Bimorph

Abstract: Advances in low power VLSI design, along with the potentially low duty cycle of wireless sensor nodes open up the possibility of powering small wireless computing devices from scavenged ambient power. A broad review of potential power scavenging technologies and conventional energy sources is first presented. Low-level vibrations occurring in common household and office environments as a potential power source are studied in depth. The goal of this paper is not to suggest that the conversion of vibrations is the best or most versatile method to scavenge ambient power, but to study its potential as a viable power source for applications where vibrations are present. Different conversion mechanisms are investigated and evaluated leading to specific optimized designs for both capacitive MicroElectroMechancial Systems (MEMS) and piezoelectric converters. Simulations show that the potential power density from piezoelectric conversion is significantly higher. Experiments using an off-the-shelf PZT piezoelectric bimorph verify the accuracy of the models for piezoelectric converters. A power density of 70 @mW/cm^3 has been demonstrated with the PZT bimorph. Simulations show that an optimized design would be capable of 250 @mW/cm^3 from a vibration source with an acceleration amplitude of 2.5 m/s^2 at 120 Hz.

Abstract: About the Authors. Preface. 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. Index.

Abstract: Piezoelectric transduction has received great attention for vibration-to-electric energy conversion over the last five years. A typical piezoelectric energy harvester is a unimorph or a bimorph cantilever located on a vibrating host structure, to generate electrical energy from base excitations. Several authors have investigated modeling of cantilevered piezoelectric energy harvesters under base excitation. The existing mathematical modeling approaches range from elementary single-degree-of-freedom models to approximate distributed parameter solutions in the sense of Rayleigh–Ritz discretization as well as analytical solution attempts with certain simplifications. Recently, the authors have presented the closed-form analytical solution for a unimorph cantilever under base excitation based on the Euler–Bernoulli beam assumptions. In this paper, the analytical solution is applied to bimorph cantilever configurations with series and parallel connections of piezoceramic layers. The base excitation is assumed to be translation in the transverse direction with a superimposed small rotation. The closed-form steady state response expressions are obtained for harmonic excitations at arbitrary frequencies, which are then reduced to simple but accurate single-mode expressions for modal excitations. The electromechanical frequency response functions (FRFs) that relate the voltage output and vibration response to translational and rotational base accelerations are identified from the multi-mode and single-mode solutions. Experimental validation of the single-mode coupled voltage output and vibration response expressions is presented for a bimorph cantilever with a tip mass. It is observed that the closed-form single-mode FRFs obtained from the analytical solution can successfully predict the coupled system dynamics for a wide range of electrical load resistance. The performance of the bimorph device is analyzed extensively for the short circuit and open circuit resonance frequency excitations and the accuracy of the model is shown in all cases.

Abstract: Thin film shape memory alloys (SMAs) have the potential to become a primary actuating mechanism for mechanical devices with dimensions in the micron-to-millimeter range requiring large forces over long displacements. The work output per volume of thin film SMA microactuators exceeds that of other microactuation mechanisms such as electrostatic, magnetic, thermal bimorph, piezoelectric, and thermopneumatic, and it is possible to achieve cycling frequencies on the order of 100 Hz due to the rapid heat transfer rates associated with thin film devices. In this paper, a quantitative comparison of several microactuation schemes is made, techniques for depositing and characterizing Ni-Ti-based shape memory films are evaluated, and micromachining and design issues for SMA microactuators are discussed. The substrate curvature method is used to investigate the thermo-mechanical properties of Ni-Ti-Cu SMA films, revealing recoverable stresses up to 510 MPa, transformation temperatures above 32/spl deg/C, and hysteresis widths between 5 and 13/spl deg/C. Fatigue data shows that for small strains, applied loads up to 350 MPa can be sustained for thousands of cycles. Two micromachined shape memory-actuated devices-a microgripper and microvalve-also are presented.

Abstract: Vibration energy scavenging, harvesting ambient vibrations in structures for conversion into usable electricity, provides a potential power source for emerging technologies including wireless sensor networks. Most vibration energy scavenging devices developed to date operate effectively at a single specific frequency dictated by the device's design. However, for this technology to be commercially viable, vibration energy scavengers that generate usable power across a range of driving frequencies must be developed. This paper details the design and testing of a tunable-resonance vibration energy scavenger which uses the novel approach of axially compressing a piezoelectric bimorph to lower its resonance frequency. It was determined that an axial preload can adjust the resonance frequency of a simply supported bimorph to 24% below its unloaded resonance frequency. The power output to a resistive load was found to be 65–90% of the nominal value at frequencies 19–24% below the unloaded resonance frequency. Prototypes were developed that produced 300–400 µW of power at driving frequencies between 200 and 250 Hz. Additionally, piezoelectric coupling coefficient values were increased using this method, with keff values rising as much as 25% from 0.37 to 0.46. Device damping increased 67% under preload, from 0.0265 to 0.0445, adversely affecting the power output at lower frequencies. A theoretical model modified to include the effects of preload on damping predicted power output to within 0–30% of values obtained experimentally. Optimal load resistance deviated significantly from theory, and merits further investigation.