# Basic Analytical Tools for the Design of Resonant Vibration Transducers

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## Abstract

The presented review of existing work on electromagnetic inertial vibration transducers in Chap. 1 shows that there has been much interest in the design of vibration energy harvesting devices. Consequently excellent work has been done by numerous research facilities and a multiplicity of micro– and centimeter scale prototype vibration transducers has been developed. The basic analytical theory behind most of the presented devices is commonly known in the energy harvesting society. It is based on a well understood linear second–order spring–mass–damper system with base excitation. Specific analysis of vibration transducers was first proposed by Williams and Yates [15]. Since then the theory has been modified and described in various ways even though the basic findings are more or less the same. In this respect, an analytical expression for the maximum output power that can be extracted from a certain vibration was derived (also for constrains such as the limitation of the inner displacement of the seismic mass [64]) and the optimization of parameters such as the optimal load resistance or the electromagnetic damping factor was discussed. However, as will be shown, in most of these cases it is rather difficult even impossible to use the results of the analytical modelling directly for the design process of application oriented developments. This is because the theory does not consider geometrical parameters and is based on simplifying assumptions which often do not correlate well with the “real world” (e.g. random vibration instead of harmonic excitation, complex load circuit instead of simple resistance or appreciable magnetic flux leakage instead of homogeneous magnetic field distribution). However the analytical modelling is useful for understanding the influence of the most important system parameters. Furthermore it offers a deeper insight into the overall system behavior.

## Keywords

Maximum Output Power Tunnel Borer Machine Electromagnetic Coupling Acceleration Amplitude Vibration Source## References

- 3.Available in the internet: state April 2010Google Scholar
- 15.C.B. Williams, R.B. Yates, Analysis of a micro–electric generator for microsystems, in
*Proceedings of Transducers’95: Eurosensors IX*. The 8th International Conference on Solid–State Sensors and Actuators, and Eurosensors*IX*, Stockholm, June 1995, pp. 369–372Google Scholar - 16.C.R. Mc Innes, D.G. Gorman, M.P. Cartmell, Enhanced vibrational energy harvesting using non–linear stochastic resonance. J. Sound Vibrat.
**318**(4–5), 655–662 (2008)ADSCrossRefGoogle Scholar - 20.D. Spreemann, A. Willmann, B. Folkmer, Y. Manoli, Characterization and in situ test of vibration transducers for energy–harvesting in automobile applications, in
*Proceeding of PowerMEMS 2008*, Sendai, Japan, November 2008, pp. 261–264Google Scholar - 23.D. Spreemann, D. Hoffmann, E. Hymon, B. Folkmer, Y. Manoli, Über die Verwendung nichtlinearer Federn für miniaturisierte Vibrationswandler, in
*Proceedings of Mikrosystemtechnik Kongress*, Dresden, 15–17 Oct 2007 (in German)Google Scholar - 28.D.J. Inman,
*Engineering Vibration*, 2nd edn. (Prentice Hall, Upper Saddle River, 2000). ISBN ISBN 0–13–726142–XGoogle Scholar - 30.E.I. Rivin,
*Passive Vibration Isolation*(ASME Press, New York, 2003). ISBN 0-79-180187-XCrossRefGoogle Scholar - 35.G. Genta,
*Vibration of Structures and Machines: Practical Aspects*, 3rd edn. (Springer, New York/Berlin/Heidelberg, 1998). ISBN ISBN 978–0–387–98506–0Google Scholar - 38.H.A. Wheeler, Simple inductance formulas for radio coils. Proc. IRE
**16**(10), 1398–1400 (1928)CrossRefGoogle Scholar - 47.E. Kallenbach, R. Eick, P. Quendt, T. Ströhla, K. Feindt, M. Kallenbach,
*Elektromagnete Grundlagen, Berechnung, Entwurf und Anwendung*(Teubner, Stuttgart, 2003). ISBN ISBN 3–519–16163–XGoogle Scholar - 48.L. Meirovitch,
*Elements of Vibration Analysis*(Tata McGraw-Hill, New York, 1986). ISBN ISBN-10: 9780070413429Google Scholar - 58.N.G. Stephen, On energy harvesting from ambient vibration. J. Sound Vibrat.
**293**, 409–425 (2005)ADSCrossRefGoogle Scholar - 64.P.D. Mitcheson, T.C. Green, E.M. Yeatman, A.S. Holmes, Architectures for vibration–driven micropower generators. IEEE/ASME J. Microelectromechanical Syst.
**13**(3), 429–440 (2004)CrossRefGoogle Scholar - 66.R. Ramlan, Effects of non–linear stiffness on performance of an energy harvesting device, PhD book, University of Southampton, 2009Google Scholar
- 73.S.J. Roundy, Energy scavenging for wireless sensor nodes with a focus on vibration to electricity conversion, PhD book, University of California, Berkley, 2003Google Scholar
- 77.T. Link, Strukturdynamische Fehlermodellierung mikromechanischer Drehratensensoren für den Einsatz in der inertialen Navigation PhD book, University of Freiburg, 2007 (in German)Google Scholar
- 80.W.T. Thomson,
*Theory of Vibrations with Applications*(Prentice Hall, Upper Saddle River, 1998). ISBN 0-13-651068-XGoogle Scholar