Upload
jwcryns
View
2.580
Download
0
Tags:
Embed Size (px)
Citation preview
Sigma Xi - Student Resarch Showcase 1March, 2013
Experimental analysis of a piezoelectric energy harvesting system for harmonic, random, and sine on random vibration
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
JACKSON W. CRYNSB.S. Applied Mathematics, Engineering and PhysicsUniversity of Wisconsin - Madison
Sigma Xi - Student Resarch Showcase 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.
March, 2013
Sigma Xi - Student Resarch Showcase 3March, 2013
Background
What is Energy Harvesting?
Application Goals
Vibration Powered Generators (Transducers)
Piezoelectric Effect
Power Conditioning
Sigma Xi - Student Resarch Showcase
What is Energy Harvesting?
• Every process dissipates waste energy to the surrounding environment
• Ambient energy comes in many usable forms
[5]
• Convert ambient energy to usable electrical energy – transducers• Small amounts of power – mW or µW (milli-Watts or micro-Watts) [3]
• Not a new idea!4March, 2013
Electromagnetic Radiation (1) Thermal Gradient (2) Potential Energy Forms (3) Vibration (Potential + Kinetic) (4)
(5) (7)(6) (8)
Sigma Xi - Student Resarch Showcase 5
Application Goals
Supply power to off grid devicesRemote equipment
Monitors in hazardous environments
Wireless data logging and transmission
Reduce maintenance requirements and costs
Relieve dependence on primary batteries
Fits into national “green” initiatives
March, 2013
(9)
(10)
Sigma Xi - Student Resarch Showcase 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]
Piezoelectric transducers are the most energy dense [8,12]
March, 2013
Driving and Biking Walking Numerical and Theoretical Simulations
(11) (12) (13)
Sigma Xi - Student Resarch Showcase 7
Piezoelectric Effect
Electric charge accumulates in certain materials in response to applied mechanical stress [11]
This study analyzes a commercially available bimorph transducerTwo piezoelectric layers
Two electrical signals of opposite sines
March, 2013
(14) (15)
Sigma Xi - Student Resarch Showcase 8
Power Conditioning
Conditioning circuitry – the components necessary to supply power from the transducer to the target electronics with specified current and voltage characteristics
This study includes the target electronics in the conditioning circuit
March, 2013
Example conditioning circuit
(16)
Sigma Xi - Student Resarch Showcase 9March, 2013
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}
Sigma Xi - Student Resarch Showcase 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
March, 2013
Sigma Xi - Student Resarch Showcase 11March, 2013
Energy Harvesting Architecture
12
Piezoelectric transducerV25w QuickPack® actuatorproduced by Midé [24,25]
Proof mass(for frequency tuning)
Rigid clamp(fixed-free cantilever beam)
Vibration SourceLDS V721 – 1000 L shaker
Closed loop vibration control
Power conditioning circuitryStandard circuit
Energy Harvesting Architecture
March, 2013
AC signal
Exact transducer internal electrical and mechanical characteristics unknown
[17]
Sigma Xi - Student Resarch Showcase 13
Energy Harvesting Architecture
Mount in cantilever configurationInput vibration at base
Natural frequencyTune with proof mass to match source vibration
Modal analysis allows for accurate natural frequency determination
Bare natural frequency of 124.5 Hz
March, 2013
Piezoelectric Transducer Set-Up
[18]
Sigma Xi - Student Resarch Showcase 14
Energy Harvesting Architecture
AC-DC conversionTransducer creates AC signal (oscillatory)
Most microelectronics require DC
Full-wave bridge rectifier
Signal smoothingA time varying signal is damagingto DC electronics
Provide power to load Microelectronics
Resistor
Secondary (rechargeable) battery
March, 2013
Power Conditioning Duties
http://www.electronics-tutorials.ws/diode/diode_6.htmlhttp://www.eleinmec.com/article.asp?18
[19]
[20]
Sigma Xi - Student Resarch Showcase 15
Energy Harvesting Architecture
Standard (linear) InterfaceTarget 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 resistanceCR = 600 µF, RL -> variable.
Non-linear processing not considered in this studyDesigned for steady sinusoidal vibration only
Dissipates extra power
Application specific designs require additional voltage controlAdditional 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)
March, 2013
Power Conditioning Circuitry [3,7,14-16,26]
Sigma Xi - Student Resarch Showcase 16
Energy Harvesting Architecture
Test multiple scenariosHarmonic, Random – simplified
SOR – sine and random superposition for accurate testing
Characterize and control the input vibration by acceleration
Acceleration response is the most 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
March, 2013
Impedance head
Shaker armature
Sigma Xi - Student Resarch Showcase 17
Energy Harvesting Architecture
Note that input power is NOT constant for identical acceleration amplitudes at different driving frequencies and bandwidths
Mechanical sinusoidal power is proportional to velocity amplitude
Velocity is inversely proportional to the natural frequency for a given acceleration
[20]
Similarly input power increases with bandwidth since more sine components are incorporated
Input power variations are not of concern in design, however, since ambient power is of no cost to the developer
March, 2013
Sigma Xi - Student Resarch Showcase 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
March, 2013
Sigma Xi - Student Resarch Showcase 19March, 2013
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]
Sigma Xi - Student Resarch Showcase 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]
March, 2013
Sigma Xi - Student Resarch Showcase 21
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
Literature Review and Harvester Validation
March, 2013
[21]
Sigma Xi - Student Resarch Showcase 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
March, 2013
[22] [23]
Sigma Xi - Student Resarch Showcase 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
March, 2013
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
Sigma Xi - Student Resarch Showcase 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
March, 2013
Sigma Xi - Student Resarch Showcase 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
March, 2013
Quadratic trend is clearly exhibited at two natural frequencies.
Sigma Xi - Student Resarch Showcase 26
Literature Review and Harvester Validation
Sinusoidal – Natural Frequency VariationTheoretical Expectations:
Transducer cantilever displacement is inversely proportional to the natural frequency squaredD ~
March, 2013
For identical input amplitudes: lower natural frequencies harvest more power. *
* Consequence of input power variations
Sigma Xi - Student Resarch Showcase 27
Literature Review and Harvester Validation
March, 2013
Sinusoidal – Impedance VariationTheoretical 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
Sigma Xi - Student Resarch Showcase 28
Literature Review and Harvester Validation
March, 2013
Sinusoidal – Impedance Variation (cont’d)Theoretical Expectations:
Optimal resistance is inversely proportional to the natural frequency
Ropt ~
As natural frequency increases, optimal impedance decreases and peak narrows
Sigma Xi - Student Resarch Showcase 29
Literature Review and Harvester Validation
March, 2013
Sinusoidal –Frequency Response Function (FRF) for powerTheoretical 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
Sigma Xi - Student Resarch Showcase 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 repeatabilityRandom 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
March, 2013
Sigma Xi - Student Resarch Showcase 31
Literature Review and Harvester Validation
Random – Amplitude VariationTheoretical Expectations:
Power scales linearly with spectral density
Power scales inversely with natural frequency, as with sinusoidal
March, 2013
As derived in [18], harvested power varies linearly with spectral density
Sigma Xi - Student Resarch Showcase 32
Literature Review and Harvester Validation
Random – Impedance VariationTheoretical Expectations:
Random vibration has higher optimal resistance than sinusoidal vibration
Optimal impedance scales inversely with natural frequency
March, 2013
Optimal resistance is higher for random vibration than sinusoidal vibration for both frequencies, and decreases with natural frequency for each vibration type
33
Literature Review and Harvester Validation
Random – Bandwidth VariationTheoretical 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
March, 2013 Sigma Xi - Student Resarch Showcase
Except for random statistical deviations from one point the next, average harvested power is constant over all bandwidths
Sigma Xi - Student Resarch Showcase 34
Literature Review and Harvester Validation
Random – Frequency VariationTheoretical Expectations:
Harvested power is inversely proportional to transducer natural frequency
March, 2013
For identical input amplitudes and bandwidths, higher natural frequencies produced less power
Sigma Xi - Student Resarch Showcase 35
Literature Review and Harvester Validation
Harvester met and agreed with theoretical predictions for special casesSteady state sinusoidal vibration
Flat broadband vibration
Limitations of idealized studiesReal 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
March, 2013
Sigma Xi - Student Resarch Showcase 36
Expanded Vibration Testing
March, 2013
Short bandwidth and non-flat random profiles
Sinusoidal and random component interaction
Multiple sinusoidal component interaction
Expanded Vibration Testing
Random – Short Bandwidth VariationTest 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.
Sigma Xi - Student Resarch Showcase 38
Expanded Vibration Testing
Random – Non-Flat profileTest 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)
March, 2013
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.
39
Expanded Vibration Testing
March, 2013
SOR – Constant Sinusoid, Variable Spectral DensityTest 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
Sigma Xi - Student Resarch Showcase 40
Expanded Vibration Testing
SOR – Optimal ResistanceDetermine 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?
March, 2013
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
41
Expanded Vibration Testing
SOR – Multiple Sinusoidal ComponentsTest 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
March, 2013
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% higherMore than 1 Hz separation, harvested power is only a few % higher
Sigma Xi - Student Resarch Showcase 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)
March, 2013
43
Expanded Vibration Testing
SOR – Multiple Sinusoidal Components (cont’d)
Amplitude beating is dependent on frequency separationFRF suggests beating should decrease with separation
March, 2013
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)
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
Sigma Xi - Student Resarch Showcase 45
Expanded Vibration Testing
Voltage FluctuationsInteractions 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 loadSee 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
March, 2013
46
Expanded Vibration Testing
Voltage Fluctuations (cont’d)Load supply voltage fluctuations scale with amplitude
Multiple sinusoidal components and random vibrations alter waveform
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
Sample time responses for 500 Hz bandwidth random signals supplied to a transducer tuned to 58.3 Hz at varying spectral densitiesPeak to peak:0.36 V at 2.5e-4 g2/Hz and3.61 V at 5e-3 g2/Hz
Sigma Xi - Student Resarch Showcase 47March, 2013
Discussion and Design Implications
Sigma Xi - Student Resarch Showcase 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 impedanceLower 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 vibrationOnly 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
March, 2013
Sigma Xi - Student Resarch Showcase 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 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
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
References1. 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
External Image Sources
1. http://idol.union.edu/malekis/Phys%20&%20Pol%202010/PNP_EMWaves.htm2. http://pediatrics.about.com/od/yourbabyweekbyweek/ss/baby_wk_eighten_6.htm3. http://www.physicsclassroom.com/class/energy/u5l1b.cfm4. http://reliabilityweb.com/index.php/maintenance_tips/what_is_machine_vibration/5. http://salestores.com/texinti1teac.html6. http://news.cnet.com/2300-11386_3-10001391-11.html7. http://www.calctool.org/CALC/eng/electronics/parallel_plate8. http://www.digikey.com/product-detail/en/V25W/V25W-ND/24028629. [2]10. http://www.networkwaste.co.uk/network-news/battery-basic11. [15]12. [3]13. [9]14. http://www.rmcybernetics.com/science/high_voltage/mineral_elec.htm15. [13]16. [24]17. [1]18. [24]19. http://www.indiastudychannel.com/experts/18455-what-Differences-between-half-wave-full-wave.aspx20. http://tymkrs.com/forum/viewtopic.php?id=3821. [14]22. [1]23. [18]
53