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Piezoelectric Energy Harvesting



Piezoelectric Energy Harvesting

Alper Erturk, Daniel J. Inman

ISBN: 978-1-119-99135-9 April 2011 416 Pages

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The transformation of vibrations into electric energy through the use of piezoelectric devices is an exciting and rapidly developing area of research with a widening range of applications constantly materialising. With Piezoelectric Energy Harvesting, world-leading researchers provide a timely and comprehensive coverage of the electromechanical modelling and applications of piezoelectric energy harvesters. They present principal modelling approaches, synthesizing fundamental material related to mechanical, aerospace, civil, electrical and materials engineering disciplines for vibration-based energy harvesting using piezoelectric transduction.

Piezoelectric Energy Harvesting provides the first comprehensive treatment of distributed-parameter electromechanical modelling for piezoelectric energy harvesting with extensive case studies including experimental validations, and is the first book to address modelling of various forms of excitation in piezoelectric energy harvesting, ranging from airflow excitation to moving loads, thus ensuring its relevance to engineers in fields as disparate as aerospace engineering and civil engineering.

Coverage includes:

  • Analytical and approximate analytical distributed-parameter electromechanical models with illustrative theoretical case studies as well as extensive experimental validations
  • Several problems of piezoelectric energy harvesting ranging from simple harmonic excitation to random vibrations 
  • Details of introducing and modelling piezoelectric coupling for various problems
  • Modelling and exploiting nonlinear dynamics for performance enhancement, supported with experimental verifications
  • Applications ranging from moving load excitation of slender bridges to airflow excitation of aeroelastic sections 
  • A review of standard nonlinear energy harvesting circuits with modelling aspects.
About the Authors.


1. Introduction to Piezoelectric Energy Harvesting.

1.1 Vibration-Based Energy Harvesting Using Piezoelectric Transduction.

1.2 An Examples of a Piezoelectric Energy Harvesting System.

1.3 Mathematical Modeling of Piezoelectric Energy Harvesters.

1.4 Summary of the Theory of Linear Piezoelectricity.

1.5 Outline of the Book.

2. Base Excitation Problem for Cantilevered Structures and Correction of the Lumped-Parameter Electromechanical Model.

2.1 Base Excitation Problem for the Transverse Vibrations.

2.2 Correction of the Lumped-Parameter Base Excitation Model for Transverse Vibrations.

2.3 Experimental Case Studies for Validation of the Correction Factor.

2.4 Base Excitation Problem for Longitudinal Vibrations and Correction of its Lumped-Parameter Model.

2.5 Correction Factor in the Electromechanically Coupled Lumped-Parameter Equations and a Theoretical Case Study.

2.6 Summary.

2.7 Chapter Notes.

3. Analytical Distributed-Parameter Electromechanical Modeling of Cantilevered Piezoelectric Energy Harvesters.

3.1 Fundamentals of the Electromechanically Coupled Distributed-Parameter Model.

3.2 Series Connection of the Piezoceramic Layers.

3.3 Parallel Connection of Piezoceramic Layers.

3.4 Equivalent Representation of the Series and the Parallel Connection Cases.

3.5 Single-Mode Electromechanical Equations for Modal Excitations.

3.6 Multi-mode and Single-Mode Electromechanical FRFs.

3.7 Theoretical Case Study.

3.8 Summary.

3.9 Chapter Notes.

4. Experimental Validation of the Analytical Solution for Bimorph Configurations.

4.1 PZT-5H Bimorph Cantilever without a Tip Mass.

4.2 PZT-5H Bimorph Cantilever with a Tip Mass.

4.3 PZT-5A Bimorph Cantilever.

4.4 Summary.

4.5 Chapter Notes.

5. Dimensionless Equations, Asymptotic Analyses, and Closed-Form Relations for Parameter Identification and Optimization.

5.1 Dimensionless Representation of the Single-Mode Electromechanical FRFs.

5.2 Asymptotic Analyses and Resonance Frequencies.

5.3 Identification of Mechanical Damping.

5.4 Identification of the Optimum Electrical Load for Resonance Excitation.

5.5 Intersection of the Voltage Asymptotes and a Simple Technique for the Experimental Identification of the Optimum Load Resistance.

5.6 Vibration Attenuation Amplification from the Short-Circuit to Open-Circuit Conditions.

5.7 Experimental Validation for a PZT-5H Bimorph Cantilever.

5.8 Summary.

5.9 Chapter Notes.

6. Approximate Analytical Distributed-Parameter Electromechanical Modeling of Cantilevered Piezoelectric Energy Harvesters.

6.1 Unimorph Piezoelectric Energy Harvester Configuration.

6.2 Electromechanical Euler-Bernoulli Model with Axial Deformations.

6.3 Electromechanical Rayleigh Model with Axial Deformations.

6.4 Electromechanical Timoshenko Model with Axial Deformations.

6.5 Modeling of Symmetric Configurations.

6.6 Presence of a Tip Mass in the Euler-Bernoulli, Rayleigh, and Timoshenko Models.

6.7 Comments on the Kinematically Admissible Trial Functions.

6.8 Experimental Validation of the Assumed-Modes Solution for a Bimorph Cantilever.

6.9 Experimental Validation for a Two-Segment Cantilever.

6.10 Summary.

6.11 Chapter Notes.

7. Modeling of Piezoelectric Energy Harvesting for Various Forms of Dynamic Loading.

7.1 Governing Electromechanical Equations.

7.2 Periodic Excitation.

7.3 White Noise Excitation.

7.4 Excitation Due to Moving Loads.

7.5 Local Strain Fluctuations on Large Structures.

7.6 Numerical Solution for General Transient Excitation.

7.7 Case Studies.

7.8 Summary.

7.9 Chapter Notes.

8. Modeling and Exploiting Mechanical Nonlinearities in Piezoelectric Energy Harvesting.

8.1 Perturbation Solution of the Piezoelectric Energy Harvesting Problem: the Method of Multiple Scales.

8.2 Monostable Duffing Oscillator with Piezoelectric Coupling.

8.3 Bistable Duffing Oscillator with Piezoelectric Coupling: the Piezomagnetoelastic Energy Harvester.

8.4 Experimental Performance Results of the Bistable Peizomagnetoelastic Energy Harvester.

8.5 A Bistable Plate for Piezoelectric Energy Harvesting.

8.6 Summary.

8.7 Chapter Notes.

9. Piezoelectric Energy Harvesting from Aeroelastic Vibrations.

9.1 A Lumped-Parameter Piezoaeroelastic Energy Harvester Model for Harmonic Response.

9.2 Experimental Validations of the Lumped-Parameter Model at the Flutter Boundary.

9.3 Utilization of System Nonlinearities in Piezoaeroelastic Energy Harvesting.

9.4 A Distributed-Parameter Piezoaeroelastic Model for Harmonic Response: Assumed-Modes Formulation.

9.5 Time-Domain and Frequency-Domain Piezoaeroelastic Formulations with Finite-Element Modeling.

9.6 Theoretical Case Study for Airflow Excitation of a Cantilevered Plate.

9.7 Summary.

9.8 Chapter Notes.

10. Effects of Material Constants and Mechanical Damping on Power Generation.

10.1 Effective Parameters of Various Soft Ceramics and Single Crystals.

10.2 Theoretical Case Study for Performance Comparison of Soft Ceramics and Single Crystals.

10.3 Effective Parameters of Typical Soft and Hard Ceramics and Single Crystals.

10.4 Theoretical Case Study for Performance Comparison of Soft and Hard Ceramics and Single Crystals.

10.5 Experimental Demonstration for PZT-5A and PZT-5H Cantilevers.

10.6 Summary.

10.7 Chapter Notes.

11. A Brief Review of the Literature of Piezoelectric Energy Harvesting Circuits.

11.1 AC-DC Rectification and Analysis of the Rectified Output.

11.2 Two-Stage Energy Harvesting Circuits: DC-DC Conversion for Impedance Matching.

11.3 Synchronized Switching on Inductor for Piezoelectric Energy Harvesting.

11.4 Summary.

11.5 Chapter Notes.

Appendix A. Piezoelectric Constitutive Equations.

Appendix B. Modeling of the Excitation Force in Support Motion Problems of Beams and Bars.

Appendix C. Modal Analysis of a Uniform Cantilever with a Tip Mass.

Appendix D. Strain Nodes of a Uniform Thin Beam for Cantilevered and Other Boundary Conditions.

Appendix E. Numerical Data for PZT-5A and PZT-5H Piezoceramics.

Appendix F. Constitutive Equations for an Isotropic Substructure.

Appendix G. Essential Boundary Conditions for Cantilevered Beams.

Appendix H. Electromechanical Lagrange Equations Based on the Extended Hamilton’s Principle.


“This is certainly an interesting book for those who design vibrational piezoelectric energy-harvesting devices, providing an extensive review of many of the modeling techniques used.”  (IEEE Electrical Insulation Magazine, 1 May 2013)