Skip to main content

Advertisement

SpringerLink
Log in

Enhancement of the performance of nonlinear vibration energy harvesters by exploiting secondary resonances in multi-frequency excitations

  • Regular Article
  • Published:
The European Physical Journal Plus Aims and scope Submit manuscript

Abstract

This study is concerned with utilizing secondary resonances in order to harvest energy from low-frequency excitations. Nonlinearities give rise to secondary resonances, which can potentially activate large-amplitude responses when the excitation frequency is a fraction of the fundamental frequency of the system. Such resonances offer an untapped and unique opportunity for harvesting vibratory energy from excitation sources with low-frequency components. This issue has propelled the current study. Based on multi-frequency excitation, we develop a novel theoretical framework for a piezomagnetoelastic energy harvester to enhance its performance. The proposed scheme is implemented in both monostable and bistable piezomagnetoelastic under low-frequency excitations. It is shown throughout the paper that when the excitation frequencies are certain fractions of the system's fundamental frequency, the combination and simultaneous resonance activate large-amplitude responses. Another advantage of the scheme is that the energy could be harvested from low-frequency ambient vibrations, which is a considerable concern in this field of study. Different responses of the system, such as low-amplitude and high-amplitude limit-cycle oscillations and chaotic motions, are studied through perturbation theory and numerical techniques. Various numerical tools, including phase portrait, Poincare section, and Lyapunov exponent, are used to explore complex dynamical behavior of the system. The performance of the harvester is also compared in different regions. Numeral simulations clearly confirm that the proposed framework dramatically enhances the performance of the energy harvester.

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

Fig. 1
Fig. 2
Fig. 3
Fig. 4
Fig. 5
Fig. 6
Fig. 7
Fig. 8
Fig. 9
Fig. 10
Fig. 11
Fig. 12
Fig. 13
Fig. 14
Fig. 15
Fig. 16

Similar content being viewed by others

Abbreviations

\(r\) :

Nondimensional cantilever tip deflection

\(v\) :

Dimensionless output voltage

\(t\) :

Dimensionless time

\(\mu_{{\text{a}}}\) :

Viscose damping coefficient term

\(\alpha\) :

Nondimensional linear stiffness of the system

\(\beta\) :

Coefficient of the cubic nonlinearity

\(\theta_{1}\) :

Dimensionless piezoelectric coupling term in the mechanical equation

\(z\left( t \right)\) :

Dimensionless excitation

\(\mu_{{\text{c}}}\) :

Reciprocal of the dimensionless time constant of the resistive–capacitive circuit

\(R_{{\text{l}}}\) :

Load resistance

\(f_{1}\) :

Dimensionless amplitudes of first excitation

\(f_{2}\) :

Dimensionless amplitudes of second excitation

\( {\Omega }_{1}\) :

Dimensionless frequency of first excitation

\({\Omega }_{2}\) :

Dimensionless frequency of second excitation

\(\varepsilon\) :

Bookkeeping parameter

\(\sigma\) :

Detuning parameter

References

  1. R.N. Torah, M.J. Tudor, K. Patel, I.N. Garcia, S.P. Beeby, Autonomous low power microsystem powered by vibration energy harvesting. IEEE, pp. 264–267.

  2. S.F. Ali, S. Adhikari, Energy harvesting dynamic vibration absorbers. J. Appl. Mech. 80, 1 (2013)

    Article  Google Scholar 

  3. M.F. Daqaq, R. Masana, A. Erturk, D. Dane Quinn, On the role of nonlinearities in vibratory energy harvesting: a critical review and discussion. Appl. Mech. Rev. 66, 1 (2014)

    Google Scholar 

  4. C. Wei, X. Jing, A comprehensive review on vibration energy harvesting: Modelling and realization. Renew. Sustain. Energy Rev. 74, 1–18 (2017)

    Article  MathSciNet  Google Scholar 

  5. A. Erturk, D.J. Inman, Broadband piezoelectric power generation on high-energy orbits of the bistable Duffing oscillator with electromechanical coupling. J. Sound Vib. 330, 2339–2353 (2011)

    Article  ADS  Google Scholar 

  6. S. Priya, D.J. Inman, Energy Harvesting Technologies (Springer, 2009).

    Book  Google Scholar 

  7. H. Farokhi, A. Gholipour, M.H. Ghayesh, Efficient broadband vibration energy harvesting using multiple piezoelectric bimorphs. J. Appl. Mech. 87, 1 (2020)

    Article  Google Scholar 

  8. S. Boisseau, G. Despesse, B.A. Seddik, Nonlinear H-shaped springs to improve efficiency of vibration energy harvesters. J. Appl. Mech. 80, 1 (2013)

    Article  Google Scholar 

  9. F. Cottone, H. Vocca, L. Gammaitoni, Nonlinear energy harvesting. Phys. Rev. Lett. 102, 080601 (2009)

    Article  ADS  Google Scholar 

  10. H. Alrabaiah, M.A. Safi, M.H. DarAssi, B. Al-Hdaibat, S. Ullah, M.A. Khan, S.A.A. Shah, Optimal control analysis of hepatitis B virus with treatment and vaccination. Results Phys. 19, 103599 (2020)

    Article  Google Scholar 

  11. M. Awais, F.S. Alshammari, S. Ullah, M.A. Khan, S. Islam, Modeling and simulation of the novel coronavirus in Caputo derivative. Results Phys. 19, 103588 (2020)

    Article  Google Scholar 

  12. M.A. Khan, A. Atangana, Modeling the dynamics of novel coronavirus (2019-nCov) with fractional derivative. Alexandria Eng. J. 59, 2379–2389 (2020)

    Article  Google Scholar 

  13. M.A. Khan, A. Atangana, E. Alzahrani, The dynamics of COVID-19 with quarantined and isolation. Adv. Differ. Equ. 2020, 1–22 (2020)

    Article  MathSciNet  Google Scholar 

  14. S.C. Stanton, Nonlinear electroelastic dynamical systems for inertial power generation (2011).

  15. S.C. Stanton, C.C. McGehee, B.P. Mann, Nonlinear dynamics for broadband energy harvesting: Investigation of a bistable piezoelectric inertial generator. Physica D 239, 640–653 (2010)

    Article  ADS  Google Scholar 

  16. S. Leadenham, A. Erturk, Nonlinear M-shaped broadband piezoelectric energy harvester for very low base accelerations: primary and secondary resonances. Smart Mater. Struct. 24, 055021 (2015)

    Article  ADS  Google Scholar 

  17. M.A. Karami, D.J. Inman, Nonlinear hybrid energy harvesting utilizing a piezo-magneto-elastic spring, in International Society for Optics and Photonics, pp. 76430U.

  18. A. Erturk, J. Hoffmann, D.J. Inman, A piezomagnetoelastic structure for broadband vibration energy harvesting. Appl. Phys. Lett. 94, 254102 (2009)

    Article  ADS  Google Scholar 

  19. S.C. Stanton, A. Erturk, B.P. Mann, D.J. Inman, Resonant manifestation of intrinsic nonlinearity within electroelastic micropower generators. Appl. Phys. Lett. 97, 254101 (2010)

    Article  ADS  Google Scholar 

  20. A.H. Nayfeh, P.F. Pai, Linear and Nonlinear Structural Mechanics (Wiley, 2008).

    MATH  Google Scholar 

  21. F.C. Moon, P.J. Holmes, A magnetoelastic strange attractor. J. Sound Vib. 65, 275–296 (1979)

    Article  ADS  Google Scholar 

  22. M. Amin Karami, D.J. Inman, Powering pacemakers from heartbeat vibrations using linear and nonlinear energy harvesters. Appl. Phys. Lett. 100, 042901 (2012)

    Article  ADS  Google Scholar 

  23. R. Masana, M.F. Daqaq, Energy harvesting in the super-harmonic frequency region of a twin-well oscillator. J. Appl. Phys. 111, 044501 (2012)

    Article  ADS  Google Scholar 

  24. R.L. Harne, K.W. Wang, On the fundamental and superharmonic effects in bistable energy harvesting. J. Intell. Mater. Syst. Struct. 25, 937–950 (2014)

    Article  Google Scholar 

  25. R. Masana, M.F. Daqaq, Exploiting super-harmonic resonances of a bi-stable axially-loaded beam for energy harvesting under low-frequency excitations. pp. 999–1008.

  26. R. Masana, M.F. Daqaq, Relative performance of a vibratory energy harvester in mono-and bi-stable potentials. J. Sound Vib. 330, 6036–6052 (2011)

    Article  ADS  Google Scholar 

  27. S. Roundy, Y. Zhang, Toward self-tuning adaptive vibration-based microgenerators, in International Society for Optics and Photonics, pp. 373–384.

  28. E.S. Leland, P.K. Wright, Resonance tuning of piezoelectric vibration energy scavenging generators using compressive axial preload. Smart Mater. Struct. 15, 1413 (2006)

    Article  ADS  Google Scholar 

  29. M.A.E. Mahmoud, E.M. Abdel-Rahman, R.R. Mansour, E.F. El-Saadany, Springless Vibration Energy Harvesters, pp. 703–711.

  30. D.A.W. Barton, S.G. Burrow, L.R. Clare, Energy harvesting from vibrations with a nonlinear oscillator. J. Vib. Acoust. 132, 1 (2010)

    Article  Google Scholar 

  31. R.L. Harne, M. Thota, K.W. Wang, Bistable energy harvesting enhancement with an auxiliary linear oscillator. Smart Mater. Struct. 22, 125028 (2013)

    Article  ADS  Google Scholar 

  32. S. Leadenham, A. Erturk, Harmonic balance analysis and experimental validation of a nonlinear broadband piezoelectric energy harvester for low ambient vibrations, in American Society of Mechanical Engineers, pp. V008T013A050.

  33. N.G. Stephen, On energy harvesting from ambient vibration. J. Sound Vib. 293, 409–425 (2006)

    Article  ADS  Google Scholar 

  34. Q.-M. Wang, L.E. Cross, Constitutive equations of symmetrical triple layer piezoelectric benders. IEEE Trans. Ultrason. Ferroelectr. Freq. Control 46, 1343–1351 (1999)

    Article  Google Scholar 

  35. A. Erturk, D.J. Inman, Piezoelectric Energy Harvesting (Wiley, 2011).

    Book  Google Scholar 

  36. H.-X. Zou, W.-M. Zhang, K.-X. Wei, W.-B. Li, Z.-K. Peng, G. Meng, A compressive-mode wideband vibration energy harvester using a combination of bistable and flextensional mechanisms. J. Appl. Mech. 83, 1 (2016)

    Article  Google Scholar 

  37. L.-Q. Chen, W.-A. Jiang, Internal resonance energy harvesting. J. Appl. Mech. 82, 1 (2015)

    ADS  Google Scholar 

  38. A.H. Nayfeh, Introduction to Perturbation Techniques (Wiley, 2011).

    MATH  Google Scholar 

  39. M.A. Karami, D.J. Inman, Equivalent damping and frequency change for linear and nonlinear hybrid vibrational energy harvesting systems. J. Sound Vib. 330, 5583–5597 (2011)

    Article  ADS  Google Scholar 

  40. J. Baker, S. Roundy, P. Wright, Alternative Geometries for Increasing Power Density in Vibration Energy Scavenging for Wireless Sensor Networks, pp. 5617.

Download references

Acknowledgements

The research was supported by the Taif University Researchers Supporting Project No. (TURSP-2020/77), Taif University, Taif, Saudi Arabia. Additionally, the research was supported by the National Natural Science Foundation of China (Grant Nos. 11971142, 11401192, 61673169, 11701176, 11626101, 11601485). José Francisco Gómez Aguilar acknowledges the support provided by CONACyT: cátedras CONACyT para jóvenes investigadores 2014 and SNI-CONACyT.

Author information

Authors and Affiliations

  1. Department of Mechanical Engineering, University of Manitoba, Winnipeg, R3T 5V6, Canada

    Hadi Jahanshahi

  2. Institute of Water Resources and Hydropower Research, Northwest A&F University, Yangling, 712100, Shaanxi, People’s Republic of China

    Diyi Chen

  3. Key Laboratory of Agricultural Soil and Water Engineering in Arid and Semiarid Areas, Ministry of Education, Northwest A&F University, Yangling, 712100, Shaanxi, People’s Republic of China

    Diyi Chen

  4. Department of Mathematics, Huzhou University, Huzhou, 313000, People’s Republic of China

    Yu-Ming Chu

  5. Hunan Provincial Key Laboratory of Mathematical Modeling and Analysis in Engineering, Changsha University of Science & Technology, Changsha, 410114, People’s Republic of China

    Yu-Ming Chu

  6. CONACyT-Tecnológico Nacional de México/CENIDET, Interior Internado Palmira S/N, Col. Palmira, 62490, Cuernavaca, Morelos, Mexico

    J. F. Gómez-Aguilar

  7. Department of Mechanical Engineering, College of Engineering, Taif University, P.O.Box 11099, Taif, 21944, Saudi Arabia

    Ayman A. Aly

Authors
  1. Hadi Jahanshahi
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Diyi Chen
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Yu-Ming Chu
    View author publications

    You can also search for this author in PubMed Google Scholar

  4. J. F. Gómez-Aguilar
    View author publications

    You can also search for this author in PubMed Google Scholar

  5. Ayman A. Aly
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding authors

Correspondence to Yu-Ming Chu or J. F. Gómez-Aguilar.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Jahanshahi, H., Chen, D., Chu, YM. et al. Enhancement of the performance of nonlinear vibration energy harvesters by exploiting secondary resonances in multi-frequency excitations. Eur. Phys. J. Plus 136, 278 (2021). https://doi.org/10.1140/epjp/s13360-021-01263-9

Download citation

  • Received:

  • Accepted:

  • Published:

  • DOI: https://doi.org/10.1140/epjp/s13360-021-01263-9

Search

Navigation