Energy harvesting from fluid flow using piezoelectrics: A critical review

Abstract The ambient energy as an available and harvestable energy source which has a high potential to generate electricity for powering electronics devices. Piezoelectric materials, as one of the well-known energy harvesting mechanisms, play a significant role in converting ambient energy into electrical energy, particularly in small electronic devices such as measuring devices in remote or hostile environments where batteries are not an acceptable option. For this reason, piezoelectric energy harvester (PEH) can help to optimize the weight of structures. In addition, PEH can produce an output voltage in response to the inputs such as thermal, electrical, mechanical and electromagnetic energies. This paper provides a holistic review of the energy harvesting techniques from fluid flow using piezoelectric materials. To this end, the recently conducted research studies in the context of energy harvesting based on the fluid flow motion have been reviewed, considering various modeling and methods for improving the PEH efficiency. Various types of energy harvesting mechanisms, based on vibration by using piezoelectric, have been investigated to identify their opportunities and challenges.

[1]  Renwen Chen,et al.  Analysis of piezoelectric–electromagnetic hybrid vibration energy harvester under different electrical boundary conditions , 2015 .

[2]  X. Tan,et al.  High-Performance Piezoelectric Crystals, Ceramics, and Films , 2018, Annual Review of Materials Research.

[3]  Ronald W. Yeung,et al.  Piezoelectric devices for ocean energy: a brief survey , 2015 .

[4]  Zhong Lin Wang.  Triboelectric nanogenerators as new energy technology for self-powered systems and as active mechanical and chemical sensors. , 2013, ACS nano.

[5]  Elena Blokhina,et al.  Electrostatic vibration energy harvester with combined effect of electrical nonlinearities and mechanical impact , 2014 .

[6]  Amos Ullmann,et al.  The piezoelectric valve-less pump - improved dynamic model , 2002 .

[7]  L. Schmidt‐Mende,et al.  ZnO - nanostructures, defects, and devices , 2007 .

[8]  Jayant Sirohi,et al.  Piezoelectric wind energy harvester for low-power sensors , 2011 .

[9]  Abdessattar Abdelkefi,et al.  Aeroelastic energy harvesting: A review , 2016 .

[10]  P. Smithmaitrie,et al.  Perspective microscale piezoelectric harvester for converting flow energy in water way , 2015 .

[11]  Just L. Herder,et al.  Bistable vibration energy harvesters: A review , 2013 .

[12]  Y. Andreopoulos,et al.  An experimental study of the dissipative and vortical motion in turbulent boundary layers , 2001, Journal of Fluid Mechanics.

[13]  Ryan L. Harne,et al.  A review of the recent research on vibration energy harvesting via bistable systems , 2013 .

[14]  Ann Marie Sastry,et al.  Powering MEMS portable devices—a review of non-regenerative and regenerative power supply systems with special emphasis on piezoelectric energy harvesting systems , 2008 .

[15]  Joseph R. Burns,et al.  The Energy Harvesting Eel: a small subsurface ocean/river power generator , 2001 .

[16]  Ali H. Nayfeh,et al.  Design of piezoaeroelastic energy harvesters , 2012 .

[17]  Xuedong Chen,et al.  A piezoelectric energy harvester based on flow-induced flexural vibration of a circular cylinder , 2012 .

[18]  Yaowen Yang,et al.  Comparative study of tip cross-sections for efficient galloping energy harvesting , 2013 .

[19]  Dong Sam Ha,et al.  Broadband electromagnetic vibration energy harvesting system for powering wireless sensor nodes , 2013 .

[20]  Daniel Mihai Toma,et al.  An ocean kinetic energy converter for low-power applications using piezoelectric disk elements , 2013 .

[21]  Gregorio Boccalero,et al.  Fluttering conditions of an energy harvester for autonomous powering , 2017 .

[22]  Daniel J. Inman,et al.  On the energy harvesting potential of piezoaeroelastic systems , 2010 .

[23]  S. H. Kim,et al.  Micromachined PZT cantilever based on SOI structure for low frequency vibration energy harvesting , 2009 .

[24]  Alper Erturk,et al.  Electromechanical Modeling of Piezoelectric Energy Harvesters , 2009 .

[25]  Daniel J. Inman,et al.  A Distributed Parameter Electromechanical Model for Cantilevered Piezoelectric Energy Harvesters , 2008 .

[26]  Jin-Ho Lee,et al.  An electromagnetic energy scavenger from direct airflow , 2009 .

[27]  Yunfeng Shi,et al.  Harvesting energy from water flow over graphene. , 2011, Nano letters.

[28]  Earl H. Dowell,et al.  Power extraction from aeroelastic limit cycle oscillations , 2011 .

[29]  S. Banerjee,et al.  Large-Area Synthesis of High-Quality and Uniform Graphene Films on Copper Foils , 2009, Science.

[30]  Adrien Badel,et al.  Vibration energy harvesting device using P(VDF-TrFE) hybrid fluid diaphragm , 2016 .

[31]  Xiaobiao Shan,et al.  A study of vortex-induced energy harvesting from water using PZT piezoelectric cantilever with cylindrical extension , 2015 .

[32]  Abdessattar Abdelkefi,et al.  Modeling and performance analysis of cambered wing-based piezoaeroelastic energy harvesters , 2013 .

[33]  Chang Kyu Jeong,et al.  Highly‐Efficient, Flexible Piezoelectric PZT Thin Film Nanogenerator on Plastic Substrates , 2014, Advanced materials.

[34]  Nathan Jackson,et al.  Influence of aluminum nitride crystal orientation on MEMS energy harvesting device performance , 2013 .

[35]  Brian S. Pearson,et al.  Design for energy: Modeling of spectrum, temperature and device structure dependences of solar cell energy production , 2015 .

[36]  Gursel Alici,et al.  A review on performance enhancement techniques for ambient vibration energy harvesters , 2017 .

[37]  Juan G. Santiago,et al.  A review of micropumps , 2004 .

[38]  Xiaobiao Shan,et al.  A Novel Piezoelectric Energy Harvester Using the Macro Fiber Composite Cantilever with a Bicylinder in Water , 2015 .

[39]  Daniel J. Inman,et al.  Piezoaeroelastic Modeling and Analysis of a Generator Wing with Continuous and Segmented Electrodes , 2010 .

[40]  M. Eugeni,et al.  A Review on Mechanisms for Piezoelectric-Based Energy Harvesters , 2018, Energies.

[41]  R. van Schaijk,et al.  Harvesting energy from airflow with a michromachined piezoelectric harvester inside a Helmholtz resonator , 2011 .

[42]  Srinivas Tadigadapa,et al.  Electroactive polymer based microfluidic pump , 2006 .

[43]  Zhong Lin Wang,et al.  Harvesting water wave energy by asymmetric screening of electrostatic charges on a nanostructured hydrophobic thin-film surface. , 2014, ACS nano.

[44]  Dung-An Wang,et al.  Piezoelectric energy harvesting from flow-induced vibration , 2010 .

[45]  Daniel J. Inman,et al.  A distributed parameter electromechanical and statistical model for energy harvesting from turbulence-induced vibration , 2014 .

[46]  Soon-Duck Kwon,et al.  A T-shaped piezoelectric cantilever for fluid energy harvesting , 2010 .

[47]  Daniel J. Inman,et al.  On the optimal energy harvesting from a vibration source using a PZT stack , 2009 .

[48]  Peyman Firoozy,et al.  Broadband energy harvesting using nonlinear vibrations of a magnetopiezoelastic cantilever beam , 2017 .

[49]  Daniel J. Inman,et al.  Modeling and Analysis of Piezoelectric Energy Harvesting From Aeroelastic Vibrations Using the Doublet-Lattice Method , 2011 .

[50]  X. D. Xie,et al.  Potential of a piezoelectric energy harvester from sea waves , 2014 .

[51]  Amos Ullmann.  The piezoelectric valve-less pump—performance enhancement analysis , 1998 .

[52]  Zhong Lin Wang.  ZnO Nanowire and Nanobelt Platform for Nanotechnology , 2009 .

[53]  Yiannos Manoli,et al.  Energy Harvesting from Fluid Flow in Water Pipelines for Smart Metering Applications , 2013 .

[54]  Franco Mastroddi,et al.  Shunted piezoelectric patches in elastic and aeroelastic vibrations , 2003 .

[55]  Yiannis Andreopoulos,et al.  Interactions of vortices with a flexible beam with applications in fluidic energy harvesting , 2014 .

[56]  A. Erturk,et al.  Nanoscale flexoelectric energy harvesting , 2014 .

[57]  Amin Bibo,et al.  Energy harvesting under combined aerodynamic and base excitations , 2013 .

[58]  Daniel J. Inman,et al.  An experimentally validated bimorph cantilever model for piezoelectric energy harvesting from base excitations , 2009 .

[59]  Amin Bibo,et al.  Investigation of Concurrent Energy Harvesting from Ambient Vibrations and Wind , 2013 .

[60]  N. Elvin,et al.  Energy Harvesting from Highly Unsteady Fluid Flows using Piezoelectric Materials , 2010 .

[61]  Xiaobiao Shan,et al.  Energy-Harvesting Performances of Two Tandem Piezoelectric Energy Harvesters with Cylinders in Water , 2016 .

[62]  Wanlin Guo,et al.  Generating electricity by moving a droplet of ionic liquid along graphene. , 2014, Nature nanotechnology.

[63]  D. Mandal,et al.  The influence of hydrogen bonding on the dielectric constant and the piezoelectric energy harvesting performance of hydrated metal salt mediated PVDF films. , 2015, Physical chemistry chemical physics : PCCP.

[64]  Michael P. Païdoussis,et al.  Cantilevered flexible plates in axial flow: Energy transfer and the concept of flutter-mill , 2009 .

[65]  Stewart Sherrit,et al.  Piezoelectric Energy Harvesting in Internal Fluid Flow , 2015, Sensors.

[66]  Muhammad R. Hajj,et al.  Piezoelectric energy harvesting from vortex-induced vibrations of circular cylinder , 2013 .

[67]  Qifa Zhou,et al.  AlN piezoelectric thin films for energy harvesting and acoustic devices , 2018, Nano Energy.

[68]  A. Velazquez,et al.  Energy-Harvesting Microresonator Based on the Forces Generated by the Karman Street Around a Rectangular Prism , 2009, Journal of Microelectromechanical Systems.

[69]  Christopher R. Bowen,et al.  Pyroelectric materials and devices for energy harvesting applications , 2014 .

[70]  Bin Li,et al.  Harvesting low-frequency acoustic energy using quarter-wavelength straight-tube acoustic resonator , 2013 .

[71]  Mergen H. Ghayesh,et al.  Ambient vibration energy harvesters: A review on nonlinear techniques for performance enhancement , 2018, International Journal of Engineering Science.

[72]  Muhammad R. Hajj,et al.  Performance analysis of galloping-based piezoaeroelastic energy harvesters with different cross-section geometries , 2014 .

[73]  Yaowen Yang,et al.  Toward Broadband Vibration-based Energy Harvesting , 2010 .

[74]  Matthew Bryant,et al.  Aeroelastic flutter energy harvester design: the sensitivity of the driving instability to system parameters , 2011 .

[75]  Ephrahim Garcia,et al.  Development of an aeroelastic vibration power harvester , 2009, Smart Structures and Materials + Nondestructive Evaluation and Health Monitoring.

[76]  Jie Shen,et al.  Enhanced piezoelectric property and promoted depolarization temperature in Fe doped Bi1/2(Na0.8K0.2)1/2TiO3 lead-free ceramics , 2017 .

[77]  Xuecang Geng,et al.  Advantages and Challenges of Relaxor-PbTiO3 Ferroelectric Crystals for Electroacoustic Transducers- A Review. , 2015, Progress in materials science.

[78]  Jan M. Rabaey,et al.  Improving power output for vibration-based energy scavengers , 2005, IEEE Pervasive Computing.

[79]  Christopher J. Morris,et al.  Optimization of a circular piezoelectric bimorph for a micropump driver , 2000 .

[80]  Daniel J. Inman,et al.  Estimation of Electric Charge Output for Piezoelectric Energy Harvesting , 2004 .

[81]  David L. Hu,et al.  Tree-inspired piezoelectric energy harvesting , 2009 .

[82]  Quan Wang,et al.  Energy harvesting from transverse ocean waves by a piezoelectric plate , 2014 .

[83]  Ji Su,et al.  Development, characterization, and theoretical evaluation of electroactive polymer-based micropump diaphragm , 2005 .

[84]  Mohamed Sukri Mat Ali,et al.  Flow-induced vibration of a square cylinder and downstream flat plate associated with micro-scale energy harvester , 2018 .

[85]  Xinxin Li,et al.  Bi-resonant structure with piezoelectric PVDF films for energy harvesting from random vibration sources at low frequency , 2016 .

[86]  Jorge Lopes,et al.  Energy harvesting from hydroelectric systems for remote sensors , 2016 .

[87]  L. Stein,et al.  Hydromechanical and physiological mechanical-to-electrical power converter with PVDF film , 1987 .

[88]  Ilan Fono,et al.  A Piezoelectric Valve-Less Pump-Dynamic Model , 2001 .

[89]  J. Andreopoulos,et al.  Wall-vorticity flux dynamics in a two-dimensional turbulent boundary layer , 1996, Journal of Fluid Mechanics.

[90]  A. Barrero-Gil,et al.  Dual mass system for enhancing energy extraction from Vortex-Induced Vibrations of a circular cylinder , 2016 .

[91]  Robert Mosé,et al.  An experiment of a hydropower conversion system based on vortex-induced vibrations in a confined channel , 2018 .

[92]  L. Bu,et al.  Non-resonant electrostatic energy harvester for wideband applications , 2013 .

[93]  Tao Zhang,et al.  Performance evaluation of a valveless micropump driven by a ring-type piezoelectric actuator. , 2006, IEEE transactions on ultrasonics, ferroelectrics, and frequency control.

[94]  Ming Cheng,et al.  The state of the art of wind energy conversion systems and technologies: A review , 2014 .

[95]  Yu Zhou,et al.  Current micropump technologies and their biomedical applications , 2009 .

[96]  Hasan Selim,et al.  A review on the methods for biomass to energy conversion systems design , 2013 .

[97]  Timothy C. Green,et al.  Energy Harvesting From Human and Machine Motion for Wireless Electronic Devices , 2008, Proceedings of the IEEE.

[98]  Mohamed Sultan Mohamed Ali,et al.  Micro-scale energy harvesting devices: Review of methodological performances in the last decade , 2016 .

[99]  Bo Liu,et al.  Novel energy harvesting: A macro fiber composite piezoelectric energy harvester in the water vortex , 2015 .

[100]  Dung-An Wang,et al.  A Piezoelectric Energy Harvester Based on Pressure Fluctuations in Kármán Vortex Street , 2011 .

[101]  Abdessattar Abdelkefi,et al.  Theoretical modeling and nonlinear analysis of piezoelectric energy harvesting from vortex-induced vibrations , 2014 .

[102]  A. G. Avila Bernal,et al.  The modelling of an electromagnetic energy harvesting architecture , 2012 .

[103]  Henry A. Sodano,et al.  A review of power harvesting using piezoelectric materials (2003–2006) , 2007 .

[104]  Eun Kyung Lee,et al.  Porous PVDF as effective sonic wave driven nanogenerators. , 2011, Nano letters.

[106]  Andrew Truitt,et al.  A review on active wind energy harvesting designs , 2013 .

[107]  Oliver G. Schmidt,et al.  Scalable single crystalline PMN-PT nanobelts sculpted from bulk for energy harvesting , 2017 .

[108]  Olivier Doaré,et al.  Energy harvesting efficiency of piezoelectric flags in axial flows , 2012, Journal of Fluid Mechanics.

[109]  T.C. Green,et al.  Architectures for vibration-driven micropower generators , 2004, Journal of Microelectromechanical Systems.

[110]  Hongjun Zhu,et al.  CFD analysis of energy harvesting from flow induced vibration of a circular cylinder with an attached free-to-rotate pentagram impeller , 2018 .

[111]  Prasanta Kumar Panda,et al.  Review: environmental friendly lead-free piezoelectric materials , 2009, Journal of Materials Science.

[112]  Eric Cross,et al.  Materials science: Lead-free at last , 2004, nature.

[113]  Yaowen Yang,et al.  Vibration energy harvesting using macro-fiber composites , 2009 .

[114]  Nguyen Duy Vinh,et al.  Ocean-based electricity generating system utilizing the electrochemical conversion of wave energy by ionic polymer-metal composites , 2017 .

[115]  Zheng Lin,et al.  Dynamics of a mechanical frequency up-converted device for wave energy harvesting , 2016 .

[116]  L. Tran-Huu-Hue,et al.  Ultrasonic transducer based on highly textured PMN-PT piezoelectric ceramic , 2007 .

[117]  T. Kinsey,et al.  Parametric Study of an Oscillating Airfoil in a Power-Extraction Regime , 2008 .

[118]  Daniel J. Inman,et al.  Artificial piezoelectric grass for energy harvesting from turbulence-induced vibration , 2012 .

[119]  C. Hierold,et al.  Spatially resolved Raman spectroscopy of single- and few-layer graphene. , 2006, Nano letters.

[120]  H. Wikle,et al.  The design, fabrication and evaluation of a MEMS PZT cantilever with an integrated Si proof mass for vibration energy harvesting , 2008 .

[121]  Massimo De Vittorio,et al.  Piezoelectric MEMS vibrational energy harvesters: Advances and outlook , 2017 .

[122]  Qiang Zhu,et al.  Modeling the capacity of a novel flow-energy harvester , 2009 .

[123]  Othman Sidek,et al.  A review of vibration-based MEMS piezoelectric energy harvesters , 2011 .

[124]  L. Tran-Huu-Hue,et al.  Piezoelectric textured ceramics: Effective properties and application to ultrasonic transducers. , 2006, Ultrasonics.

[125]  John A. Rogers,et al.  Recent progress in flexible and stretchable piezoelectric devices for mechanical energy harvesting, sensing and actuation , 2016 .

[126]  Paul Muralt,et al.  Ferroelectric thin films for micro-sensors and actuators: a review , 2000 .

[127]  Hyung-Jo Jung,et al.  The experimental validation of a new energy harvesting system based on the wake galloping phenomenon , 2011 .

[128]  Hod Lipson,et al.  Ambient wind energy harvesting using cross-flow fluttering , 2011 .

[129]  F. Fan,et al.  Flexible Nanogenerators for Energy Harvesting and Self‐Powered Electronics , 2016, Advanced materials.

[130]  Muhammad R. Hajj,et al.  Global nonlinear distributed-parameter model of parametrically excited piezoelectric energy harvesters , 2012 .

[131]  Marco P. Soares dos Santos,et al.  Graphene-based materials and structures for energy harvesting with fluids – A review , 2018, Materials Today.

[132]  Elias Siores,et al.  An investigation of energy harvesting from renewable sources with PVDF and PZT , 2011 .

[133]  G. Stemme,et al.  A valveless diffuser/nozzle-based fluid pump , 1993 .

[134]  Mukund Patel,et al.  Book Review: Wind and Solar Power Systems—Design, Analysis, and Operation , 2006 .

[135]  Daniel J. Inman,et al.  Piezoelectric energy harvesting from broadband random vibrations , 2009 .

[136]  Yiannis Andreopoulos,et al.  Energy harvesting prospects in turbulent boundary layers by using piezoelectric transduction , 2015 .

[137]  Paul K. Wright,et al.  Vortex shedding induced energy harvesting from piezoelectric materials in heating, ventilation and air conditioning flows , 2012 .

[138]  Xiao Hu,et al.  Design and implementation of an out-of-plane electrostatic vibration energy harvester with dual-charged electret plates , 2015 .

[139]  Steve Dunn,et al.  Piezoelectric nanogenerators – a review of nanostructured piezoelectric energy harvesters , 2015 .

[140]  B. Cheng,et al.  Performance enhancements in poly(vinylidene fluoride)-based piezoelectric nanogenerators for efficient energy harvesting , 2019, Nano Energy.

[141]  Zhong Lin Wang,et al.  A One‐Structure‐Based Hybridized Nanogenerator for Scavenging Mechanical and Thermal Energies by Triboelectric–Piezoelectric–Pyroelectric Effects , 2016, Advanced materials.

[142]  Xiaotong Gao,et al.  Flow Energy Harvesting Using Piezoelectric Cantilevers With Cylindrical Extension , 2013, IEEE Transactions on Industrial Electronics.

[143]  Christopher R. Bowen,et al.  Piezoelectric and ferroelectric materials and structures for energy harvesting applications , 2014 .

[144]  Zhiqiang Sun,et al.  Harvesting vortex energy in the cylinder wake with a pivoting vane , 2015 .

[145]  M. N. Sahinkaya,et al.  A review of wave energy converter technology , 2009 .

[146]  Renwen Chen,et al.  Parameter tuning of piezoelectric–electromagnetic hybrid vibration energy harvester by magnetic force: Modeling and experiment , 2017 .

[147]  Daniel J. Inman,et al.  Towards autonomous sensing , 2006, SPIE Smart Structures and Materials + Nondestructive Evaluation and Health Monitoring.

[148]  Y. V. Andel,et al.  Vibration energy harvesting with aluminum nitride-based piezoelectric devices , 2009 .

[149]  Sang‐Woo Kim,et al.  Energy harvesting based on semiconducting piezoelectric ZnO nanostructures , 2012 .

[150]  Daniel J. Inman,et al.  An electromechanical finite element model for piezoelectric energy harvester plates , 2009 .

[151]  Yaowen Yang,et al.  On the modeling methods of small-scale piezoelectric wind energy harvesting , 2017 .

[152]  Xi Chen,et al.  1.6 V nanogenerator for mechanical energy harvesting using PZT nanofibers. , 2010, Nano letters.

[153]  Konstantinos Gkoumas,et al.  Piezoelectric energy harvesting from vortex shedding and galloping induced vibrations inside HVAC ducts , 2018 .

[154]  Andreas Tünnermann,et al.  All inkjet-printed piezoelectric polymer actuators: Characterization and applications for micropumps in lab-on-a-chip systems , 2013 .

[155]  Michael W. Shafer,et al.  Power and efficiency analysis of a flapping wing wind energy harvester , 2012, Smart Structures and Materials + Nondestructive Evaluation and Health Monitoring.

[156]  Muhammad R. Hajj,et al.  Performance enhancement of piezoelectric energy harvesters from wake galloping , 2013 .

[157]  Zhong Lin Wang,et al.  Piezoelectric Nanogenerators Based on Zinc Oxide Nanowire Arrays , 2006, Science.

[158]  Matthias Müllenborn,et al.  Fabrication and characterization of truly 3-D diffuser/nozzle microstructures in silicon , 1997 .

[159]  R. Meyer,et al.  Comparison of the properties of tonpilz transducers fabricated with 001 fiber-textured lead magnesium niobate-lead titanate ceramic and single crystals. , 2009, The Journal of the Acoustical Society of America.

[160]  Patrick Hu,et al.  Validation of a hybrid electromagnetic–piezoelectric vibration energy harvester , 2016 .

[161]  António F.O. Falcão,et al.  Wave energy utilization: A review of the technologies , 2010 .

[162]  Alperen Toprak,et al.  Piezoelectric energy harvesting: State-of-the-art and challenges , 2014 .

[163]  Xingjian Jing,et al.  A comprehensive review on vibration energy harvesting: Modelling and realization , 2017 .

[164]  Matthew Bryant,et al.  Modeling and Testing of a Novel Aeroelastic Flutter Energy Harvester , 2011 .

[165]  Albert P. Pisano,et al.  Corrugated aluminum nitride energy harvesters for high energy conversion effectiveness , 2011 .

[166]  A. Nayfeh,et al.  Piezoelectric energy harvesting from transverse galloping of bluff bodies , 2012 .

[167]  Y. Andreopoulos,et al.  Wake of a cylinder: a paradigm for energy harvesting with piezoelectric materials , 2010 .

[168]  Abdessattar Abdelkefi,et al.  An energy harvester using piezoelectric cantilever beams undergoing coupled bending–torsion vibrations , 2011 .

[169]  Yiannis Andreopoulos,et al.  The performance of a self-excited fluidic energy harvester , 2012 .

[170]  A. Barrero-Gil,et al.  Enhanced mechanical energy extraction from transverse galloping using a dual mass system , 2015 .

[171]  Roussel Rahman,et al.  Vibration energy harvesting in a small channel fluid flow using piezoelectric transducer , 2016 .

[172]  A. Erturk,et al.  On the Role of Nonlinearities in Vibratory Energy Harvesting: A Critical Review and Discussion , 2014 .

[173]  Ali Bakhshandeh Rostami,et al.  Renewable energy harvesting by vortex-induced motions: Review and benchmarking of technologies , 2017 .

[174]  Jaehwan Kim,et al.  A review of piezoelectric energy harvesting based on vibration , 2011 .

[175]  A. Smits,et al.  Energy harvesting eel , 2001 .

[176]  D. Inman,et al.  Nonlinear piezoelectricity in electroelastic energy harvesters: Modeling and experimental identification , 2010 .

[177]  X. D. Xie,et al.  Ocean wave energy harvesting with a piezoelectric coupled buoy structure , 2015 .

[178]  Muhammad R. Hajj,et al.  Phenomena and modeling of piezoelectric energy harvesting from freely oscillating cylinders , 2012 .

[179]  Yongmin Yang,et al.  Metamaterials-based enhanced energy harvesting: A review , 2014 .

[180]  Lin Zheng.  Advances in ocean wave energy converters using piezoelectric materials , 2011 .

[181]  Dibin Zhu,et al.  Vibration Energy Harvesting: Machinery Vibration, Human Movement and Flow Induced Vibration , 2011 .

[182]  Muhammad R. Hajj,et al.  Effects of nonlinear piezoelectric coupling on energy harvesters under direct excitation , 2012 .

[183]  Huajun Sun,et al.  A brief review of Ba(Ti 0.8 Zr 0.2 )O 3 -(Ba 0.7 Ca 0.3 )TiO 3 based lead-free piezoelectric ceramics: Past, present and future perspectives , 2018 .

[184]  S. Priya.  Modeling of electric energy harvesting using piezoelectric windmill , 2005 .

[185]  Ali H. Nayfeh,et al.  Modeling and analysis of piezoaeroelastic energy harvesters , 2012 .

[186]  Muhammad R. Hajj,et al.  Modeling, validation, and performance of low-frequency piezoelectric energy harvesters , 2014 .

[187]  Luca Bruzzone,et al.  Mechanical design and simulation of an onshore four-bar wave energy converter , 2017 .

[188]  Stephen J. Elliott,et al.  Output power and efficiency of electromagnetic energy harvesting systems with constrained range of motion , 2013 .

[189]  Ali H. Nayfeh,et al.  Power harvesting from transverse galloping of square cylinder , 2012 .

[190]  Martin A. Afromowitz,et al.  DESIGN, FABRICATION AND TESTING OF FIXED-VALVE MICRO-PUMPS , 1995 .

[191]  D. Inman,et al.  On Mechanical Modeling of Cantilevered Piezoelectric Vibration Energy Harvesters , 2008 .

[192]  Q. Tang,et al.  The era of water-enabled electricity generation from graphene , 2016 .