This document summarizes research conducted on experimental analysis of a piezoelectric energy harvesting system under various vibration conditions. The research aims to show that accurate experimental testing is essential for harvester development by determining the implications of complex vibration characteristics on harvester performance. The research tests a commercially available piezoelectric transducer and conditioning circuit under harmonic, random, and sine on random vibration scenarios. The results show that theoretical power harvesting predictions require simplifying assumptions about input vibration and transducer characteristics that do not apply to real-world conditions. Testing more complex vibration profiles provides a more accurate representation of ambient vibrations and is valuable for harvester development.

1. Experimental analysis of a piezoelectric
energy harvesting system for
harmonic, random, and sine on random
vibration
JACKSON W. CRYNS
B.S. Applied Mathematics, Engineering and Physics
University of Wisconsin - Madison
Research conducted under Brian K. Hatchell (PNNL) in fulfillment of DOE Office of Science, Science
Undergraduate Laboratory Internship (SULI) and to support projects contracted by the U.S. Army
Sigma Xi - Student Research Showcase 2013
March, 2013 Sigma Xi - Student Resarch Showcase 1

2. Abstract
Advancements in low power electronics in the past decade allow systems to run off of
progressively less energy and even eliminate the need for external power supplies
completely. The key to self-sustaining electronics is the ability to harness energy from
the surrounding environment and turn it into usable electrical energy, or Energy
Harvesting. In many industrial applications, ambient energy is readily available in the
form of mechanical vibrations. Piezoelectric ceramics provide a compact, energy dense
means of transducing mechanical vibrations of the environment to electrical power.
Harvesting power with a commercially available piezoelectric vibration powered
generator using a full-wave rectifier conditioning circuit is experimentally compared for
varying sinusoidal, random and sine on random (SOR) input vibration scenarios. Much
of the available literature focuses on maximizing harvested power through theoretical
predictions and power processing circuits that require accurate knowledge of generator
internal electromechanical characteristics and idealization of input vibration, which
cannot be assumed in general application. Characteristics of complex vibration sources
significantly alter power generation and processing requirements, likely rendering
idealized analysis inaccurate. Going beyond idealized steady state sinusoidal and
simplified random vibration input, SOR testing allows for more accurate representation
of real world ambient vibration and is an invaluable tool in harvester development.
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3. Background
What is Energy Harvesting?
Application Goals
Vibration Powered Generators (Transducers)
Piezoelectric Effect
Power Conditioning
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4. What is Energy Harvesting?
• Every process dissipates waste energy to the surrounding environment
• Ambient energy comes in many usable forms
[5]
Electromagnetic Radiation (1) Thermal Gradient (2) Potential Energy Forms (3) Vibration (Potential + Kinetic) (4)
• Convert ambient energy to usable electrical energy – transducers
• Small amounts of power – mW or µW (milli-Watts or micro-Watts) [3]
(5) (6) (7) (8)
• Not a new idea!
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5. Application Goals
Supply power to off grid devices
Remote equipment
Monitors in hazardous environments (9)
Wireless data logging and transmission
Reduce maintenance requirements and costs
Relieve dependence on primary batteries
(10)
Fits into national “green” initiatives
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6. Vibration Powered Generators (Transducers)
Machines, moving parts and large power generators present
significant vibration energy [2, 3, 8]
Three transduction mechanisms [1, 8, 10]:
Electrostatic – parallel plate capacitor
Electromagnetic – magnetic induction
Piezoelectric – piezoelectric effect
Numerous studies have been conducted on power transduction [15,3,9]
(11) (12) (13)
Driving and Biking Walking Numerical and Theoretical Simulations
Piezoelectric transducers are the most energy dense [8,12]
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7. Piezoelectric Effect
Electric charge accumulates in certain materials in response to
applied mechanical stress [11]
(14) (15)
This study analyzes a commercially available bimorph transducer
Two piezoelectric layers
Two electrical signals of opposite sines
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8. Power Conditioning
Conditioning circuitry – the components necessary to supply power
from the transducer to the target electronics with specified current and
voltage characteristics
(16)
Example conditioning circuit
This study includes the target electronics in the conditioning circuit
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9. Research Overview
Research Goals {10}
Energy Harvesting Architecture {11 – 18 }
Literature Review and Harvester Validation {19 – 36}
Expanded Vibration Testing {37 – 46}
Discussion and Design Implications {47 – 50}
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10. Research Goals
Convince the reader that accurate experimental testing is an
invaluable and essential tool in harvester development
Determine implications of complex vibration characteristics on
harvester performance
Show that theoretical power harvesting predictions and numerical
simulations require assumptions that cannot be made in general
application:
Oversimplifying assumptions of input vibration
Exact knowledge of transducer internal electrical and mechanical
characteristics
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11. Energy Harvesting
Architecture
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12. Energy Harvesting Architecture
Piezoelectric transducer
V25w QuickPack® actuator
produced by Midé [24,25]
AC signal
Proof mass
(for frequency tuning)
Rigid clamp
(fixed-free cantilever beam)
Vibration Source Exact transducer internal electrical and
mechanical characteristics unknown
LDS V721 – 1000 L shaker
Closed loop vibration control
[17]
Power conditioning circuitry
Standard circuit
March, 2013 12

13. Energy Harvesting Architecture
Piezoelectric Transducer Set-Up
Mount in cantilever configuration
Input vibration at base
Natural frequency
[18]
Tune with proof mass to match source vibration
Modal analysis allows for accurate natural frequency determination
Bare natural frequency of 124.5 Hz
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14. Energy Harvesting Architecture
Power Conditioning Duties
AC-DC conversion [19]
Transducer creates AC signal (oscillatory)
Most microelectronics require DC
Full-wave bridge rectifier
Signal smoothing
A time varying signal is damaging
to DC electronics
[20]
Provide power to load
Microelectronics
Resistor
Secondary (rechargeable) battery
http://www.electronics-tutorials.ws/diode/diode_6.html
http://www.eleinmec.com/article.asp?18
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15. Energy Harvesting Architecture
Power Conditioning Circuitry [3,7,14-16,26]
Standard (linear) Interface
Target electronics (load) modeled represented by resistor
Net transfer of energy through transient components is null, thus equivalent
resistance is sufficient
Capacitance is constant, locate optimal impedance by varying resistance
CR = 600 µF, RL -> variable.
Non-linear processing not considered in this study
Designed for steady sinusoidal vibration only
Dissipates extra power
Application specific designs require additional voltage control
Additional control circuitry always dissipates extra power
Circuit used here finds the maximum available power for harvesting
(except for loses in rectifier bridge and capacitor leakage)
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16. Energy Harvesting Architecture
Test multiple scenarios Impedance head
Harmonic, Random – simplified
SOR – sine and random
superposition for accurate testing
Characterize and control the input
vibration by acceleration
Acceleration response is the most Shaker armature
common form of vibration
measurement and characterization
Allows for subsequent validation in
other experiments
Method assumes harvester does
not alter input dynamics (source is
much larger than harvester) [31]
Monitor force and acceleration with
PCB impedance head 288D01
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17. Energy Harvesting Architecture
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18. Energy Harvesting Architecture
Fundamental Objective:
How does power harvesting vary with input acceleration
characteristics, transducer natural frequency, and load resistance?
Measure voltage and current delivered to load to find harvested power
Measure input acceleration and force to find input power, when needed
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19. Literature Review and
Harvester Validation
General
Sinusoidal input vibration*
Flat random vibration*
*Analytical relations for purely sinusoidal and flat broadband vibration have been developed in other
works for custom developed harvesters and simulations [6, 9 ,18-20]
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20. Literature Review and Harvester Validation
Properly developed harvesters can harvest tens to hundreds of mW of
power [1, 3, 6-9]
Vibration Energy Harvesters (VEH) require careful development for
effective power conversion
Characterization of ambient source vibration
Tuning of transducer to achieve resonance
Determination of optimal impedance
Harvesting electrical power induces mechanical damping and alters
the transducer vibration dynamics, creating an electromechanical
system [9]
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21. Literature Review and Harvester Validation
Conditioning circuitry designs can range from a few analog
components to complex architectures controlled by firmware [3,7,14-
16,26]
Non-linear power processing has been shown to significantly increase
harvested power over passive (standard) power processing
Synchronized Charge Extraction (SEC)
Synchronized Switch Harvesting with Inductor (SSHI)
Additional control circuitry dissipates extra power, reducing efficiency
[21]
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22. Literature Review and Harvester Validation
Previous research heavily focused on two idealized vibration cases:
steady state sinusoidal vibration sources and flat, broadband
random profiles [1, 6, 7, 9, 12, 13, 16, 17]
Analysis and modeling are simplified in these cases
Non-linear SSHI requires steady state sinusoidal
Non-linear SEC performance drops in non-sinusoidal vibration
environments
Many studies omit inclusion of the significant power loss from additional
control circuitry that can be on the order of hundred of μW []
No studies addressed voltage fluctuations induced by random vibration
[22] [23]
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23. Literature Review and Harvester Validation
Few studies incorporated more complex vibrational sources [2,18]
Sinusoidal and flat random vibration inputs are scarce in application
Real ambient conditions can be accurately modeled by incorporating both
random and sinusoidal content
Acceleration Spectral Density of a
typical Apache Helicopter flight is
significantly more complex than
sinusoidal or flat random vibration
• Peaks are accounted for by
sinusoidal components superposed
on top of a random profile
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24. Literature Review and Harvester Validation
Experimental Sinusoidal Input Validation
Unless otherwise stated, harvester is driven at the transducer natural
frequency
Sinusoidal vibrations are characterized by driving frequency and
amplitude
“Amplitude” refers to acceleration amplitude, zero to peak
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25. Literature Review and Harvester Validation
Sinusoidal – Amplitude variation
Theoretical Expectations:
Displacement and voltage scale linearly with input amplitude
Power scales quadratically with voltage and thus amplitude
Quadratic trend is clearly exhibited
at two natural frequencies.
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26. Literature Review and Harvester Validation
For identical input amplitudes:
lower natural frequencies harvest
more power. *
* Consequence of input power variations
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27. Literature Review and Harvester Validation
Sinusoidal – Impedance Variation
Theoretical Expectations:
Resistance (impedance) effects harvested power
Optimal resistance varies with natural frequency
Optimal resistance is around 40 kΩ and 15 kΩ for 58.3Hz and 124.5 Hz respectively
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28. Literature Review and Harvester Validation
Sinusoidal – Impedance Variation (cont’d)
As natural frequency
increases, optimal impedance
decreases and peak narrows
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29. Literature Review and Harvester Validation
Sinusoidal –Frequency Response Function (FRF) for power
Theoretical expectations:
All mechanical vibratory systems have a frequency dependent transfer
function
Deviating from natural frequency lowers the resulting transducer dynamic
amplitudes and thus harvested power
Harvested power drops by
approximately 50% within 1 Hz deviation
from natural frequency, reinforcing the
importance of accurate tuning of
transducer
Implies that there is an approximate
non-negligible transducer bandwidth of
+/- 3 Hz in which power is generated
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30. Literature Review and Harvester Validation
Experimental Random Input Validation
The terms broadband and random vibration are often used
interchangeably, but random vibrations need not be broad in general
Power is averaged of 100s samples to increase repeatability
Random vibrations vary statistically in time [18]
Random vibrations are characterized by Power Spectral Density
(PSD), or acceleration spectral density, profile in units of [g2/Hz]
Integrating the PSD over a frequency range and taking the square root
results in the Root Mean Square (RMS) level of vibration in g’s for that
filtered frequency range
“Amplitude” refers to spectral density near the transducer natural
frequency
It is shown later that spectral densities far from the resonant frequency
negligibly influence the harvester
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31. Literature Review and Harvester Validation
Random – Amplitude Variation
Theoretical Expectations:
Power scales linearly with spectral density
Power scales inversely with natural frequency, as with sinusoidal
As derived in [18], harvested power
varies linearly with spectral density
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32. Literature Review and Harvester Validation
Random – Impedance Variation
Theoretical Expectations:
Random vibration has higher optimal resistance than sinusoidal vibration
Optimal impedance scales inversely with natural frequency
Optimal resistance is higher for
random vibration than
sinusoidal vibration for both
frequencies, and decreases
with natural frequency for
each vibration type
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33. Literature Review and Harvester Validation
Random – Bandwidth Variation
Theoretical Expectations:
Power is independent of input bandwidth when significantly longer than
that of transducer
Unspecified results for short bandwidths or varying spectral density profile
shapes
Except for random statistical
deviations from one point the
next, average harvested power
is constant over all bandwidths
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34. Literature Review and Harvester Validation
Random – Frequency Variation
Theoretical Expectations:
Harvested power is inversely proportional to transducer natural frequency
For identical input amplitudes and
bandwidths, higher natural frequencies produced
less power
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35. Literature Review and Harvester Validation
Harvester met and agreed with theoretical predictions for special cases
Steady state sinusoidal vibration
Flat broadband vibration
Limitations of idealized studies
Real sources commonly consist of numerous sinusoidal peaks, complex
random profiles, nonlinear and transient interactions
No found studies incorporated non-flat random profiles
No found studies incorporated multiple sinusoidal components
No found studies incorporated interactions of both sinusoidal and random
content
No found studies addressed time variations in random vibrations
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36. Expanded Vibration Testing
Short bandwidth and non-flat random profiles
Sinusoidal and random component interaction
Multiple sinusoidal component interaction
March, 2013 Sigma Xi - Student Resarch Showcase 36

37. Expanded Vibration Testing
Random – Short Bandwidth Variation
Test varying bandwidths with identical gRMS values
Each random profile in the left plot has a 0.1414 gRMS acceleration level
(note that 50 Hz and 500 Hz expand beyond plot window)
Each scenario was supplied to the bare transducer to produce right plot
The harvester gets progressively worse at harvesting power as bandwidth increases, for
identical input power and gRMS levels.

38. Expanded Vibration Testing
Random – Non-Flat profile
Test impact of spectral density profile variations
Varying shape outside the transducer natural frequency
Identical in the bandwidth of the transducer (124.5 Hz 3 Hz)
Three profiles produced nearly identical
output powers of 0.65, 0.67, and 0.71
μW respectively.
Implies harvested power depends only
on the spectral density near the natural
frequency, other densities do not affect
harvested power.
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39. Expanded Vibration Testing
SOR – Constant Sinusoid, Variable Spectral Density
Test the effects of noise when harvesting from sinusoidal peak
0.3 g sinusoidal peak and increasing spectral density, PSDs plotted on left
Linear superposition suggests that power should increase, above the
sinusoidal power, as seen in random vibration
Harvested power increases with spectral density, however differently from the random
case due to time domain variations and imperfect super position in control software
March, 2013 39

40. Expanded Vibration Testing
SOR – Optimal Resistance
Determine the optimal resistance when both sinusoidal and random
content is present
Sinusoidal and random cases had significantly different optimal resistances
Does SOR bridge this gap?
Optimal resistance increases from
~15kΩ for sinusoidal to ~45kΩ for
random as spectral density
increases.
In other words, as vibration
dominance shifts from sinusoidal to
random, so does the optimal
resistance
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41. Expanded Vibration Testing
SOR – Multiple Sinusoidal Components
Test interactions of two dominant sinusoidal components
Two tones seen within 3 Hz of each other in Apache helicopter vibration
More components increase input power in the transducer bandwidth
FRF shows that harvested power value depends of frequency separation
Test two tones of 0.3 g amplitude at 58.3 Hz natural frequency
As frequency separation
increases, harvested power approaches
that of a single sinusoid at the natural
frequency.
At 0.25 Hz separation, average harvested
power is 28% higher
More than 1 Hz separation, harvested
power is only a few % higher
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42. Expanded Vibration Testing
SOR – Multiple Sinusoidal Components (cont’d)
Multiple sine components induce significant amplitude beating in
source vibration and output voltage
With negligible random vibration levels, input vibration reaches zero (left)
Filter capacitor prevents load voltage from dropping to zero and alters the
input voltage from the transducer (right)
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43. Expanded Vibration Testing
SOR – Multiple Sinusoidal Components (cont’d)
Amplitude beating is dependent on frequency separation
FRF suggests beating should decrease with separation
As frequency separation
increases, beat amplitude approaches
zero
For two sinusoidal components 0.25 Hz
apart, load voltage beats at nearly
100% of single sine component voltage
(~8 V at 58.3 Hz and 3.5 V at 124.5 Hz)
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44. Expanded Vibration Testing
SOR – Multiple Sinusoidal Components (cont’d)
Inclusion of more sine components in the transducer bandwidth
amplifies effects
Average harvested power and amplitude beating both increase
As number of sinusoidal components increases, responses approaches
that of random vibration with high spectral density
Test three 0.3 g sine components supplied to the bare transducer
March, 2013 44

45. Expanded Vibration Testing
Voltage Fluctuations
Interactions between frequencies induce fluctuations in voltage
delivered to the load
DC electronics are typically, designed to utilize a constant voltage supply
Even slight voltage fluctuations cause electronic devices to drop out of
regulation, affect sensor readings and damage the components
No found studies discussed implications of voltage fluctuations
Sinusoidal vibrations provide nearly constant voltage to the load
See the left plot on slide 18 (the capacitor voltage is the voltage supplied to the load)
Random vibrations induce significant voltage supply fluctuations
SOR vibrations can result in quite complicated vibration interactions
and voltage supply waveforms
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46. Expanded Vibration Testing
Voltage Fluctuations (cont’d)
Load supply voltage fluctuations scale with amplitude
Multiple sinusoidal components and random vibrations alter waveform
Sample time responses for 500 Hz bandwidth
random signals supplied to a transducer tuned
to 58.3 Hz at varying spectral densities
Peak to peak:
0.36 V at 2.5e-4 g2/Hz and
3.61 V at 5e-3 g2/Hz
Input power within the transducer natural frequency scales average power
(i.e. including a single sinusoidal component, as in slide 39, translates
waveform vertically but does not increase fluctuation intensity)
March, 2013 46

47. Discussion and Design
Implications
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48. Discussion and Design Implications
Steady state, sinusoidal vibration is the most ideal form of input
vibration
Only requires design for natural frequency and optimal impedance
Lower frequencies harvest more power for similar amplitudes
No significant voltage fluctuations
No time dependencies
Rarely seen application
Random vibration is the least ideal form of input vibration
Only requires design for natural frequency and optimal impedance
Significantly less efficient than sinusoidal
In order to harvest significant power spectral densities, more than 1e-3 g2/Hz
are typically needed
Usually only 1e-6 to 1e-4 g2/Hz in application [2,8,32]
Overshadowed by voltage fluctuations, requires additional charge control
circuitry
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49. Discussion and Design Implications
Designing a harvester for use with complex vibration sources requires
acknowledgement of more characteristic factors than sinusoidal or
random vibration
Sinusoidal frequencies, number of sinusoidal components, separation
between sinusoidal components, random spectral density
profile, determination of optimal impedance
Ignoring random content or nearby sinusoidal content gives a poor
representation of harvested power and load voltage
Ignoring random content gives incorrect optimal impedance
Harvested power gains from additional random component or multiple
sinusoidal components are overshadowed by induced voltage fluctuations
Improper source vibration and harvester response representation
during development hurts application
Lowers power harvesting ability and efficiency
Omitting necessary voltage control and processing circuitry can bring
about unexpected consequences such as inaccurate sensor
readings, poor circuit functionality and possible damage to target
electronics
March, 2013 Sigma Xi - Student Resarch Showcase 49

50. Conclusion
Idealized sinusoidal and random vibration studies are NOT sufficient
for general harvester development
Environments with sufficiently low noise or random vibration levels and
sufficiently spread dominant frequencies may suffice
Theoretical and numerical predictions hinge upon exact knowledge of
transducer mechanical and electrical properties
This cannot be assumed in general
Internal transducer electrical and mechanical properties are unknown
unless custom developed by applicant
Sine on random vibration testing and experimental validation is an
essential tool in harvester development
SOR testing can recreate almost any vibration environment
SOR control can provide accurate quantitative results when harvesting
from complex vibrational sources
March, 2013 Sigma Xi - Student Resarch Showcase 50

51. Acknowledgements
Brian Hatchell for mentoring me through this experimental process
and providing the inspiration for the project
Emiliano Santiago-Rojas for applying electrical expertise and making
this cross discipline application possible
Karen Wieda for advising and aiding my assimilating into the PNNL
research environment
A special thanks to:
Department of Energy – Office of Science and the U.S. Army for making
this research project possible
51

52. References
1. Lefeuvre E, Badel A, Richard C, Petit L, Guyomar D. A comparison between several vibration-powered piezoelectric generators for standalone systems. Sensors and Actuators A. 2005;126:12.
Epub 15 Dec. 2005.
2. Hatchell BK, Marotta SA, Mauss FJ, Amaya IA, Skorpik JR, Silvers KL. Missile Captive Carry Monitoring and Helicopter Identification Using a Capacitive MEMS Accelerometer. Structural Health
Monitoring. 2012;11(2):12. Epub September 27, 2011.
3. Chao PCP. Energy Harvesting Electronics for Vibratory Devices in Self-Powered Sensors. Ieee Sensors Journal. 2011 Dec;11(12):3106-21. PubMed PMID: WOS:000296459700006. English.
4. Roundy S, Leland ES, Baker J, Carleton E, Reilly E, Lai E, et al. Improving power output for vibration-based energy scavengers. Ieee Pervas Comput. 2005 Jan-Mar;4(1):28-36. PubMed PMID:
WOS:000227171800006. English.
5. Want R, Farkas KI, Narayanaswami C. Energy harvesting and conservation. Ieee Pervas Comput. 2005 Jan-Mar;4(1):14-7. PubMed PMID: WOS:000227171800004. English.
6. Shu YC, Lien IC. Analysis of power output for piezoelectric energy harvesting systems. Smart Materials and Structures. 2006;15(6):1499.
7. Tan YK, Lee JY, Panda SK. Maximize Piezoelectric Energy Harvesting Using Synchronous Charge Extraction Technique For Powering Autonomous Wireless Transmitter. 2008 Ieee International
Conference on Sustainable Energy Technologies (Icset), Vols 1 and 2. 2008:1123-8. PubMed PMID: WOS:000268749500214. English.
8. Sodano HA, Inman DJ, Park G. Comparison of piezoelectric energy harvesting devices for recharging batteries. Journal of Intelligent Material Systems and Structures. 2005 Oct;16(10):799-807.
PubMed PMID: WOS:000232275100003. English.
9. Tang LH, Yang YW, Tan YK, Panda SK. Applicability of Synchronized Charge Extraction Technique for Piezoelectric Energy Harvesting. Proc Spie. 2011;7977:7. PubMed PMID:
WOS:000297558900017. English.
10. Torres EO, Rincón-Mora GA. Electrostatic Energy Harvester and Li-Ion Charger Circuit for Micro-Scale Applications.5.
11. Zuo L, Scully B, Shestani J, Zhou Y. Design and characterization of an electromagnetic energy harvester for vehicle suspensions. Smart Materials and Structures. 2010;19:10. Epub 25 February
2010.
12. Liao YB, Lin YR, Sodano HA. Optimal Parameters and Power Characteristics of Piezoelectric Energy Harvesters with an RC Circuit. Proc Spie. 2011;7977(79770W):16. PubMed PMID:
WOS:000297558900030. English.
13. Mukherjee A, Datta U. Comparative Study of Piezoelectric Materials Properties for Green Energy Harvesting from Vibration. 2010 Annual IEEE India Conference. 2010;978-1-4244-9074-5:4.
14. Corporation C. EnerChip EP Universal Energy Harvester Eval Kit. www.cymbet.com2011.
15. Elmes J, Gaydarzhiev V, Mensah A, Rustom K, Shen J, Batarseh I. Maximum energy harvesting control for oscillating energy harvesting systems. Ieee Power Electron. 2007:2792-8. PubMed PMID:
WOS:000252375205026. Epub 2/07. English.
16. Lefeuvre E, Badel A, Richard C, Guyomar D. High performance piezoelectric vibration energy Smart Structures and Materials 2004: Smart Structures and Integrated Systems. 2004;5390:379-87.
PubMed PMID: WOS:000223848600039. English.
17. Renno JM, Daqaq MF, Inman DJ. On the optimal energy harvesting from a vibration source. Journal of Sound and Vibration. 2009 2/6/;320(1–2):386-405.
18. Blystad LCJ, Halvorsen E, Husa S. Piezoelectric MEMS energy harvesting systems driven by harmonic and random vibrations. Ultrasonics, Ferroelectrics and Frequency Control, IEEE Transactions
on. 2010;57(4):908-19.
19. Lefeuvre E, Badel A, Richard C, Guyomar D. Energy harvesting using piezoelectric materials: Case of random vibrations. J Electroceram. 2007 Dec;19(4):349-55. PubMed PMID:
WOS:000251795200018. English.
20. Stephen NG. On energy harvesting from ambient vibration. Journal of Sound and Vibration. 2006 5/30/;293(1–2):409-25.
21. Yaowen Y, Tang L. Equivalent Circuit Modeling of Piezoelectric Energy Harvesters. Journal Of Intelligent Material Systems and Structures. 2009;20:12.
22. High JW, Wilkie WK. Method of Fabricating NASA-Standard Macro-Fiber Composite Piezoelectric Actuators. In: NASA, editor. http://wayback.archive-
it.org/1792/20100210052417/http://hdl.handle.net/2060/20030063125: Langley Research Center; 2003.
23. So-Nam Y, Young-Bog H, Jung-Ho P, editors. Energy harvester using PZT actuator with a cantilver. ICCAS-SICE, 2009; 2009 18-21 Aug. 2009.
24. Corporation MT. Volture Piezoelectric Energy Harvesters. 06/03/2010 ed. www.mide.com2010.
25. Corporation MT. Volture Products - Material Properties. www.mide.com2010.
26. Sprott JC. Introduction to Modern Electronics. USA: John Wiley & Sons; 1981.
27. Winter M, Brodd RJ. What Are Batteries, Fuel Cells, and Supercapacitors? 2004:25. Epub 09/28/2004.
28. Group SIB. VH AA 1500 Super High Energy series. In: Saft, editor. 2012.
29. Ottman GK, Hofmann HF, Bhatt AC, Lesieutre GA. Adaptive piezoelectric energy harvesting circuit for wireless remote power supply. Power Electronics, IEEE Transactions on. 2002;17(5):669-76.
30. Howard CQ, Snyder SD, Hansen CH. CALCULATION OF VIBRATORY POWER TRANSMISSION FOR USE IN ACTIVE VIBRATION CONTROL. Journal of Sound and Vibration. 2000
6/15/;233(4):569-81.
31. Han SB. Analysis on Natural Frequency Distortion Due to the Attachment of Shaker. P Soc Photo-Opt Ins. 1995;2460:1715-21. PubMed PMID: WOS:A1995BC60K00249. English.
32. Hassan MA, Coats D, Gouda K, Yong-June S, Bayoumi A, editors. Analysis of nonlinear vibration-interaction using higher order spectra to diagnose aerospace system faults. Aerospace
Conference, 2012 IEEE; 2012 3-10 March 2012.
52

53. External Image Sources
1. http://idol.union.edu/malekis/Phys%20&%20Pol%202010/PNP_EMWaves.htm
2. http://pediatrics.about.com/od/yourbabyweekbyweek/ss/baby_wk_eighten_6.htm
3. http://www.physicsclassroom.com/class/energy/u5l1b.cfm
4. http://reliabilityweb.com/index.php/maintenance_tips/what_is_machine_vibration/
5. http://salestores.com/texinti1teac.html
6. http://news.cnet.com/2300-11386_3-10001391-11.html
7. http://www.calctool.org/CALC/eng/electronics/parallel_plate
8. http://www.digikey.com/product-detail/en/V25W/V25W-ND/2402862
9. [2]
10. http://www.networkwaste.co.uk/network-news/battery-basic
11. [15]
12. [3]
13. [9]
14. http://www.rmcybernetics.com/science/high_voltage/mineral_elec.htm
15. [13]
16. [24]
17. [1]
18. [24]
19. http://www.indiastudychannel.com/experts/18455-what-Differences-between-half-wave-full-wave.aspx
20. http://tymkrs.com/forum/viewtopic.php?id=38
21. [14]
22. [1]
23. [18]
53