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Mathematical Modelling of Piezoelectric Generators on the Base of the Kantorovich Method

  • Arkadiy N. SolovievEmail author
  • Valerii A. Chebanenko
  • Ivan A. Parinov
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  • 770 Downloads
Part of the Advanced Structured Materials book series (STRUCTMAT, volume 81)

Abstract

In this chapter, applied semi-analytical theories were constructed, allowing preliminary estimations of the output characteristics of piezoelectric generators (PEG) of various configurations. The developed theories are based on the Hamiltonian principle, extended to the theory of electroelasticity. In the first part of the work, within the framework of the Euler-Bernoulli hypotheses, a model for a cantilever PEG was developed. The main model’s peculiarity is the consideration of the structural features of cantilever PEGs. In the second part, a model was developed for multilayer stacked PEGs, where the energy generation process was considered as forced oscillations of an electroelastic rod. Solutions for both cases were carried out using the Kantorovich method. The adequacy of the theories obtained in both cases was verified by comparison with finite-element calculations.

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Notes

Acknowledgements

This work has been supported by the Government Contract (project part) 9.1001.2017/PCh, by the Russian Foundation for the Basic Research Grant 16-58-52013 MNT-a and by Russian State Mission 007-01114-16 PR (project 0256-2015-0074).

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Copyright information

© Springer Nature Singapore Pte Ltd. 2018

Authors and Affiliations

  • Arkadiy N. Soloviev
    • 1
    Email author
  • Valerii A. Chebanenko
    • 2
  • Ivan A. Parinov
    • 3
  1. 1.Don State Technical University, Gagarin sq., 1 & I. I. Vorovich Institute of Mathematics, Mechanics and Computer SciencesSouthern Federal UniversityRostov-on-DonRussia
  2. 2.Southern Scientific Center of Russian Academy of ScienceRostov-on-DonRussia
  3. 3.I. I. Vorovich Institute of Mathematics, Mechanics and Computer SciencesSouthern Federal UniversityRostov-on-DonRussia

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