Preloaded freeplay wide-bandwidth low-frequency piezoelectric harvestersN. Sharpes, A. Abdelkefi, M. R. Hajj, J. Heo, K.-H. Cho, and S. Priya Citation: Applied Physics Letters 107, 023902 (2015); doi: 10.1063/1.4926911 View online: http://dx.doi.org/10.1063/1.4926911 View Table of Contents: http://scitation.aip.org/content/aip/journal/apl/107/2?ver=pdfcov Published by the AIP Publishing Articles you may be interested in Low-frequency and wideband vibration energy harvester with flexible frame and interdigital structure AIP Advances 5, 047151 (2015); 10.1063/1.4919711 An innovative tri-directional broadband piezoelectric energy harvester Appl. Phys. Lett. 103, 203901 (2013); 10.1063/1.4830371 Frequency up-converted wide bandwidth piezoelectric energy harvester using mechanical impact J. Appl. Phys. 114, 044902 (2013); 10.1063/1.4816249 Enhanced broadband piezoelectric energy harvesting using rotatable magnets Appl. Phys. Lett. 102, 173901 (2013); 10.1063/1.4803445 Nonlinear output properties of cantilever driving low frequency piezoelectric energy harvester Appl. Phys. Lett. 101, 223503 (2012); 10.1063/1.4768219

This article is copyrighted as indicated in the article. Reuse of AIP content is subject to the terms at: http://scitation.aip.org/termsconditions. Downloaded to IP:

198.82.31.252 On: Wed, 15 Jul 2015 15:02:40

Preloaded freeplay wide-bandwidth low-frequency piezoelectric harvesters

N. Sharpes,1,2 A. Abdelkefi,3 M. R. Hajj,1,4 J. Heo,5 K.-H. Cho,5 and S. Priya1,2,61Center for Energy Harvesting Materials and Systems (CEHMS), Virginia Tech, Blacksburg,Virginia 24061, USA2Department of Mechanical Engineering, Virginia Tech, Blacksburg, Virginia 24061, USA3Department of Mechanical and Aerospace Engineering, New Mexico State University, Las Cruces,New Mexico 88003, USA4Department of Engineering Science and Mechanics, Virginia Tech, Blacksburg, Virginia 24061, USA5Samsung Advanced Institute of Technology, SAMSUNG ELECTRONICS CO., LTD., Yokohama 230-0027, Japan6Bio-Inspired Materials and Devices Laboratory (BMDL), Virginia Tech, Blacksburg, Virginia 24061, USA

(Received 22 May 2015; accepted 6 July 2015; published online 15 July 2015)

We propose a technique for increasing the bandwidth of resonant low-frequency (<100Hz) piezo-

electric energy harvesters based on the modification of the clamped boundary condition of cantile-

vers, termed here as preloaded freeplay boundary condition. The effects of the preloaded freeplay

boundary condition are quantified in terms of the fundamental frequency, frequency response, and

power output for two beam configurations, namely, classical cantilevered bimorph piezoelectric

energy harvester and zigzag unimorph piezoelectric energy harvester. A comparative analysis was

performed between both the harvesters to empirically establish the advantages of the preloaded

freeplay boundary condition. Using this approach, we demonstrate that the coupled degree-of-free-

dom dynamics results in an approximate 4–7 times increase in half-power bandwidth over the fixed

boundary condition case.VC 2015 AIP Publishing LLC. [http://dx.doi.org/10.1063/1.4926911]

Low frequency excitation sources, such as automobiles,

the human body, industrial machines, electronic devices, and

domestic appliances, are sources of mechanical energy in the

form of vibrations, that can be scavenged to power or recharge

the low power devices such as cell phones, MEMS compo-

nents,1,2 pacemakers,3 cameras,4 and wireless sensors and

actuators.5,6 The demand for energy harvesters for battery

charging or replacement exists in scenarios where mainte-

nance is expensive and time consuming.7,8 Wasted mechani-

cal energy can be converted into usable electrical energy

through transduction mechanisms, such as electromagnetic,9

electrostatic,10 or piezoelectric.11–13 It has been shown by

Marin et al. that the piezoelectric transduction becomes rele-

vant at the smaller size scales in the vicinity of 1 cm3.14

A significant impediment in the deployment of vibration-

based piezoelectric energy harvesting devices has been the limi-

tation that most of the low frequency transducers, usually in the

form of unimorph or bimorph cantilever beams, extract energy

in a very narrow bandwidth around the transducer’s fundamental

frequency. In such devices, slight deviation from the fundamen-

tal frequency causes a significant reduction in the level of har-

vested power, in some cases by orders of magnitudes. Because

the ambient energy sources can include multiple and time vary-

ing frequencies, this impediment has directed the research in

designing structures whose resonant frequency can be actively

modulated to match the frequency of ambient vibrations.

Recent strategies for conforming the frequency response

of an energy harvester to its vibration source are based on

exploiting nonlinearities through harvester geometry, boundary

and loading conditions to tune the resonance frequency and

broaden the bandwidth. Ben Ayed et al. modeled the frequency

response and power output of linear and quadratic geometri-

cally tapered piezoelectric cantilevers.15 Masana and Daqaq

characterized the effect of axial loading of the natural fre-

quency of pre-critical buckling load beams.16 A study by

Challa et al. determined the response of a cantilever beam with

permanent magnet tip mass, to attractive and repulsive forces

from external magnets by varying proximity to the beam.17 In

a work by Mann and Sims, a low frequency system was

designed using two fixed magnets to levitate a center oscillat-

ing magnet.18 In investigations by Shahruz19 and Sari et al.,20

wide bandwidth response was achieved by creating arrays of

geometrically varying cantilevers. Tang et al. as well as

Twiefel and Westermann have compiled reviews of other nota-

ble broadband vibration energy harvesting techniques.21,22

In order to design the low-frequency and broadband

energy harvesters, we propose a drastically different

approach. This approach was established by inducing a sec-

ond degree-of-freedom (termed here as preloaded freeplay),

which has a resonant frequency near the natural frequency of

the harvester, the interaction between which creates a

broader resonant plateau rather than a sharp peak. In order to

verify this approach, we implemented the concept on two

different structures. First, we designed a unimorph zigzag

piezoelectric energy harvester (PEH) that consisted of steel

substrate and piezoelectric layer. Second, a conventional

bimorph cantilever energy harvester consisting of aluminum

and piezoelectric layers was utilized. These harvesters were

subjected to direct vibration excitations and measurements

were performed to determine the effects of the tip mass and

electrical load resistance on the performance of these har-

vesters with and without the preloaded freeplay effects.

Generally, a PEH is affixed to a vibration source either

by a clamp, where it can be considered rigidly connected, or

otherwise bounded where it is said to have a freeplay nonli-

nearity. The characterization of freeplay has been studied in

the context of aeroelastic vibrations, where it is considered a

negative effect, since it can create instabilities and make it dif-

ficult to control aircraft.23 However, in this paper, we propose

to utilize freeplay as a positive effect in energy harvesting.

0003-6951/2015/107(2)/023902/5/$30.00 VC 2015 AIP Publishing LLC107, 023902-1

APPLIED PHYSICS LETTERS 107, 023902 (2015)

This article is copyrighted as indicated in the article. Reuse of AIP content is subject to the terms at: http://scitation.aip.org/termsconditions. Downloaded to IP:

198.82.31.252 On: Wed, 15 Jul 2015 15:02:40

We start by proposing a clamp which is connected to the

vibration source (shaker) by a screw with threads that are

slightly mismatched with those on the shaker adapter.

Through this modification, the screw is still able to be tight-

ened and secure the clamp to the shaker as shown in Figure

1(a). However, there is a larger than normal air gap between

the external threads of the clamp screw and internal threads

of the shaker adapter as shown in Figure 1(b). The preloaded

(tightened) screw with the clamp acts as a spring-mass sys-

tem as shown in Figure 1(c). When this spring-mass system

resonates, there is enough force to overcome the applied

force due to the preload condition. This phenomenon causes

a freeplay to occur between the clamp-screw and shaker

adapter, creating a second degree-of-freedom. Therefore,

there is a degree-of-freedom caused by the stiffness of the

PEH (kbeam) and another degree-of-freedom between the

clamp and the vibration source (kscrew). It is important to

note that this freeplay condition and subsequent second

degree-of-freedom only exist in the frequency band where

the clamp-screw system resonates and at all other times it

can be considered as a single degree-of-freedom system. By

tuning the natural frequency of the clamp-screw system near

the natural frequency of the PEH system, a broadband fre-

quency response is created. Hence, the electrical perform-

ance of the device was maintained at the optimum level

across a larger range of frequencies. We will demonstrate

this principle on two different structures and use the results

to discuss the physical basis behind the enhancement.

The effect of the proposed preloaded freeplay boundary

condition on energy harvesting capabilities was investigated for

one-dimensional (1D) cantilever (Figure 2(a)) and two-

dimensional (2D) zigzag (Figure 2(c)) PEHs. These two struc-

tures were chosen, as it has been shown that 1D and 2D beam

shapes can have advantages over one another in certain situa-

tions, and we sought to examine the different effects, if any,

freeplay would have on these PEH beam shapes.24,25 The

dimensions were chosen for each design, as shown in the sche-

matics in Figures 2(a) and 2(c), such that the zigzag would have

25.4mm � 25.4mm in cross-sectional area and the cantilever

will also have same surface area. In this way, we can perform

comparative analysis independent of the area of the harvester.

The piezoelectric material and the base excitation (0.1G) were

kept at the same level in all cases to allow for the reasonable

comparisons to be made between the power outputs of the two

harvester structures. The properties of the piezoelectric material,

Lead zirconate titanate (PZT), are listed in Table I. Details on

the experimental characterization system are provided in the

supplementary material.26

We start our analysis by comparing the deflections of the

two configurations. Deflection of the beam tips was measured

at their respective first resonant frequencies by integrating

laser vibrometer data with respect to time. A detailed descrip-

tion of experimental procedure and equipment information is

provided in the supplementary material.26 It was found that

the tip deflections of the two configurations were quite similar,

with the cantilever and zigzag piezoelectric energy harvesters

having maximum deflections of approximately 66 lm and 57

lm, respectively, at 0.1G base acceleration and 0 g tip mass.

Next, tip masses of 0 g, 0.47 g, 0.94 g, 1.42 g, and 1.88 g were

employed to examine their influence on the frequency

response. We observed that for both systems increasing the tip

mass results in a decrease in natural frequency and increase in

the amplitude of vibration. Figure 3(a) shows the variation of

the fundamental frequency as a function of the tip mass.

Clearly, for all tip mass cases, it can be noted that the zigzag

harvester has the lower fundamental frequency. The differ-

ence between the two systems is exceedingly evident at 0 g tip

mass, where the harvester’s shape was mostly responsible for

its frequency response characteristics. The natural frequency

of the clamp-screw, designated as the spring frequency, is not

a function of the tip mass. For each tip mass case, a frequency

FIG. 1. Representations of the preloaded freeplay phenomenon: (a) a physical representation of the piezoelectric energy harvester (PEH), clamp, and shaker

system, in which the clamp and shaker are held together by (b) a preloaded (tightened) screw with slightly mismatched threads allowing a larger than normal

air gap between threads. When the excitation frequency is at the fundamental frequency of the clamp-screw system, (c) the response is enough to overcome the

preload force and induce a second degree-of-freedom, with one degree due to the stiffness of the PEH (kbeam) and one due to the proposed preloaded freeplay

(kscrew). (Multimedia view) [URL: http://dx.doi.org/10.1063/1.4926911.1].

FIG. 2. Schematic (dimensions in millimeters) and constructed prototypes

mounted in a test clamp attached to shaker, for cantilever (a) and (b), and

zigzag in (c) and (d). Note that both the configurations have a surface area of

approximately 645mm2.

TABLE I. List of piezoelectric material properties.

Supplier American piezoceramics

Material APC 850 (PZT)

�d31 (pC/N) 175

�g31 (mV m/N) 12.4

023902-2 Sharpes et al. Appl. Phys. Lett. 107, 023902 (2015)

This article is copyrighted as indicated in the article. Reuse of AIP content is subject to the terms at: http://scitation.aip.org/termsconditions. Downloaded to IP:

198.82.31.252 On: Wed, 15 Jul 2015 15:02:40

response function was generated. As Figures 3(b) and 3(c)

show, whenever the natural frequency of the PEH is near the

spring frequency, a broadband effect was observed as the res-

onant peaks of the harvester and spring frequencies combined,

maintaining an elevated level of beam deflection across a

wider band of frequencies. It is important to note that for the

other cases, where the natural frequency of the PEH is tuned

to a frequency not near the spring frequency, the system

behaves as a simple single degree-of-freedom system.

After finding the frequency regions where the broadband

effect was observed, sweeps of frequency and electrical load

resistance were conducted to locate the maximum power

point. In Figure 4, it can be seen that the regions where the

beam dynamics are broadband (Figure 3) are also resulting

in a larger frequency region whereby power output was

maintained at a high level (dashed lines), as compared to a

fix boundary condition single degree-of-freedom system

(solid lines). What is interesting is that for the normal case,

the average power output has a higher peak than the spring

case for the range of 55.2Hz and 56.2Hz (around 1Hz

difference). On the other hand, we note that including the

spring effect is very beneficial for all frequencies outside the

resonant range (55.2Hz–56.2Hz). In the approximate range

of frequencies between 54Hz and 58Hz, a broadband

response of the harvester takes place. In fact, any variation

in this range yields almost the same level of average har-

vested power. This result is the same for all electrical load

resistances.

Similar to the zigzag geometry, for the normal case of

the cantilever piezoelectric energy harvester, the average

power output has a higher peak than the spring case. On the

other hand, we note that including the spring effect is benefi-

cial only for certain frequencies outside the resonant range.

In the range of frequencies between 64Hz and 71Hz, a

broadband response of the harvester takes place. Unlike the

zigzag energy harvester, the classical cantilever beam case is

better than the two degree-of-freedom (“Spring”) case when

the excitation frequency is larger than 66.5Hz. For lower

values of excitation frequency, maximum harvested power is

obtained when including the spring effect.

FIG. 4. Power output as a function of frequency and electrical load resistance in the broadband interaction range for cantilever (a) and zigzag (b) systems, with

the solid lines with filled points corresponding to the “normal” (clamped) boundary condition and the dashed lines with non-filled points corresponding to the

“spring” (preloaded freeplay) boundary condition.

FIG. 3. Dynamics of systems subjected to preloaded freeplay effects. (a) Dependency of “Spring” (preloaded freeplay) frequency, cantilever and zigzag natural

frequencies on tip mass. Note the natural frequency of the PEHs is inversely proportional to the tip mass, while the spring frequency is largely independent of

the tip mass. Frequency response functions for cantilever (b) and zigzag (c) for each point in (a), measured in arbitrary decibel units, showing the induced

broadband effects due to the interaction of the two degrees of freedom as the fundamental frequency of the PEH approaches the spring frequency.

023902-3 Sharpes et al. Appl. Phys. Lett. 107, 023902 (2015)

This article is copyrighted as indicated in the article. Reuse of AIP content is subject to the terms at: http://scitation.aip.org/termsconditions. Downloaded to IP:

198.82.31.252 On: Wed, 15 Jul 2015 15:02:40

We can conclude that if the available excitation fre-

quency is in the resonant frequency range, the energy har-

vesters with fixed boundary condition are better than the

harvesters with preloaded freeplay boundary condition.

Outside the resonant range, including the spring effect

results in higher values of the power output, as shown in

Figures 5(c) and 5(d). The preloaded freeplay clamp spring

broadband effect was shown to be very beneficial for the

zigzag system but less effective for the cantilever bimorph

system because of the greater compliance of the zigzag

structure, making it more sensitive to the induced second

degree-of-freedom. This is evident in Figures 5(a) and 5(b)

where the increase in half-power bandwidth is larger for

the zigzag structure than the cantilever bimorph.

Additionally, from Figure 5, we can see that PEH half-

power bandwidth is largely unaffected by load resistance,

and power output displays the normal parabolic trend

(when plotted on log-log scale) with or without the pre-

loaded freeplay effect.

Tuning the frequency and amplitude at which the pre-

loaded freeplay phenomenon occurs is accomplished by con-

trolling the mass of the clamp and tightness of the connection

(preload). As Figure 6(a) demonstrates, adding mass to the

clamp both lowers the spring frequency and causes an increase

in amplitude. Here, the “Normal” case is taken to mean when

the freeplay effect is not introduced. The “Screw” case is when

the freeplay (spring) effect is introduced, and the

“ScrewþMass” case is adding approximately 35 g of addi-

tional mass to the 400 g clamp. In addition, tightening the con-

nection between the clamp and vibration source has little effect

on spring frequency (Figure 6(c)), but proves to reduce the am-

plitude of freeplay effect, as preload is increased. Here, “Snug”

refers to a preload whereby the clamp and vibration source are

securely connected, and “Fully Tightened” refers to a preload

whereby the screw cannot be tightened any further by hand

with a 5 cm hex wrench. Figures 6(b) and 6(d) show a qualita-

tive illustration of the effects seen in Figures 6(a) and 6(c),

respectively. The shaded regions below the “Preload Line” rep-

resent the area where the response of the clamp is not large

enough to overcome the preload of the tightened screw and the

system remains a single degree-of-freedom system. Above this

region, the response is large enough to overcome the preload

and induce a second degree-of-freedom. A combination of

adjustments in clamp mass and tightening of the clamp screw

FIG. 5. Half-power bandwidth

and power output at as function

of electrical load resistance for

cantilever (a) and (c), and zigzag

(b) and (d) systems.

0

FIG. 6. Effect of clamp mass (a) and screw tightness (c) on frequency and

amplitude of preloaded freeplay effect. Illustrations (b) and (d) offer a quali-

tative depiction of the effects seen in (a) and (c), respectively, and when one

degree-of-freedom (DOF) or two are present.

023902-4 Sharpes et al. Appl. Phys. Lett. 107, 023902 (2015)

This article is copyrighted as indicated in the article. Reuse of AIP content is subject to the terms at: http://scitation.aip.org/termsconditions. Downloaded to IP:

198.82.31.252 On: Wed, 15 Jul 2015 15:02:40

can move the effects of the freeplay condition to a frequency

range, which are near to the harvester dynamics. This tuning

capability is demonstrated for the 0.42 g tip mass case of the

zigzag harvester and 0.94 g tip mass case of the cantilever har-

vester, where the spring frequency was adjusted to approxi-

mately 65.5Hz and 57Hz, respectively, to broaden the existing

peaks of the harvester response.

In conclusion, a two degrees-of-freedom piezoelectric

energy harvester was proposed based on the modification of

the beam’s boundary conditions to be the described “preloaded

freeplay” condition, rather than fixed. The results showed that

tuned broadband energy harvesters can be designed using a

preloaded freeplay clamp spring for a spring-bending coupling

effect, combining the bandwidth of the two degrees-of-free-

dom. Depending on the available excitation frequency, the tip

mass and spring frequency can be designed to induce broad-

band effects. A comparative analysis was performed between

both cantilever bimorph and zigzag unimorph harvesters to

deterministically establish the advantages of the preloaded free-

play boundary condition. While both harvesters benefited, in

terms of broadband response, the effects of preloaded freeplay

were greater on the zigzag harvester due to it being more com-

pliant than the cantilever bimorph. Using this approach, we

have demonstrated that the coupled degree-of-freedom dynam-

ics results in an approximate 4–7 times increase in PEH half-

power bandwidth, over the fixed boundary condition case.

This increased frequency range comes with the compro-

mise of peak harvested power, as can be seen in Figure 4.

Indeed, no spectral energy (integrated area under the curves)

is gained via the preloaded approach. Rather, it is spread out

over a much larger range instead of concentrated in a narrow

band. Indeed, some energy is even lost through the freeplay.

Nevertheless, this technique is best suited for, and provides

advantages in, applications where excitation frequency is

broad, such as in impact/impulse loading (e.g., human gait

and heart beats) and noisy environments (e.g., structural

vibration), or where excitation frequency is time varying,

such as in rotating machinery which do not maintain a con-

stant operating rotation speed.

This research was supported through the Samsung Global

Research Program. The author, S.P., would like to acknowledge

the financial support from Office of Naval Research through

Center for Energy HarvestingMaterials and Systems.

1P. Muralt, “Ferroelectric thin films for micro-sensors and actuators: A

review,” J. Micromech. Microeng. 10, 136–146 (2000).2W. Zhou, W. H. Liao, and W. J. Li, “Analysis design of a self-powered

piezoelectric microaccelerometer,” Proc. SPIE 5763, 233–240 (2005).3A. Karami and D. J. Inman, “Powering pacemakers from heartbeat vibra-

tions using linear and nonlinear energy harvesters,” Appl. Phys. Lett. 100,

042901 (2012).

4A. Abdelkefi and M. Ghommem, “Piezoelectric energy harvesting from

morphing wing motions for micro air vehicles,” Theor. Appl. Mech. Lett.

3, 052001 (2013).5S. Roundy and P. K. Wright, “A piezoelectric vibration-based generator

for wireless electronics,” Smart Mater. Struct. 13, 1131 (2004).6D. J. Inman and B. L. Grisso, “Towards autonomous sensing,” Proc. SPIE

6174, 61740T (2006).7K. A. Cook-Chennault, N. Thambi, and A. M. Sastry, “Powering MEMS

portable devices—A review of nonregenerative and regenerative power

supply systems with emphasis on piezoelectric energy harvesting sys-

tems,” Smart Mater. Struct. 17, 043001 (2008).8S. Priya, “Advances in energy harvesting using low profile piezoelectric

transducers,” J. Electroceram. 19, 165–182 (2007).9N. N. H. Ching, H. Y. Wong, W. J. Li, P. H. W. Leong, and Z. Wen, “A

laser micromachined multi-modal resonating power transducer for wire-

less sensing systems sensors and actuators,” Sens. Actuators, A 97–98,

685–690 (2002).10T. Sterken, P. Fiorini, K. Baert, R. Puers, and G. Borghs, “An electret-

based electrostatic l-generator,” in 12th International Conference on Solid

State Sensors, Actuators and Microsystems TRANDSUCERS ’03 (2003),

pp. 1291–1294.11H. Sodano, G. Park, and D. J. Inman, “A review of power harvesting from

vibration using piezoelectric materials,” Shock Vib. Dig. 36, 197–205 (2004).12S. R. Anton and H. A. Sodano, “A review of power harvesting using

piezoelectric materials (2003–2006),” Smart Mater. Struct. 16, 1–21

(2007).13A. Abdelkefi, “Global nonlinear analysis of piezoelectric energy harvest-

ing from ambient and aeroelastic vibrations,” Ph.D. dissertation (Virginia

Polytechnic Institute and State University, Blacksburg, VA, 2012).14A. Marin, S. Bressers, and S. Priya, “Multiple cell configuration electro-

magnetic vibration energy harvester,” J. Appl. Phys. 44, 295501 (2011).15S. Ben Ayed, A. Abdelkefi, F. Najar, and M. R. Hajj, “Design and per-

formance of variable-shaped piezoelectric energy harvesters,” J. Intell.

Mater. Syst. Struct. 25, 174–186 (2014).16R. Masana and M. F. Daqaq, “Electromechanical modeling and nonlinear anal-

ysis of axially loaded energy harvesters,” J. Vib. Acoust. 133, 011007 (2011).17V. R. Challa, M. G. Prasad, Y. Shi, and F. T. Fisher, “A vibration energy

harvesting device with bidirectional resonance frequency tunability,”

Smart Mater. Struct. 75, 1–10 (2008).18B. P. Mann and N. D. Sims, “Energy harvesting from the nonlinear oscilla-

tions of magnetic levitation,” J. Sound Vib. 319, 515–530 (2009).19S. M. Shahruz, “Limits of performance of mechanical band-pass filters

used in energy scavenging,” J. Sound Vib. 293, 449–461 (2006).20I. Sari, T. Balkan, and H. Kulah, “An electromagnetic micro power gener-

ator for wideband environmental vibrations,” Sens. Actuators, A 145–146,

405–413 (2008).21L. Tang, Y. Yang, and C. K. Soh, “Toward broadband vibration-based

energy harvesting,” J. Intell. Mater. Syst. Struct. 21, 1867–1897 (2010).22J. Twiefel and H. Westermann, “Survey on broadband techniques for vibra-

tion energy harvesting,” J. Intell. Mater. Syst. Struct. 24, 1291–1302 (2013).23A. Abdelkefi, R. Vasconcellos, F. D. Marques, and M. R. Hajj, “Modeling

and identification of freeplay nonlinearity,” J. Sound Vib. 331(8),

1898–1907 (2012).24N. Sharpes, A. Abdelkefi, and S. Priya, “Comparative analysis of one-

dimensional and two-dimensional cantilever piezoelectric energy harvest-

ers,” Energy Harvesting Syst. 1(3–4), 209–216 (2014).25D. J. Apo, M. Sanghadasa, and S. Priya, “Vibration modeling of arc-based

cantilevers for energy harvesting applications,” Energy Harvesting Syst.

1(1–2), 57–68 (2014).26See supplementary material at http://dx.doi.org/10.1063/1.4926911 for

details about experimental setup, test specimen fabrication, and deflection

analysis.

023902-5 Sharpes et al. Appl. Phys. Lett. 107, 023902 (2015)

This article is copyrighted as indicated in the article. Reuse of AIP content is subject to the terms at: http://scitation.aip.org/termsconditions. Downloaded to IP:

198.82.31.252 On: Wed, 15 Jul 2015 15:02:40