This paper reviews the state-of-the art in vibration energy harvesting for wireless, self-powered microsystems. Vibration-powered generators are typically, although not exclusively, inertial spring and mass systems. The characteristic equations for inertial-based generators are presented, along with the specific damping equations that relate to the three main transduction mechanisms employed to extract energy from the system. These transduction mechanisms are: piezoelectric, electromagnetic and electrostatic. Piezoelectric generators employ active materials that generate a charge when mechanically stressed. A comprehensive review of existing piezoelectric generators is presented, including impact coupled, resonant and human-based devices. Electromagnetic generators employ electromagnetic induction arising from the relative motion between a magnetic flux gradient and a conductor. Electromagnetic generators presented in the literature are reviewed including large scale discrete devices and wafer-scale integrated versions. Electrostatic generators utilize the relative movement between electrically isolated charged capacitor plates to generate energy. The work done against the electrostatic force between the plates provides the harvested energy. Electrostatic-based generators are reviewed under the classifications of in-plane overlap varying, in-plane gap closing and out-of-plane gap closing; the Coulomb force parametric generator and electret-based generators are also covered. The coupling factor of each transduction mechanism is discussed and all the devices presented in the literature are summarized in tables classified by transduction type; conclusions are drawn as to the suitability of the various techniques.

/pdf/energy-harvesting-vibration-sources-for-microsystems-46t885pwdp.pdf

Energy harvesting vibration sources for microsystems applications

The Theory of Matrices. By F R. Gantmacher. Two volumes, pp. 374 and 276. 1959. (Translated from the Russian by K. A. Hirsch; Chelsea Publishing Company, New York)

Preface. Symbols. Chapter 1. Introduction: Basic Concepts and Terminology. Chapter 2. Vibration of Discrete Systems: Brief Review. Chapter 3. Derivation of Equations: Equilibrium Approach. Chapter 4. Derivation of Equations: Variation Approach. Chapter 5. Derivation of Equations: Integral Equation Approach. Chapter 6. Solution Procedure: Eigenvalue and Modal Analysis Approach. Chapter 7. Solution Procedure: Integral Transform Methods. Chapter 8. Transverse Vibration of Strings. Chapter 9. Longitudinal Vibration of Bars. Chapter 10. Torsional Vibration of Shafts. Chapter 11. Transverse Vibration of Beams. Chapter 12. Vibration of Circular Rings and Curved Beams. Chapter 13.Vibration of Membranes. Chapter 14. Transverse Vibration of Plates. Chapter 15. Vibration of Shells. Chapter 16. Elastic Wave Propagation. Chapter 17. Approximate Analytical Methods. A. Basic Equations of Elasticity. B. Laplace and Fourier Transforms. Index.

/pdf/vibration-of-continuous-systems-463s95iwfy.pdf

Vibration of continuous systems

Vibration energy harvesting is receiving a considerable amount of interest as a means for powering wireless sensor nodes This paper presents a small (component volume 01 cm3, practical volume 015 cm3) electromagnetic generator utilizing discrete components and optimized for a low ambient vibration level based upon real application data The generator uses four magnets arranged on an etched cantilever with a wound coil located within the moving magnetic field Magnet size and coil properties were optimized, with the final device producing 46 µW in a resistive load of 4 k? from just 059 m s-2 acceleration levels at its resonant frequency of 52 Hz A voltage of 428 mVrms was obtained from the generator with a 2300 turn coil which has proved sufficient for subsequent rectification and voltage step-up circuitry The generator delivers 30% of the power supplied from the environment to useful electrical power in the load This generator compares very favourably with other demonstrated examples in the literature, both in terms of normalized power density and efficiency

/pdf/a-micro-electromagnetic-generator-for-vibration-energy-acpebp9i50.pdf

A micro electromagnetic generator for vibration energy harvesting

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.

/pdf/an-experimentally-validated-bimorph-cantilever-model-for-qzwpq105mk.pdf

N.G. Stephen

Papers

On energy harvesting from ambient vibration

Timoshenko’s Shear Coefficient From a Beam Subjected to Gravity Loading

A second order beam theory

The second spectrum of Timoshenko beam theory - Further assessment

Shape functions of three-dimensional Timoshenko beam element