Skip to main content

Advertisement

SpringerLink
Log in

Modeling and analysis of piezoelectric beam with periodically variable cross-sections for vibration energy harvesting

  • Published:
Applied Mathematics and Mechanics Aims and scope Submit manuscript

Abstract

A bimorph piezoelectric beam with periodically variable cross-sections is used for the vibration energy harvesting. The effects of two geometrical parameters on the first band gap of this periodic beam are investigated by the generalized differential quadrature rule (GDQR) method. The GDQR method is also used to calculate the forced vibration response of the beam and voltage of each piezoelectric layer when the beam is subject to a sinusoidal base excitation. Results obtained from the analytical method are compared with those obtained from the finite element simulation with ANSYS, and good agreement is found. The voltage output of this periodic beam over its first band gap is calculated and compared with the voltage output of the uniform piezoelectric beam. It is concluded that this periodic beam has three advantages over the uniform piezoelectric beam, i.e., generating more voltage outputs over a wide frequency range, absorbing vibration, and being less weight.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

References

  1. Kim, H. S., Kim, J. H., and Kim, J. A review of piezoelectric energy harvesting based on vibration. International Journal Precision Engineering and Manufacturing, 12, 1129–1141 (2011)

    Article  Google Scholar 

  2. Li, F. and Song, Z. Vibration analysis and active control of nearly periodic two-span beams with piezoelectric actuator/sensor pairs. Applied Mathematics and Mechanics (English Edition), 36, 279–292 (2015) DOI 10.1007/s10483-015-1912-6

    Article  MathSciNet  MATH  Google Scholar 

  3. Elvin, N. and Erturk, A. Advances in Energy Harvesting Methods, Springer, New York, 17–52 (2013)

    Book  Google Scholar 

  4. Eichhorn, C., Goldschmidtboeing, F., and Woias, P. A frequency tunable piezoelectric energy converter based on a cantilever beam. Proceedings of Power MEMS, Tohoku University Press, Sendai, 309–312 (2008)

    Google Scholar 

  5. Reissman, T., Wolff, E. M., and Garcia, E. Piezoelectric resonance shifting using tunable nonlinear stiffness. SPIE Proceeding of Active and Passive Smart Structures and Integrated Systems, 7288, 7288G (2009)

    Google Scholar 

  6. Zhu, D., Roberts, S., Tudor, J., and Beeby, S. Closed loop frequency tuning of a vibration-based microgenerator. Proceedings of Power MEMS, Tohoku University Press, Sendai, 229–232 (2008)

    Google Scholar 

  7. Shahruz, S. M. Design of mechanical band-pass filters for energy scavenging. Journal of Sound and Vibration, 292, 987–998 (2006)

    Article  Google Scholar 

  8. Steurer, W. and Sutter-Widmer, D. Photonic and phononic quasi crystals. Journal of Physics D: Applied Physics, 40, 229–247 (2007)

    Article  Google Scholar 

  9. Rao, S. S. Vibration of Continuous Systems, John Wiley & Sons, Hoboken, 321–323 (2007)

    Google Scholar 

  10. Muthalif, A. G. A. and Nordin, N. H. D. Optimal piezoelectric beam shape for single and broadband vibration energy harvesting: modeling, simulation and experimental results. Mechanical System and Signal Processing, 54–55, 417–426 (2015)

    Article  Google Scholar 

  11. Kittel, C. Introduction to Solid State Physics, 8th ed., John Wiley & Sons, New York (2005)

    MATH  Google Scholar 

  12. ANSI/IEEE Std 176-1987. IEEE Standard on Piezoelectricity, Standards Committee of the IEEE Ultrasonic, Ferroelectrics, and Frequency Control Society, New York (1988)

    Google Scholar 

  13. Aryanpur, R. Two Bimorph Piezoelectric Energy Harvester for Vibrations, M. Sc. dissertation, Tufts University, Medford, 20–22 (2012)

    Google Scholar 

  14. Bellman, R. and Casti, J. Differential quadrature and long-term integration. Journal of Mathematical Analysis and Applications, 34, 235–238 (1971)

    Article  MathSciNet  MATH  Google Scholar 

  15. Xiang, H. J. and Shi, Z. F. Analysis of flexural vibration band gaps in periodic beams using differential quadrature method. Computer and Structures, 87, 1559–1566 (2009)

    Article  Google Scholar 

  16. Eftekhari, S. A. A differential quadrature procedure for inplane vibration analysis of variable thickness circular arches traversed by a moving point load. Applied Mathematical Modelling, 40, 4640–4663 (2016)

    Article  MathSciNet  Google Scholar 

  17. Wu, T. Y. and Liu, G. R. A differential quadrature as a numerical method to solve differential equations. Computational Mechanics, 24, 197–205 (1999)

    Article  MathSciNet  MATH  Google Scholar 

  18. Shu, C. Differential Quadrature and Its Applications in Engineering, Springer, London, 52–65 (2000)

    Book  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Department of Mechanical Engineering, Yazd University, Yazd, 89195-741, Iran

    M. Hajhosseini & M. Rafeeyan

Authors
  1. M. Hajhosseini
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. M. Rafeeyan
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to M. Hajhosseini.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Hajhosseini, M., Rafeeyan, M. Modeling and analysis of piezoelectric beam with periodically variable cross-sections for vibration energy harvesting. Appl. Math. Mech.-Engl. Ed. 37, 1053–1066 (2016). https://doi.org/10.1007/s10483-016-2117-8

Download citation

  • Received:

  • Revised:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s10483-016-2117-8

Key words

Chinese Library Classification

2010 Mathematics Subject Classification

Search

Navigation