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ISSN: 2475-4811 (print)
ISSN: 2475-482X (online)
Journal of Vibration Testing and System Dynamics

C. Steve Suh (editor), Pawel Olejnik (editor),

Xianguo Tuo (editor)

Pawel Olejnik (editor)

Lodz University of Technology, Poland

Email: pawel.olejnik@p.lodz.pl

C. Steve Suh (editor)

Texas A&M University, USA

Email: ssuh@tamu.edu

Xiangguo Tuo (editor)

Sichuan University of Science and Engineering, China

Email: tuoxianguo@suse.edu.cn

Global Sensitivity and Stability Analysis of a Parametrically Excited Energy Harvesting System

Journal of Vibration Testing and System Dynamics 7(3) (2023) 253--263 | DOI:10.5890/JVTSD.2023.09.001

Luiz Oreste Cauz$^{1,2}$, F\'{a}bio Roberto Chavarette$^{1}$, Estev\~ao Fuzaro de Almeida$^{1}$

$^{1}$ Department of Mechanical Engineering, S~ao Paulo State University, (FEIS - UNESP) - Ilha Solteira, S~ao Paulo State, Brazil

$^{2}$ Universidades Estadual de Mato Grosso do Sul - UEMS, Nova Andradina, Mato Grosso do Sul, Brazil

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Abstract

Energy harvesting is the process of capturing and transforming ambient energy into a useable form. Solar energy, thermal gradients, acoustical and mechanical vibrations are all examples of energy harvesting sources. Vibration Energy Harversting Systems (VEHS) are systems that employ vibrations as a source. VEHS-based energy harvesters are known as a supplementary power source, which provide small amounts of energy for slow-load applications or to charge and operate remote devices and sensors whose require small amounts of energy to operate, such as hearing aids, pacemakers, spinal cord stimulators, and microelectromechanical systems. The objective of this work is to analyze the stability of a parametrically excited energy harvesting system that uses piezoelectric materials as a transducer. The objective is to optimize the energy produced by analyzing the system's behavior while the physical parameter values are changed. In this regard, it is essential to do a preliminary global sensitivity analysis of the physical parameters in order to determine which parameters, when altered, influence more to energy production. The Sobol' indices are used to do the sensitivity analysis. The stability analysis is then performed using the results of Floquet's Theory and the state transition matrix approximation techniques developed by Sinha and Butcher. Sinha and Butcher's technique, based on Picard iterations and Chebyshev polynomial expansions, aims to find approximate solutions for periodic systems in time. An essential characteristic that is well documented in the literature is that vibrational energy harvesting systems have efficient responses when the physical parameters of the system are set so that the system operates in resonance with the parametric excitation source. As a result, when the system is in resonance with the external excitation source, significant system stability outcomes are obtained.

References

  1. [1] Challa, V.R., Prasad, M., Shi, Y., and Fisher, F.T., (2008), A vibration energy harvesting device with bidirectional resonance frequency tunability, Smart Materials and Structures, 17(1), 15-35.
  2. [2] Eichhorn, C., Goldschmidtboeing, F., Porro, Y., and Woias, P. (2009), A piezoelectric harvester with an integrated frequency-tuning mechanism, Power MEMS, 45-48.
  3. [3] Zhu, D. (2011), Vibration energy harvesting: machinery vibration, human movement and flow induced vibration, Sustainable Energy Harvesting Technologies-Past, Present and Future, 1, 22-54.
  4. [4] Marelli, S., Lamas, C., Sudret, B., Konakli, K., and Mylonas, C. (2019), Uqlab user manual-sensitivity analysis, 2-106.
  5. [5] Abdelkefi, A., Hajj, M., and Nayfeh, A.H., (2012), Uncertainty quantification of piezoelectric energy harvesters from aeroelastic vibrations, MATEC Web of Conferences, EDP Sciences, Vol. 1.
  6. [6] Colón, D., Cunha, Jr, A., Kaczmarczyk, S., and Balthazar, J.M. (2017), On dynamic analysis and control of an elevator system using polynomial chaos and Karhunen-Lo\`{e}ve approaches, Procedia engineering, Elsevier, 199, 1629-1634.
  7. [7] Pereira, M.F.V, Balthazar, J.M., dos Santos, D.A., Tusset, A.M., Castro, D.F., and Prado, I.A.A. (2017), A note on polynomial chaos expansions for designing a linear feedback control for nonlinear systems, Nonlinear Dynamics, 87, 1653-1666.
  8. [8] Ruiz, O.R. and Meruane, V. (2017), Uncertainties propagation and global sensitivity analysis of the frequency response function of piezoelectric energy harvesters, Smart Materials and Structures, 26(6), 065003.
  9. [9] Aloui, R., Larbi, W., and Chouchane, M., (2019), Global sensitivity analysis of piezoelectric energy harvesters, Composite Structures, 228, 111317.
  10. [10] Aloui, R., Larbi, W., and Chouchane, M., (2020), Uncertainty quantification and global sensitivity analysis of piezoelectric energy harvesting using macro fiber composites, Smart Materials and Structures, 29(9), 095014.
  11. [11] Daqaq, M.F., Stabler, C., Qaroush, Y., and Seuaciuc-Osorio, T. (2009), Investigation of power harvesting via parametric excitations, Journal of Intelligent Material Systems and Structures, 20, 545-557.
  12. [12] Norenberg, J.P., Cunha Jr, A., da Silva, S., and Varoto, P.S. (2021), Global sensitivity analysis of (a) symmetric energy harvesters, Nonlinear Dynamics, 109(2), 443-458.
  13. [13] Marelli, S. and Sudret, B. (2015), Uqlab user manual-polynomial chaos expansions, Chair of risk, Safety $\&$ Uncertainty Quantification, ETH Zürich, 0.9-104 edition, 97-110.
  14. [14] Sinha, S.C. and Butcher, E.A. (1997), Symbolic computation of fundamental solution matrices for linear time-periodic dynamical systems, Journal of Sound and Vibration, 206(1), 61-85.
  15. [15] Monteiro, L.H.A. (2011), Sistemas Din\^amicos, Editora Livraria da Fisica, S\~ao Paulo, Brazil, 670 p.
  16. [16] Andrade, E.X.L., Bracciali, C.F., and Rafaeli, F.R. (2012), Introdu\c{c\~{a}o aos Polin\^{o}ios Ortogonais}, Sociedade Brasileira de Matem{a}tica Aplicada e Computacional, S\~ao carlos - SP, Brazil. 144 p.
  17. [17] Mesquita, A.J.N. (2007), Analise da estabilidade de sistemas din\^amicos periodicos usando teoria de sinha.
  18. [18] Peruzzi, N. (2005), Analise da estabilidade de sistemas din\^amicos periodicos usando teoria de sinha, Ph.D. thesis, Universidade Estadual de Campinas.
  19. [19] Naifeh, A.H. and Balachandran, B. (1995), Applied Nonlinear Dynamics, John Wiley.
  20. [20] Wolf, A. et al, (1985), Determining lyapunov exponents from a time series, Physica D: Nonlinear Phenomena, Elsevier, 16(3), 285-317.
  21. [21] Fuzaro de Almeida, E., Fuzaro de Almeida, E., Salvador, J.P.F., and Ferreira, L.V.G. (2021), insane\_hapex, URL https://github.com/estevaofuzaro98/inSANE\_HAPEX.
  22. [22] Norenberg, J.P., Peterson, J.V., Lopes V.G., Luo R., de la Roca L., Pereira M., Ribeiro J.G.T., and Cunha. Jr.A. (2021), Stonehenge-suite for nonlinear analysis of energy harvesting systems, Software Impacts, 10, 100161.
  23. [23] Meirovitch, L. (2010), Methods of Analytical Dynamics, Courier Corporation.
  24. [24] Sch\"obi, R., Marelli, S., and Sudret, B. (2017), Uqlab user manual-pc-kriging, Report UQLab-V1, 1-109.

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