EXPERIMENTAL VALIDATION OF A POROUS PIEZOELECTRIC …michael.friswell.com/PDF_Files/C414.pdf · Department of Mechanical Engineering Claverton Down, Bath, BA2 7AY, UK Key words: Energy

Experimental Validation of a Porous Piezoelectric Energy Harvester

VIII ECCOMAS Thematic Conference on Smart Structures and MaterialsSMART 2017

A. Guemes, A. Benjeddou, J. Rodellar and J. Leng (Eds)

EXPERIMENTAL VALIDATION OF A POROUSPIEZOELECTRIC ENERGY HARVESTER

GERMAN MARTINEZ-AYUSO∗, HAMED HADDADKHODAPARAST∗,YAN ZHANG†, CHRISTOPHER R. BOWEN†,

MICHAEL I. FRISWELL∗, ALEXANDER D. SHAW∗, HADI MADINEI∗

AND JAMES I. ROSCOW†

∗ Swansea UniversityCollege of Engineering, Bay Campus

Fabian Way, Crymlyn Burrows,Swansea SA1 8EN, UK

† University of BathDepartment of Mechanical EngineeringClaverton Down, Bath, BA2 7AY, UK

Key words: Energy Harvesting, Porous material, Piezoelectricity, Model Validation, PhysicalExperiment

Abstract. In this paper, a homogenised finite element model is developed to predict the energyharvesting capabilities of a porous piezoelectric energy harvester. The harvester consists of aporous piezoelectric patch bonded to a cantilever beam. The material properties of the porouspiezoelectric material are estimated by the Mori-Tanaka homogenisation method, which is ananalytical method that provides the material properties as a function of the porosity of thepiezoelectric composite. These material properties are then used in a finite element model ofthe harvester that predicts the deformation and voltage output for a given base excitation of thecantilever beam, onto which the piezoelectric element is bonded. Experiments are performedto validate the numerical model, based on the fabrication and testing of several demonstratorscomposed of porous piezoelectric patches with different percentages of porosity bonded to analuminium cantilever beam. The electrical load is simulated using a resistor and the voltageis measured to estimate the energy generated. The beam is excited in a range of frequenciesclose to the first and second modes using base excitation. The effects of the porosity and theassumptions made for homogenisation are discussed.

1 INTRODUCTION

Piezo-electric materials can act as sensors or actuators in engineering structures. Embeddedsensors in structures are an important application of piezo-electric materials and are used to trackstrain and damage in structures such as buildings, aircraft and bridges. Wireless sensor networks

1

630

German Martınez-Ayuso, Hamed Haddad Khodaparast, Yan Zhang, Christopher R. Bowen, Michael I.Friswell, Alexander D. Shaw, Haid Madinei and James I. Roscow

are increasingly being used in areas such as the aerospace industry, where control and monitoringof slender and light-weight structures is becoming more important. Furthermore, these sensorscan also harvest energy, in addition to measuring the deformation. The energy harvestingcapability of these sensors must be optimised by carefully selecting their configuration andappropriate materials selection. Porous piezoelectric materials have shown promise as sensorsand energy harvesters due to their beneficial figures of merit when the porosity is increased.

Traditionally, porosity has been considered a defect in the fabrication process or a non valu-able property in many applications, such as concrete fabrication, steelworks industry, etc. Recentscientific advances in last decades are changing the perception of porosity by both scientists andengineers [10]. Different authors have points regarding the possible applications of porosity indifferent fields, from construction using porous metals [14] to bioengineering using porous ti-tanium in bones implants [2]. The aerospace industry is interested in such materials for theirgood thermal isolation properties and reduced weight [8]. Porous silicon has been proposed forimportant electronic applications [4]. Some authors [20, 23, 19, 22] have studied porous ceramicsfrom different points of view such as thermal shock isolation, catalyst supports, etc. However,less attention has been given to porous ceramics for energy harvesting. Energy harvesting is thecapability of devices to scavenge energy from the surrounding environment from energy sourcessuch as vibrations, light, thermal gradients, etc. Piezoelectric ceramics have been studied inlast decades not only for its energy harvesting capabilities but also for their sensor and actuatorcapability. These materials have important applications such as ink-jet printers, sonar transduc-ers, heart rate monitors, hydrophones, air bag sensors, etc. When acting as a sensor they canbe used for structural health monitoring (SHM) or to power small devices. Sodano et al. [21]presented an extensive review of the applications of piezoelectric materials to energy harvesting.Friswell and Adhikari have explored the possibilities of piezoelectric devices to harvest energyfrom non-linear vibration [7] and from broadband excitation [1]. Bowen et al. [3] studied howthe porosity affect the piezoelectric and dielectric coefficients. Roscow [17] has reviewed themanufacturing process of porous piezoelectric materials.

In this paper the capability of the porous piezoelectric material for energy harvesting isassessed by comparing the predictions from a homogenised numerical model with those ob-tained experimentally. The composite material is homogenized using analytical theories suchas Mori-Tanaka and included in a numerical model based on the finite element method whichincludes the geometry of the energy harvester. The porous piezo patches used for experimentaldemonstrators, are fabricated using two different methods, Burnt polymer spheres (Bur-PS) andfreeze-casting. These patches are bonded to an aluminium beam and tested with a shaker whichprovides harmonic base excitation in a wide range of frequencies to the beam. The spectrumof the voltage outputs are measured and compared with those obtained by numerical modelpredictions.

The structure of this paper is summarised as follows. The porous material manufacture pro-cess is detailed in section 2. Given the composite nature of the porous material, a homogenizationprocess has to be performed to obtain the material properties. An analytical homogenizationmethod known as Mori-Tanaka method is presented in Section 4. The obtained properties areused in the next section to create a finite element model of the cantilever beam demonstrator.The demonstrator fabrication, as well as the testing parameters, are presented in the next sec-tion. Finally, the results and discussion are presented followed by the conclusions of the present

2

631


study.

2 MANUFACTURE OF POROUS MATERIAL

In this study, commercial available barium titanate powders (BaTiO3, d33=147 pC/N, rel-ative permittivity ϵT

33/ϵ0 =1470 [18, 17] , deionized water and poly(acrylic acid) (PAA, Mv100,000, Sigma Aldrich) and polyethylene glycol (PEG, Mv 8,000, Sigma Aldrich) are used asstarting materials, freezing vehicle, dispersant and binder/pore forming agent (PFA), respec-tively.

For the burned out polymer spheres (BURPS) method, barium titanate powders mixed withPEG in different proportions by weight are uniaxially pressed at 300MPa to form the disks. Forfreeze casting, suspensions with barium titanate powders, 3 wt.% dispersant and 3 wt.% binderare ball-milled for 24 h in zirconia media and de-aired by stirring in a vacuum desiccator untilcomplete removal of air bubbles. Freezing of the suspension and aqueous solution are carriedout as described previously in [26, 25] by pouring them into a transparent aligned cylindricalpolydimethylsiloxane (PDMS) mould, which is then transported to a copper cold finger andplaced in a liquid nitrogen container. The frozen barium titanate pillars are then freeze-driedto remove the ice dendrites. The disks and freeze-dried barium titanate pillars are heat-treatedat 500 C for 2h to remove the organic additives, followed by heat-treatment at 1200 C for 2hand then finally allowed to cool down naturally in the closed furnace. The sintered ceramics arethen cut to a diameter of 10 mm and thickness of 1 mm by a cutting machine.

After the manufacture of the porous disks, the piezoelectric strain coefficient, d31, was mea-sured using a Berlincourt Piezometer (PM25, Take Control, UK), which applies an alternatingforce of 0.1 N at a frequency of 97 Hz. Measurements of the relative permittivity of the sinteredporous barium titanate were carried out at room temperature using an impedance analyzer(Solartron 1260, Hampshire, UK). However, not all the material properties required to modelthe composite using FE method can be obtained without more advanced test. For example, theelastic modulus cannot be measured using widely used resonance technique because of the air inthe porous attenuate the resonance making the reading not reliable. Other methods to measurethese elastic properties might destroy the disk tests. Therefore, to avoid these problems, anhomogenization process is proposed in the next section to predict the complete set of materialproperties.

3 THEORETICAL HOMOGENIZATION

The porous piezoelectric material is composed of two phases; air and piezoelectric material.For each phase the material constants are well known, but the set of homogenized materialconstants must be calculated for the resultant composite. As it is stated in Section 2, notall the material properties can be obtained with accuracy or without compromising the healthof the porous ceramic disk. Hence, some material properties have to be predicted using ahomogenization approach.

One of the most commonly used approaches is to homogenize the material using analyticalmethods. Analytical methods have been used extensively to homogenize composites because oftheir accuracy and speed with respect to other approaches such as computational homogenizationusing finite element methods (FEM). One of the most well-known and validated approach is the

3

632


Mori-Tanaka method [15]. This method improves the Eshelby solution [6] given for ellipsoidalinclusions in elastic mediums. The approach may be used in multi-field physics analysis, forexample for general composite materials [16, 24] and for porous piezoelectric materials [5, 12].To perform a Mori-Tanaka homogenization, the calculation of the Eshelby tensor, S∗, is requiredand depends on the shape of the inclusion which is spherical in this case. The procedure to obtainthis tensor is comprehensively detailed in [13] and hence is not explained here. In the Mori-Tanaka method, each inclusion with properties EI where EI is composed of the elastic stiffnessmatrix (C), the piezoelectric matrix (e) and the permittivity matrix at constant strain (ks).This tensor behaves as an isolated inclusion, embedded in an infinite matrix with propertiesEM, that is loaded remotely by an applied strain, therefore, each inclusion is subjected to theaveraged stress fields acting on it from all of the other inclusions, through the superposition ofstresses. The application of this method in porous piezoelectric material is demonstrated in [11]and is compared with other homogenization methods such as self-consistent and computationalhomogenization method using FEM. In this paper, the Mori-Tanaka homogenization is presentedas an accurate method to predict the material properties. The homogenization procedure of thismethod is summarized as follows: First, an influence tensor AI,r

0 has to be calculated for everyphase r (AI,r

0 ) and percentage. This concentration tensor is written in terms of the Eshelbytensor as shown in equation 1a. These concentration tensors are then averaged to obtain thegeneral influence tensor, AI,r

(MT) and finally, the effective electro-elastic material tensor (E∗)using equation 1c.

AI,r0 =

[I + S∗

(EM

)−1 (EI,r − EM

)]−1(1a)

AI,r(MT) =

cI,rI + cM(AI,r

0 )−1 +N∑

j=1cI,rAI,j

0 (AI,r0 )−1

−1

(1b)

E∗(MT) = EM +

N∑r=1

cI,r(EI,r − EM

)AI,r

(MT) (1c)

This method is self-consistent, since the inverse of the electromechanical matrix E∗ is equal tothe compliance electromechanical matrix F ∗, which is composed by the elastic compliance (S),the piezoelectric matrix (d) and the permittivity matrix at constant stress (kT ).

4 NUMERICAL MODEL

In order to design efficient porous material energy harvesters, a reliable and accurate mod-elling technique is needed. Today, one of the most powerful tools to represent complex multi-physics is the Finite Element Method. This method is based on discretization of partial differ-ential equations that govern the problem. It can model complex geometries as well as complexmaterial properties. The porosity in piezoelectric material allows a smart distribution of thepiezoelectric mass in the energy harvester, removing piezoelectric material from the places wherethe strain is lower and reallocating it where higher strains are located. The graded distributionof porosity generates functionally graded material which can maximize the power output for agiven quantity of piezoelectric ceramic. This distribution can be accurately modelled using fi-nite element methods. Therefore FE technique is used here although this study does not include

4

633


(a) (b)

Main Resistor

Quattro System

Parallel Resistor(c)

Figure 1: Finite element model. (a) General view of the cantilever beam energy harvester with the leftside clamped. (b) Detailed view of the clamped side and the porous piezoelectric patch as well as thethe resistor which connects the top surface with the bottom surface of the porous piezoelectric disk. (c)Schematic view of the external circuit connected to the harvester.

Sample Porosity Thickness Diameter Fabrication Piezoelectric coeff. Relative Permittivitynumber (%) (mm) (mm) method d31 (pC/N) ϵ33/ϵ0

1 66.0 2.073 11.137 BURPS -10 2902 55.0 2 11.24 BURPS -60 4453 50.0 1.86 11.273 BURPS -120 5264 32.0 1.5 11.247 BURPS -190 8085 20.0 1.27 11.26 BURPS -250 11996 45.0 1.78 9.94 Freeze cast -340 5637 35.0 2.06 10.23 Freeze cast -390 7028 31.0 1.7 10.64 Freeze cast -300 788

Table 1: Demonstrator patches properties using barium titanate.

functionally graded materials. In future studies, the porosity distribution will be optimised inorder to maximize the power output.

In this study, the finite element package called ANSYS R⃝ is used in order to model theharvester. The material properties are modelled in the linear elastic range and using 3D elements.The element type used for the whole model is SOLID 227. The external resistors are modelledusing the element CIRCU94, connecting the top surface of the disk and the bottom surface.

The FE model is coupled with Matlab R⃝ which performs the homogenization process andprovides the material properties and geometrical parameters to ANSYS R⃝. An in-house Matlab R⃝

code has been developed to link ANSYS to MATLAB and can be used for optimisation/modelupdating purposes. The porous material is modelled using the homogenized parameters obtainedin Section 3.

5 EXPERIMENTAL VALIDATION

In order to validate the finite element model, a set of experiments are designed. Severalpiezoelectric patches with different percentages of porosity are prepared at the University ofBath. The percentages of the test disk range between 20% and 66% with different values ofthickness and radius, as shown in table 1.

In addition, some non-porous piezoelectric patches are used in order to compare the accuracyof the model with traditional lead zirconate titanate (PZT). These non-porous square patchesare PZT-5A1 and supplied by Morgan Advanced Ceramics. Their properties and dimensions

5

634


0 10 20 30 40 50 60 70Percentage of porosity

0

500

1000

1500

33

-60

-40

-20

0

20

d 31

(a) (b) (c)

Figure 2: (a) Material coefficients d31 (red) and ϵ33 (blue) predicted by homogenization theory “Mori-Tanaka” (solid line) compared with the values measured experimentally (dots). (b) View of the lab setup.(c) Detailed view of a porous patch attached to the aluminium beam.

are shown in table 2.The patches are attached to aluminium beams using conductive glue which acts also as

electrode. These aluminium beams have the properties specified in table 2. These piezoelectricdemonstrators are tested using an APS Dynamics Model 113-HF electrodynamic shaker (APSDynamic Juan Capistrano, CA) as an excitation source, powered by an APS amplifier Model125-230. The type of testing is a sin-step analysis for a range of frequencies between 5 Hzand 42Hz which includes the first two modes and anti-resonance mode. Two measurements areobtained, the base acceleration through an accelerometer located in shaker, and the voltagedifference between the top and bottom electrode of the piezoelectric patch using Data PhysicsQuattro analyser, which is a usb powered data acquisition.

6 RESULTS AND DISCUSSION

As it is stated in Section 2, an homogenization method for the porous piezoelectric ceramicis used to obtain the complete set of material properties of the porous PZT. In Figure 2 theresults obtained in the homogenization process for the piezoelectric coefficient d31 and the dielec-tric coefficient ϵ33 are compared with the values measured on the patches after its fabrication.The homogenized values of these coefficients indicate an overestimation of the measured val-ues. Further examinations of the disk reveal some cracks which potentially could decrease thepiezoelectric values.Also it has been observed that not all the inclusions are spherical as it isassumed in Section 3. In the case of the disk manufactured using free-casting method, the shape

PZT-5A Aluminium

Density (kg/m3) 7750 Density (kg/m3) 2700SE

33 (10−12m2/N) 17.2 Young Modulus (GPa) 70SE

11 (10−12m2/N) 16.7 Poisson Ratio 0.3d33 (pC/N) 409d31 (pC/N) 176 Beam DimensionsϵT

33/ϵ0 1800 Length x Width x Thickness (mm) 375 x 16 x 1

Table 2: Material properties of the non-porous piezoelectric patch supplied by Morgan Advance CeramicsPLC and the aluminium used for the beams.

6

635


10 20 30 40

10−5

10−3

Frequency (Hz)

Vol

tage

outp

ut(V

) Test no. 1 - Por: 0 %

(a)

10 20 30 40

10−6

10−4

10−2

Frequency (Hz)

Vol

tage

outp

ut(V

) Test no. 2 - Por: 0 %

(b)

10 20 30 40

10−5

10−3

10−1

Frequency (Hz)

Vol

tage

outp

ut(V

) Test no. 3 - Por: 0 %

(c)

10 20 30 40

10−5

10−3

10−1

Frequency (Hz)V

olta

geou

tput

(V) Test no. 4 - Por: 0 %

(d)

10 20 30 40

10−5

10−3

10−1

Frequency (Hz)

Vol

tage

outp

ut(V

) Test no. 5 - Por: 0 %

(e)

5.5 6 6.5 710−3

10−2

Frequency (Hz)

Vol

tage

outp

ut(V

) First Mode Test no. 5 - Por: 0 %

(f)Figure 3: Dynamic test results performed on the non-porous patches.

of the inclusions tends to be more cylindrical than spherical. The cylindrical inclusions reducein-plane properties whilst maintaining the benefits through thickness properties and this causesthe differences between the values of the material coefficients in different directions. In otherwords, in-plane properties of the porous piezo with spherical inclusion shapes deemed to belarger than their corresponding values for the ones with cylindrical inclusion shapes [9]. Usingthe assumption of spherical inclusions could lead to overestimate some parameters especially indirection perpendicular to the cylinders as shown in Figure 2 presented. It is observed that themain piezoelectric coefficient for the voltage output in a cantilever energy harvesting device isthe d31 which could be potentially greatly affected by the shape inclusions.

Once the material coefficients are obtained and validated, the dynamic tests are performedas stated in Section 5. In table 3 the experiment setup is shown for each test. The dynamictest are designed to account for the different fabrication methods (Free-Casting or BURPS)and percentages of porosity (it is tested disk from 20% to 66% porosity). In any harvester theexternal circuit has a strong impact on the power output. Therefore, the resistance has to beoptimized for each level of porosity to obtain the maximum power. In [12] it was probed thatthe porosity does not have too much impact on the optimal resistance, being almost the sameas the non-porous optimal resistance, defined by ωnRC = 1. This value for a natural frequency

7

636


of 5.84 Hz (obtained from FE model) is approximately 10 MΩ. The resistors configurations aredetailed in table 3 for all the dynamic test performed.

Test Sample Method Porosity Main Resistor Resistornumber number fabrication in series in parallel

1 #Ref – 0.0% 10.042 MΩ 0.9951 kΩ2 #Ref – 0.0% 14.677 MΩ 0.9951 kΩ3 #Ref – 0.0% 14.677 MΩ 9.987 kΩ4 #Ref – 0.0% 10.042 MΩ 9.987 kΩ5 #Ref – 0.0% 10.042 MΩ 9.987 kΩ6 7 Free-casting 35.0% 10.042 MΩ 9.987 kΩ7 8 Free-casting 31.0% 10.042 MΩ 9.987 kΩ8 3 BURPS 50.0% 10.042 MΩ 9.987 kΩ9 1 BURPS 66.0% 10.042 MΩ 9.987 kΩ10 2 BURPS 55.0% 10.042 MΩ 9.987 kΩ11 7 Free-Casting 35.0% 10.042 MΩ 9.987 kΩ12 2 BURPS 55.0% 10.042 MΩ 0.9951 kΩ13 6 Free-Casting 45.0% 10.042 MΩ 9.987 kΩ14 5 BURPS 20.0% 10.042 MΩ 9.987 kΩ

Table 3: Dynamic tests performed for the different valuesof porosity, fabrication method and resistance configura-tion.

Figure 4: Test no. 9 whichgot detached during dynamicexperiment.

In order to validate the FE model, non-porous patches are tested and compared with nu-merical predictions. This comparison is presented in Figure 3. Good agreement is obtainedbetween the numerical model and the voltage output obtained in the lab for different valuesof resistance connected to the harvester (see Table 3). The FE model accurately predicts thevalues of the resonance frequencies for all the tests performed. For example, in test no. 1 thedifference in frequencies of the first mode is lower than 0.5 Hz. The antiresonance frequenciesslightly decreased with respect to the experimental values but the impact of this difference isnegligible for energy harvesting. The amplitudes of the voltage output are predicted with agood accuracy especially around the first mode as Figure 3f presents. The difference betweentest no. 4 and 5, observed in Figures 3d and 3e, is due to differnet leveels of the amplitude ofbase excitation. This was achieved by increasing the acceleration from 0.0885 g (test no.5) to0.1824 g for test no. 4 in order to identify possible sources of non-linearities. Nevertheless nosources of non-linearities were identified, confirming that the energy harvester behaviour willremain linear in the ranges of base excitation amplitude tested. The damping ratio is obtainedexperimentally from half power point test and its values oscillate between 0.06 and 0.085.

To assess the reliability of the numerical model for non-porous patches, the analysis of thedynamic results are presented. In Figure 5, a comparison between the numerical model pre-diction (solid line) and the experimental values (dashed line) is presented. The experimentalvoltage output of porous demonstrator is, in general, lower than the non-porous ones becausethe matrix material is different for non-porous (PZT-5A1) and porous ones (BaTiO3). Testno. 9 is not presented in this figure because the disk detached during the dynamic test dueto crack propagation and the formation of cracks are an issue when manufacturing or testingporous material. The fabrication of the porous disk presents important stability problems whenfabricating thin patches (less than 2 mm) or high porosities (over 55%). The collapsing of thedisk is ensured for percentages over 70%. In test no. 9, the porosity is 66% which is the highest

8

637


10 20 30 40

10−6

10−4

10−2

Frequency (Hz)

Vol

tage

outp

ut(V

)

Test no. 6 - Por: 35 % (FC)

(a)

10 20 30 40

10−6

10−4

10−2

Frequency (Hz)

Vol

tage

outp

ut(V

)

Test no. 7 - Por: 31 % (FC)

(b)

10 20 30 40

10−6

10−4

10−2

Frequency (Hz)

Vol

tage

outp

ut(V

)

Test no. 8 - Por: 50 % (BS)

(c)

10 20 30 4010−8

10−5

10−2

Frequency (Hz)V

olta

geou

tput

(V)

Test no. 10 - Por: 55 % (BS)

(d)

10 20 30 40

10−7

10−5

10−3

Frequency (Hz)

Vol

tage

outp

ut(V

)

Test no. 11 - Por: 35 % (FC)

(e)

10 20 30 40

10−6

10−4

10−2

Frequency (Hz)

Vol

tage

outp

ut(V

)

Test no. 12 - Por: 55 % (BS)

(f)

10 20 30 40

10−6

10−4

10−2

Frequency (Hz)

Vol

tage

outp

ut(V

)

Test no. 13 - Por: 45 % (FC)

(g)

10 20 30 40

10−6

10−4

10−2

Frequency (Hz)

Vol

tage

outp

ut(V

)

Test no. 14 - Por: 20 % (BS)

(h)Figure 5: Dinamic test results performed on the porous piezoelectric disks. FC= Free-casting,BS=BURPS.

porosity achieved in the lab.In general, the results show good agreement between FE model predictions and measure-

ments. This is an indicator that the stiffness and mass matrix reflect the physics of the problemand hence the geometry and material properties of the porous material. The amplitude of thevoltage output varies according to the porosity and manufacturing process. For example testsno. 6 and 12 show an acceptable degree of agreement between the predicted voltage output inthe numerical model and the experimentally measured voltage. In particular, the predicted andmeasured voltages have similar values around the first resonance frequency. In general there is

9

638


a shift in the voltage output between the predictions and the experimental results. Test nos.10, 7 and 8 present the greatest shifts. A general shift in the voltage output can be possiblyrelated to wrong values of the piezoelectric coefficients. As it is mentioned in Sections 2 and 3,the values used in the FE model are obtained with Mori-Tanaka method which assumes spher-ical inclusions and no cracks inside the matrix. These cracks could decrease the piezoelectriccoefficients and the dielectric coefficients, generating the shift presented in the graphs. This alsomight be seen as an indicator of the health of the disks. It is already pointed out the fragilityof the disks and the tendency to cracks growth, hence measuring the coefficients before andafter the dynamic tests could be an approximate way to quantify damage in piezoelectric porousmaterial. It is important to notice that the experimental values of the voltage output are quitesimilar for both modes. In other words, the second mode voltage level is almost the same as thefirst mode voltage level (see Figure 5d). This is clearly different than the non-porous ones wherethe second mode harvest less power than the first mode (see Figure 3a). The lower mass perunit of length seems to benefit the power output in the second mode. This effect is interestingfor designing wide range energy harvester which their frequency range spans through multiplemodes.

Some experimental data present important changes in the voltage output close to the anti-resonance frequency, for example test nos. 7, 8 and 11. This variability is attributed to the noisedue the voltage reading resolution of the Quattro data acquisition system which does not readaccurately voltage outputs which round the microvolts (µV ). This indicates the importance ofthe fabrication method. The BURPS manufacture processing is a more developed technique forporous piezoelectric material than free-casting. Therefore higher percentages of porosity couldbe achieved using this method.

7 CONCLUSIONS

A validation scheme for porous piezoelectric energy harvesters is presented. A numericalmodel based on finite element method which account for porous using analytical “Mori-Tanaka”homogenization theory is developed and validated by comparison of voltage output with dy-namic tests performed on porous piezoelectric energy harvesters. This scheme shows promisingresults for predicting power output of energy harvester. Nevertheless more research is neededto optimise the piezoelectric material in terms of the electrical and mechanical requirement forenergy harvesting applications. Future work will involve modelling cylindrical inclusion shapesin the numerical model of porous piezo-material and stochastic modelling to take account ofmanufacturing variabilities of porous piezo-materials.

ACKNOWNLEDGES

This research is supported by Aerospace Technology Institute in the framework of “ExploitingAeroelastic Deflections For Improved Aircraft Performance” project.

The authors acknowledge the financial support from the Ser Cymru National Research Net-work and Swansea University through a Postgraduate Scholarship NRN-103.

The authors would like to acknowledge the support from Morgan Advanced Ceramics PLC.

10

639


REFERENCES

[1] S. Adhikari, M. I. Friswell, and D. J. Inman. Piezoelectric energy harvesting from broadbandrandom vibrations. Smart Materials and Structures, 18(11):115005, 2009.

[2] J. Bobyn, R. Pilliar, H. Cameron, and G. Weatherly. The optimum pore size for the fixationof porous-surfaced metal implants by the ingrowth of bone. Clinical orthopaedics and relatedresearch, 150:263–270, 1980.

[3] C. R. Bowen, A. Perry, A. C. F. Lewis, and H. Kara. Processing and properties of porouspiezoelectric materials with high hydrostatic figures of merit. Journal of the EuropeanCeramic Society, 24(2):541–545, 2004.

[4] L. T. Canham. Silicon quantum wire array fabrication by electrochemical and chemicaldissolution of wafers. Applied Physics Letters, 57(10):1046–1048, 1990.

[5] M. L. Dunn and M. Taya. Electromechanical properties of porous piezoelectric ceramics.Journal of the American Ceramic Society, 76(7):1697–1706, 1993.

[6] J. D. Eshelby. The determination of the elastic field of an ellipsoidal inclusion, and relatedproblems. In Proceedings of the Royal Society of London A: Mathematical, Physical andEngineering Sciences, volume 241, pages 376–396. The Royal Society, 1957.

[7] M. I. Friswell, S. F. Ali, O. Bilgen, S. Adhikari, A. W. Lees, and G. Litak. Non-linearpiezoelectric vibration energy harvesting from a vertical cantilever beam with tip mass.Journal of Intelligent Material Systems and Structures, 23(13):1505–1521, 2012.

[8] P. Goransson. Tailored acoustic and vibrational damping in porous solids–engineering per-formance in aerospace applications. Aerospace Science and Technology, 12(1):26–41, 2008.

[9] S. Iyer and T. Venkatesh. Electromechanical response of (3-0) porous piezoelectric materials:Effects of porosity shape. Journal of Applied Physics, 110(3):034109, 2011.

[10] A. Kelly. Why engineer porous materials? Philosophical Transactions of the Royal Societyof London A: Mathematical, Physical and Engineering Sciences, 364(1838):5–14, 2006.

[11] G. Martinez-Ayuso, M. I. Friswell, S. Adhikari, H. H. Khodaparast, and H. Berger. Homog-enization of porous piezoelectric materials. International Journal of Solids and Structures,2017.

[12] G. Martinez-Ayuso, M. I. Friswell, S. Adhikari, H. H. Khodaparast, and C. A. Featherston.Porous piezoelectric materials for energy harvesting. In International Conference on Noiseand Vibration Engineering, 2016.

[13] Y. Mikata. Determination of piezoelectric eshelby tensor in transversely isotropic piezo-electric solids. International Journal of Engineering Science, 38(6):605–641, 2000.

[14] T. Miyoshi, M. Itoh, S. Akiyama, and A. Kitahara. Alporas aluminum foam: productionprocess, properties, and applications. Advanced engineering materials, 2(4):179–183, 2000.

11

640


[15] T. Mori and K. Tanaka. Average stress in matrix and average elastic energy of materialswith misfitting inclusions. Acta Metallurgica, 21(5):571–574, 1973.

[16] O. Pierard, C. Friebel, and I. Doghri. Mean-field homogenization of multi-phase thermo-elastic composites: a general framework and its validation. Composites Science and Tech-nology, 64(10):1587–1603, 2004.

[17] J. I. Roscow, J. Taylor, and C. R. Bowen. Manufacture and characterization of porousferroelectrics for piezoelectric energy harvesting applications. Ferroelectrics, 498(1):40–46,2016.

[18] J. I. Roscow, V. Y. Topolov, C. R. Bowen, J. Taylor, and A. E. Panich. Understanding thepeculiarities of the piezoelectric effect in macro-porous batio3. Science and Technology ofadvanced MaTerialS, 17(1):769–776, 2016.

[19] J. S. Seo, D. Whang, H. Lee, S. Im Jun, J. Oh, Y. J. Jeon, and K. Kim. A homochi-ral metal–organic porous material for enantioselective separation and catalysis. Nature,404(6781):982–986, 2000.

[20] J. She, J. Yang, and T. Ohji. Thermal shock resistance of porous silicon nitride ceramics.Journal of materials science letters, 22(5):331–333, 2003.

[21] H. A. Sodano, D. J. Inman, and G. Park. A review of power harvesting from vibrationusing piezoelectric materials. Shock and Vibration Digest, 36(3):197–206, 2004.

[22] W. Staszewski, C. Boller, and G. R. Tomlinson. Health monitoring of aerospace structures:smart sensor technologies and signal processing. John Wiley & Sons, 2004.

[23] R. J. White, R. Luque, V. L. Budarin, J. H. Clark, and D. J. Macquarrie. Supported metalnanoparticles on porous materials. methods and applications. Chemical Society Reviews,38(2):481–494, 2009.

[24] T. T. Wu. The effect of inclusion shape on the elastic moduli of a two-phase material.International Journal of Solids and Structures, 2(1):1–8, 1966.

[25] Y. Zhang, Y. Bao, D. Zhang, and C. R. Bowen. Porous pzt ceramics with aligned porechannels for energy harvesting applications. Journal of the American Ceramic Society,98(10):2980–2983, 2015.

[26] Y. Zhang, L. Chen, J. Zeng, K. Zhou, and D. Zhang. Aligned porous barium ti-tanate/hydroxyapatite composites with high piezoelectric coefficients for bone tissue en-gineering. Materials Science and Engineering: C, 39:143–149, 2014.

12

641

Documents

EXPERIMENTAL VALIDATION OF A POROUS PIEZOELECTRIC …michael.friswell.com/PDF_Files/C414.pdf · Department of Mechanical Engineering Claverton Down, Bath, BA2 7AY, UK Key words: Energy