ure 1). The number of the cantilevers was influenced bydemand to create two polygon-shaped systems with differentstiffness within the same indissoluble energy harvestingdevice and to increase number of natural frequencies inspecific frequency range. Such solution gives an opportunityto obtain modal strain summation at different vibrationfrequencies. Irregular design of cross-sectional areas of thecantilevers was caused by two goals, that is, to increasestrain characteristics and to improve strain distributioncharacteristics along the cantilevers. The polygon-shaped

Shock and Vibration 3

1

z

xy

2 3 4 5

Figure 1: Isometric view of the energy harvester:A clamping bolt;B clamping frame; C M3 bolts for junction between the clampingframe and the harvester; D body of the polygon-shaped harvester;E design of cross-sectional area.

energy harvester has seven seismic masses placed at everycorner of the harvester’s body. A junction between seismicmasses and the harvester was made by lever arms. Designof such seismic masses was introduced in order to createan additional rotation moment and to increase strain in thepiezoceramic layers. Hence, an additional rotation momentand irregular design of cross-sectional areas allow obtainingalmost liner function of the strain distribution along thelength of the cantilevers.

Clamping frame serves as the coupling system betweenthe body of harvester and the host (Figure 2). Two bolts areused to clamp energy harvester to the clamping frame. Twosupporting beams are rigidly connected to the body of energyharvester and serve as connection between the body of energyharvester and clamping frame. Dimensions of the supportingbeams are designed so that vibration of the first out of planebending mode is excited when displacement of the harvesterin 𝑦 direction is generated. Such design of the supportingbeams allows avoiding structural damping of the harvestervibrations.

3. Numerical Investigation ofthe Polygon-Shaped Energy Harvester

Numerical investigation of the polygon-shaped energy har-vester was divided into two parts. At the beginning, numeri-cal investigation was performed to calculate optimal geomet-rical parameters of the cantilevers; after that mechanical andelectrical characteristics of the harvester were investigated.Modal-frequency analysis and harmonic response analysiswere studied. Finite element model (FEM) was built usingComsol 5.2 software. Boundary conditions were set as fol-lows: ends of the supporting beamswere fixed rigidly; motionof the host structure was modeled as acceleration of theharvester base in 𝑧 direction. Material properties used to

build FEM model are given in Table 1. Principle scheme ofthe harvester is shown in Figure 3.

Two optimization problems were solved sequentially inorder to obtain optimal design of the harvester. Goal ofthe first optimization problem was to find optimal lengthof the cantilevers when sum of the square differences ofthe neighboring resonant frequencies of the harvester isminimized. The resonant frequencies dominated by the firstand the second out of plane vibrationmodes of any cantileverwere used. Lengths of the eight cantilevers were chosen as thedesign variables and optimization problemwas formulated asfollows:

min𝐿

𝑛−1

∑𝑖=1

(𝑤𝑖+1 (𝐿) − 𝑤𝑖 (𝐿))2 ,

subject to 𝑙min ≤ 𝑙𝑖 ≤ 𝑙max,

𝑤min ≤ 𝑤𝑖 ≤ 𝑤max,

𝑖 = 1, . . . , 8;

(1)

here 𝐿 = (𝑙1, . . . , 𝑙8) is a vector of cantilever lengths; 𝑤𝑖is resonant frequency of the harvester dominated by thefirst vibration mode of any cantilever; 𝑙min and 𝑙max are theminimal and the maximal values of the cantilever length; 𝑛 isthe number of cantilevers and is equal to 8.

Goal of the second optimization problem was to obtainoptimal mass values of the seismic masses in order tomaximize tip displacement of the harvester in 𝑧 direction.It was solved after the optimal length of the cantilevers wasobtained. Optimization problem was formulated as follows:

max𝑀(𝑢𝑧 (𝑀)) ,

subject to 𝑚min ≤ 𝑚𝑖 ≤ 𝑚max, 𝑖 = 1, . . . , 7;(2)

here𝑀 = (𝑚1, . . . , 𝑚7) is a vector of seismic mass weights; 𝑢𝑧is harvester tip displacement in 𝑧 direction; 𝑚min and 𝑚maxare the minimal and the maximal mass values of the seismicmasses.

Both optimization problems were solved by frequencydomain studies using linear search method. Acceleration ofthe base was set to 0.5m/s2. Values of 𝑙min and 𝑙max were setto 10mm and 25mm, respectively, while length iteration stepwas 1mm. Values of𝑚min and𝑚max were set to 2.5 grams and5 grams, respectively, while step was 0.1 grams.The frequencyrange for both optimization problemswas stated from𝑤min =10Hz to 𝑤max = 450Hz. Obtained optimized parameters ofthe harvester are listed in Table 2.

The second part of numerical investigation was dedicatedto analyzing mechanical and electrical characteristics of theharvester. Geometrical parameters of the harvester werestatedwith respect to the values obtained during optimizationstudy.Modal analysis of the harvester was performed in orderto indicate natural frequencies and modal shapes of the har-vester (Figure 4). Analysis of the results revealed that energyharvester has five natural frequencies at the range from 10Hzto 240Hz. It can be noticed that the first and the second out ofplane bendingmodes of the cantilevers are dominating in the

4 Shock and Vibration

Table 1: Material properties.

Material propertiesBerylliumbronzeC17200

Piezoceramic PIC255

Density [kg/m3] 8360 7800Elastic modulus [kg/mm2] 13.4 ⋅ 1010 —Poisson’s ratio 0.34 —Isotropic structural loss factor 0.02 0.015

Relative permittivity —

In the polarization direction𝜀33𝑇/𝜀0 = 1200

Perpendicular to polarity𝜀11𝑇/𝜀0 = 1500

Elastic stiffness coefficient 𝑐33𝐷 [N/m2] — 16.6 ⋅ 1010

Dielectric loss factor, tan 𝛿 [10−3] — 20Coupling factor, 𝑘31 — 0.35Piezoelectric voltage coefficient, 𝑔31 [10

−3 Vm/N] — −11.3

WBase

y

x

WClamping

LBeam

WFixing

D1

Figure 2: Scheme of the clamping system:𝑊Clamping—35mm;𝑊Base—5mm; 𝐿Beam—10mm;𝑊Fixing—10mm;𝐷1—3.2mm.

PZT 7

PZT 3PZT 2PZT 1

PZT

9PZ

T 10

PZT 12

PZT 8

PZT 13

PZT 6

PZT 5

PZT 4

PZT 11

3

4

5

67

9

8

10

1

11

2 m1 m2

m3

m4

z

y

m5m6

m7

Figure 3: Principle scheme of the piezoelectric polygon-shapedenergy harvester: A base of harvester; B ⋅ ⋅ ⋅H seismic masses(C17200 beryllium bronze); PZT1 ⋅ ⋅ ⋅PZT13: piezoceramic layers(PIC255);0 body of harvester (C17200 beryllium bronze);1 fixedconstrain;2 direction of the excitation.

Table 2: Optimized parameters of the harvester.

Parameter Value, mm Parameter Value, g𝑙1 23 𝑚1 4.6𝑙2 15 𝑚2 4.6𝑙3 13 𝑚3 2.7𝑙4 11 𝑚4 4.6𝑙5 13 𝑚5 4.6𝑙6 16 𝑚6 2.7𝑙7 2 𝑚7 3.9𝑙8 21

obtained modal shapes of the harvester. This study showedthat the number of the natural frequencies in the analyzedfrequency range is sufficient for the multifrequency energyharvesting.

Mechanical and electrical characteristics of the harvesterwere investigated at the frequency range of 10–240Hz. Baseacceleration amplitude was set to 0.5m/s2. Amplitude graphof harvester tip acceleration in 𝑧 direction versus frequencyis shown in Figure 5.

Shock and Vibration 5

0z

y0.511.522.533.54

54.5

(a)

0

1

z

y

0.20.4

0.60.8

1.2

1.4

(b)

0

1

z

y

0.2

0.4

0.6

0.8

1.2

(c)

0z

y

0.2

0.020.040.060.080.10.120.140.160.18

(d)

0z

y

0.02

0.04

0.06

0.08

0.1

(e)

Figure 4: Modal shapes of the harvester: (a) 14.41Hz; (b) 25.926Hz; (c) 73.981Hz; (d) 199.53Hz; (e) 214.56Hz.

10−1

100

101

102

Acce

lera

tion

ampl

itude

,Zco

mpo

nent

(m/s

2)

100 150 200 25050Frequency (Hz)

Figure 5: Acceleration amplitude versus excitation frequency.

Analysis of the frequency response characteristic con-firmed results of the modal analysis. Resonant frequencieshave good coincidence with the natural frequencies obtainedduring modal analysis. Obtained characteristic showed thatthe first three resonant frequencies are located at the narrowfrequency range and are close to each other. It shows thatenergy harvester will be able to operate efficiently at thisfrequency range. On the other hand, 4th and 5th reso-nant frequencies are located at slightly higher frequencies.However, these resonant frequencies are adequately close toeach other and provide multifrequency energy harvesting atthat frequency range. Moreover, high acceleration amplitude

of the energy harvester tip at the resonance frequencieshas positive influence on the electrical characteristics ofharvester.

Investigation of strain distribution along each cantileverwas performed as well. Results of the calculations are given inFigure 6. It can be seen that, in most cases, strain distributioncharacteristics are almost liner and constant along the lengthof the cantilever except the cases when the second or highervibrationmodes occur at the cantilevers. Almost linear straincharacteristic was achieved by modifications made to thecross-sectional areas and special design of the seismicmasses.Modifications of cross-sectional areas improved strain distri-bution, while special design of the seismic masses ensuredhigher values of the strain.

Electrode configuration of piezoceramic layers was basedon the strain distribution along the length of the beam.Electrode configuration allowed proper separation of positiveand negative charges obtained when cantilevers of the har-vester vibrate at the second vibration mode. Proper electrodeconfiguration influences electrical output characteristics ofmultifrequency energy harvester. Algorithm of electrodeconfiguration was formulated as follows: partitioning of theelectrodes was made in the places where the value of staintensor component is close to zero. Therefore, five vibrationnodes of the harvester were analyzed and partitioning of theelectrodes was made at indicated nodes. As a result, thirteendifferent electrodes (PZT1–PZT13) were composed on the topsurfaces of the piezoceramic layers of the harvester (Figure 2).

Investigation of electrical characteristics was performedas well. Mechanical boundary conditions of the harvester

6 Shock and Vibration

10−5

10−4

10−3

10−2St

rain

YY

14.45Hz26 Hz74 Hz199.55Hz215 Hz

0 5 10 15Arc length

20

(a)

10−5

10−6

10−4

10−3

10−2

Stra

inYZ

14.45Hz26 Hz74 Hz199.55Hz215 Hz

Arc length0 2 4 6 8 10 12

(b)

10−5

10−6

10−4

10−3

10−2

Stra

inYY

14.45Hz26 Hz74 Hz199.55Hz215 Hz

Arc length0 2 4 6 8 10

(c)

10−5

10−6

10−4

10−3

10−2

14.45Hz26 Hz74 Hz199.55Hz215 Hz

Arc length0 2 4 6 8 10

Stra

inYY

(d)

10−5

10−6

10−4

10−3

10−2

Stra

inZZ

14.45Hz26 Hz74 Hz199.55Hz215 Hz

Arc length0.0 2.0 4.0 6.0 8.0 10.0

(e)

10−5

10−4

10−3

10−2

Stra

inYZ

14.45Hz26 Hz74 Hz199.55Hz215 Hz

Arc length0 2 4 6 8 10 12 14

(f)

10−5

10−4

10−3

10−2

Stra

inYY

14.45Hz26 Hz74 Hz199.55Hz215 Hz

Arc length0 2 4 6 8 10 12 14 1816

(g)

10−5

10−4

10−3

Stra

inYZ

14.45Hz26 Hz74 Hz199.55Hz215 Hz

Arc length0 2 4 6 8 10 12 14 1816

(h)

Figure 6: Strain characteristics at the cantilevers; (a) at 𝐿1; (b) at 𝐿2; (c) at 𝐿3; (d) at 𝐿4; (e) at 𝐿5; (f) at 𝐿6; (g) at 𝐿7; (h) at 𝐿8.

Shock and Vibration 7

were the same as in the previous numerical investigation.Electrodes were connected in parallel in order to increase thecharge value during harvester operation. The aims of inves-tigation were to obtain output voltage density and energydensity characteristics in frequency domain. Voltage densityand energy density were introduced in order to compareelectrical characteristics of the harvester at the differentresonant frequencies. Voltage density can be expressed asfollows:

𝑈𝜎 =𝑈output

𝑊PZT ⋅ ℎPZT ⋅ ∑𝑖=𝑗−1

𝑖=1 PZT𝑖; (3)

here 𝑈𝜎 is voltage density of the harvester; 𝑈output is outputvoltage of the harvester; PZT𝑖 is length of piezoceramiclayer; 𝑊PZT is width of piezoceramic layer; ℎPZT is heightof piezoceramic layer; 𝑗 is number of piezoceramic layers(Figure 3).

Energy density of the harvester was calculated as follows:

𝐸𝜎 =𝐸output

𝑊PZT ⋅ ℎPZT ⋅ ∑𝑖=𝑗−1

𝑖=1 PZT𝑖; (4)

here 𝐸𝜎 is voltage density of the harvester; 𝐸ouput is outputvoltage of the harvester; PZT𝑖 is length of piezoceramiclayer; 𝑊PZT is width of piezoceramic layer; ℎPZT is heightof piezoceramic layer; 𝑗 is number of piezoceramic layers(Figure 3).

Numerical investigation of the voltage density was per-formed while applying open-circuit boundary conditions.The results of calculations are given in Figure 7. It can beseen that peaks of voltage density and energy density wereobtained at the resonant frequencies. The highest voltagedensity was obtained at the 2nd resonant frequency andit reached 50.03mV/mm3. Other values of voltage densityare lower. However, it shows high electrical potential of theenergy harvester. Ratio between the highest voltage densityand the lowest voltage density is 6.78. It shows that voltagedensity is sensitive to the resonant frequencymode. However,several voltage density peaks at narrow frequency rangegive an opportunity to obtain multifrequency-type energyharvesting.

Analysis of energy density characteristic showed thatenergy harvester is able to provide acceptable energy feedat the different resonant frequencies. The highest energydensity was obtained at the 2nd resonant frequency as well.Maximum value of the energy density reached 604 𝜇J/mm3.In addition, itmust bementioned that energy density reachedhigh value, 481 𝜇J/mm3, at the 1st resonant frequency as well.Therefore, it can be concluded that energy harvester is ableto provide high energy feed with overcapacity at the twodifferent resonant frequencies. On the other hand, energyfeed at the other resonant frequencies is much lower. It canbe concluded that the highest efficiency of energy harvesterwill be achieved at the lower frequency, while operationat the higher frequency is less effective, but energy feed isappreciable.

Comparison of voltage density and energy density val-ues was made in order to assess electrical characteristics

50 100 150 200Frequency (Hz)

25010−1210−1110−1010−910−810−710−610−510−410−3

Voltage density (V/mm3)Energy density (J/mm3)

Figure 7: Electrical characteristics of the harvester.

14,50.0

26,1 74,2Frequency (Hz)

Voltage densityEnergy density

199,5 215,3

Volta

ge d

ensit

y (V

/mm

3)

Ener

gy d

ensit

y (J

/mm

3)

5.0 × 10−3

0.05.0 × 10−41.0 × 10−31.5 × 10−32.0 × 10−32.5 × 10−33.0 × 10−33.5 × 10−34.0 × 10−34.5 × 10−35.0 × 10−35.5 × 10−36.0 × 10−36.5 × 10−3

1.0 × 10−21.5 × 10−22.0 × 10−22.5 × 10−23.0 × 10−23.5 × 10−24.0 × 10−24.5 × 10−25.0 × 10−25.5 × 10−2

Figure 8: Summary of electrical characteristics of the harvester.

of the energy harvester at different resonant frequencies(Figure 8). Based on obtained results, it can be concludedthat voltage and energy densities vary from 7.5mV/mm3to 50.03mV/mm3 and from 120𝜇J/mm3 to 604 𝜇J/mm3,respectively. It is shown that values of voltage and energydensities are obtained at wide range, but harvester is notable to provide constant voltage and energy at the differentexcitation frequencies. On the other hand, when comparingminimumvalues of the conventional cantilever arraywith theproposed multifrequency harvester, it can be noticed that thehigher output values were obtained. In addition, stability ofelectrical characteristics is significantly improved using theproposed piezoelectric harvester.

4. Experimental Investigation ofMultifrequency Energy Harvester

Experimental investigations of mechanical and electricalcharacteristics were performed in order to confirm resultsof numerical investigation. Prototype of the energy harvesterwas made with the strict respect to the geometrical andphysical parameters used during FEMmodeling (Figure 9).

8 Shock and Vibration

Figure 9: Prototype of piezoelectric energy harvester.

05 10 20 50 100

Frequency (Hz)200 500

50

100

150

200

Mag

nitu

de (

m/s

)

Figure 10: Frequency response characteristic of the energy har-vester.

Firstly, experimental investigation of the frequencyresponse characteristic was performed with the aim to val-idate results of numerical investigation. Polytec OFV 056scanning vibrometer was used for acceleration measure-ments. Excitation of the energy harvester was performed byelectromagnetic shakerThermotron DSX-4000. A controllerof Polytec vibrometer was employed to generate frequencysweep function for the shaker. Results of harvester tipacceleration measurement are shown in Figure 10.

Results of the measurement show that the energy har-vester has five peaks in frequency range of 10–240Hz. Also,it can be seen that two additional peaks appear close tothe 1st resonant frequency. This was caused by specificcharacteristic of the function of excitation signal. However,performed measurements confirmed results of numericalmodal analysis. Differences betweenmeasured and calculatedfrequencies do not exceed 5.02%. Summary of the differencesbetween measured and calculated frequencies was made tocompare obtained results (Figure 11). It can be seen that thehighest difference comes at the 4th frequency and it reached

Diff

eren

ce (H

z)

−10

−8

−6

−4

−2−0.824

−7.262

−10.125

−6.309

0.639

0

2

2nd1stResonant frequency

3rd 4th 5th

Figure 11: Differences between measured and calculated resonantfrequencies.

(6)

(7)

(8)

(5)

(3)(2)(1)

G

V

(4)

Figure 12: Experimental setup; (1) function generator; (2) amplifier;(3) electromagnetic shaker; (4) computer; (5) data loggingmultime-ter; (6) electronic interface; (7) harvester; (8) displacement sensor.

10.125Hz. Differences are caused by mismatch of materialscharacteristics, manufacturing errors, and slight differencesin clamping.

Experimental investigation of electrical characteristicswas performed as well. Output voltage density and energydensity weremeasured in frequency range of 10–240Hz. Spe-cial experimental setup was built for this purpose (Figure 12).

Experimental setup consisted of function generator Tek-tronix AFG1062 and an amplifier that was used to driveelectromagnetic shaker. Keyence LK-G155 laser sensor wasused to measure base displacement, while Fluke 289 datalogging multimeter was used to measure amplitude of theoutput voltage. Laser sensor and multimeter were connectedto computer in order to record and manage data.

Shock and Vibration 90 15 30 45 60 75 90 105

120

135

Frequency (Hz)

PZT13PZT12

PZT11PZT10

PZT9PZT8

PZT7PZT6

PZT5PZT4

PZT3PZT2

PZT115

016

518

019

521

022

524

0

123456

Volta

ge (V

)

78910

Piez

ocera

mic

layer

Figure 13:Measured output voltage of all piezoceramic layers versusfrequency.

Firstly, characteristics of unrectified open-circuit voltagewere measured versus excitation frequency for each piezo-ceramic layer. Voltmeter was connected directly to eachpiezoceramic layer. Base acceleration of the harvester was setto 0.475m/s2. The goal of this investigation was to indicatecharacteristics of unrectified open-circuit voltage for eachpiezoceramic layer and to assess electrical performance of theharvester. Results of measurements are given in Figure 13.

The results of measurements confirmed that all piezo-ceramic layers generate voltage, while harvester operates atthe resonant frequencies. The highest output voltages wereobtained at the low resonant frequencies. The highest outputvoltage was 10.61 V and it was generated by PZT1 layerat 25Hz excitation frequency. PZT1 layer is located closeto the clamped end of the harvester (Figure 3). Analysisof the results revealed that all piezoceramic layers provideoutput voltage at five resonant frequencies. It confirms anassumption ofmodal strain summation phenomena obtainedthrough special design of the harvester. Hence, it can benoticed that all cantilevers are employed when harvesteroperates at resonant frequencies and it can be claimed thatproposed piezoelectric harvester is more advanced comparedto the conventional array of the cantilevers [25].

Next step of experimental investigation was dedicated tothe measurements of total rectified output voltage density.Electronic interface was designed and connected to theenergy harvester for this purpose. It consisted of thirteenfull diode rectifiers. The rectifiers were made from low lossSchottky diodes BAT46 and low ESR electrolytic capacitor.Voltage density at the frequency range of 10–240Hz wasmeasured. Electronic interface was switched to the open-circuit condition; that is, electrical load was approximatelyequal to 10MΩ. Results of the measurement are shown inFigure 14.

Analysis of the voltage density graph showed that voltagedensity peaks are obtained at the same frequencies as inthe previous measurements. It confirmed good agreementbetween numerical calculations and experimental measure-ments. Moreover, measurement shows that voltage densitylevel is not falling below 5.25mV/mm3. It means that energy

200.00000.00250.00500.00750.01000.01250.01500.01750.02000.02250.02500.02750.03000.03250.03500.03750.0400

40 60 80 100 120Frequency (Hz)

140 160 180 200 220 240

Volta

ge d

ensit

y (V

/mm

3)

Figure 14: Measured voltage density in frequency domain.

0.0 0

20 40 60 80 100

120

140

160

Frequency (Hz)

180

200

220

240

1.0 × 10−41 × 10−52 × 10−53 × 10−54 × 10−55 × 10−56 × 10−57 × 10−58 × 10−59 × 10−51 × 10−41 × 10−4

2.0 × 10−4

3.0 × 10−4

4.0 × 10−4

5.0 × 10−4

6.0 × 10−4

7.0 × 10−4

9.0 × 10−4

Ener

gy d

ensit

y (J

/mm

3)

Ener

gy d

ensit

y (J

/mm

3)

Figure 15: Energy density versus frequency characteristic.

harvester is able to provide sufficient voltage output atnonresonant frequency as well. The highest voltage densitywas obtained at the 2nd resonant frequency and it reached37.5mV/mm3. It is 7.14 times higher than lowest voltagedensity level. Also it can be noticed that voltage densities atthe remaining four resonant frequencies aremuch lower thanthose at the 2nd resonant frequency.

Experimental investigation of energy density at the samefrequency range was performed as well. The same experi-mental setup was used (Figure 12). The electrical interfacewas switched from open-circuit condition to the loadedcondition. Electrolytic low ESR capacitor with capacitanceof 220 𝜇F was connected as the common load. Results ofthe measurements are given in Figure 15. It can be seenthat energy density graph has five peaks as in the casediscussed before. However, peaks are slightly lower comparedto the frequency response characteristic. Such mismatchcan be explained by influence of capacitive load which wasconnected to the energy harvester through voltage rectifiers.On the other hand, shift of the resonant frequencies isrelatively small, that is, 3–5Hz. Hence, it shows that energy

10 Shock and Vibration

0.0

Volta

ge d

ensit

y (V

/mm

3)

5.0 × 10−3

1.0 × 10−2

1.5 × 10−2

2.0 × 10−2

2.5 × 10−2

3.0 × 10−2

3.5 × 10−2

4.0 × 10−2

0.01.0 × 10−42.0 × 10−43.0 × 10−44.0 × 10−45.0 × 10−46.0 × 10−47.0 × 10−48.0 × 10−49.0 × 10−4

Ener

gy d

ensit

y (J

/mm

3)

1st 2nd 3rd 4th 5thResonant frequency

Voltage densityEnergy density

Figure 16: Voltage density and energy density of the harvester at thedifferent resonant frequencies.

harvester operates sufficiently stably when capacitive load isapplied.

Also it can be noticed that the highest energy density wasobtained at the 2nd resonant frequency. Energy density at thisfrequency reached 815.16 𝜇J/mm3. It shows that maximumoutput power of the proposed harvester is 65.24𝜇W whenit operates at the 2nd resonant frequency and it is 12.68%higher value compared to the maximum output power of theconventional multifrequency cantilever array [25]. However,energy density value at the 1st resonant frequency is lowerand is equal to 708.71 𝜇J/mm3. Also, it can be seen thatenergy density values are much lower at the higher resonantfrequencies. Energy density value reached 93.23𝜇J/mm3 atthe 4th resonance frequency and 11.5 𝜇J/mm3 at the 3rdresonant frequency. Comparison of both voltage and energydensities at the different resonant frequencies is given inFigure 16. It can be seen that energy harvesting system atthe first two resonant frequencies is able to provide highenergy feed to the energy storage device and even to ensureovercapacity. However, energy harvesting system providesmuch lower energy feed at the higher resonant frequencies.

5. Conclusions

A novel design of multifrequency polygon-shaped energyharvester was proposed.Themodifications of cross-sectionalarea, additional seismic masses, and special clamping allowincreasing strain of the cantilevers and improving straindistribution along the piezoceramic layers.

Numerical and experimental investigations were per-formed. Modal analysis showed that the system has fiveresonant frequencies in the range of 10–240Hz. The first andthe second out of plane bending modes of the cantilevers aredominating in aforementioned frequency range. Moreover,numerical investigation of the strain and strain distributionshowed that strain function along the piezoceramic lay-ers is almost constant. Such strain function was achievedby modification of cross-sectional areas of the cantilevers.Numerical investigation of electrical characteristics showed

that maximum voltage and energy densities were obtained atthe 2nd resonant frequency and reached 50.03mV/mm3 and604 𝜇J/mm3, respectively.

Experimental investigation confirmed results of thenumerical modeling. The highest difference between reso-nant frequencies is 5.02%. Moreover, experimental investi-gation of electrical characteristics showed that the highestvoltage density and energy density were obtained at the2nd resonant frequency. Both voltage and energy densitiesreached 37.5mV/mm3 and 815.16 𝜇J/mm3, respectively.Maxi-mumoutput power of the harvester is 65.24𝜇W.Finally, it canbe concluded that proposed piezoelectric energy harvester isable to provide suitable energy feed through multifrequencyoperation principle.

Conflicts of Interest

The authors declare that there are no conflicts of interestregarding the publication of this paper.

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