Skip to main content

Advertisement

SpringerLink
Log in

Analytical solution and numerical validation of piezoelectric energy harvester patch for various thin multilayer composite plates

  • Original
  • Published:
Archive of Applied Mechanics Aims and scope Submit manuscript

Abstract

The study of vibrational energy harvesting using piezoelectric patch integrated on isotropic beam-like or plate-like thin structures has received significant attention over the past decade. Multilayer orthotropic composite plates are widely used in aerospace, automotive and marine applications, where they can be considered as host structures for vibration-based energy harvesting. In this paper, an exact analytical solution and numerical validation of a piezoelectric energy harvester structurally integrated to a thin multilayer orthotropic plate are presented. Electroelastic model of the thin multilayer composite plate with the piezoelectric patch harvester is developed based on a distributed parameter modeling approach with classical laminate plate theory assumptions for all-four-edge-clamped (CCCC) boundary condition. Closed-form steady-state expressions for coupled electrical outputs and structural vibration response are derived under harmonic transverse force excitation in the presence of a resistive load. Analytical electroelastic FRFs related to the voltage output as well as vibration response to force input are derived and generalized for different boundary conditions of host plate. The results of numerical and analytical models from multiple vibration modes are compared first for validating the analytical model with a case study employing a thin PZT-5A piezoceramic patch attached on the surface of a multilayer orthotropic composite CCCC plate. For this purpose, finite-element analysis is carried out by using ANSYS mechanical APDL software. Then, it is important to specify parameters in energy harvesting model, so positioning of piezoceramic patch harvester and excitation point force on the voltage output FRFs is discussed through an analysis of dynamic strain distribution on the overall plate surface. In addition, the effects of various composite laminate plates with different stacking sequences as host structures on generated power are discussed in details as well.

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

Similar content being viewed by others

References

  1. Roundy, S., Wright, P.K., Rabaey, J.: A study of low level vibrations as a power source for wireless sensor nodes. Comput. Commun. 26, 1131–1144 (2003)

    Article  Google Scholar 

  2. Zhu, P., Ren, X., Qin, W., Zhou, Z.: Improving energy harvesting in a tri-stable piezomagnetoelastic beam with two attractive external magnets subjected to random excitation. Arch. Appl. Mech. 87(1), 45–57 (2017)

    Article  Google Scholar 

  3. Gao, Y.H., Jiang, S.N., Zhu, D.B., Gao, H.T.: Theoretical analysis of a piezoelectric ceramic tube polarized tangentially for hydraulic vibration energy harvesting. Arch. Appl. Mech. 87(4), 607–615 (2017)

    Article  Google Scholar 

  4. Anton, S.R., Sodano, H.A.: A review of power harvesting using piezoelectric materials (2003–2006). Smart Mater. Struct. 16, R1–R21 (2007)

    Article  Google Scholar 

  5. Xie, X.D., Wang, Q., Wu, N.: Energy harvesting from transverse ocean waves by a piezoelectric plate. Int. J. Eng. Sci. 81, 41–48 (2014)

    Article  Google Scholar 

  6. Akbar, M., Curiel-Sosa, J.L.: Piezoelectric energy harvester composite under dynamic bending with implementation to aircraft wingbox structure. Compos. Struct. 153, 193–203 (2016)

    Article  Google Scholar 

  7. Xie, X.D., Wu, N., Yuen, K.V., Wang, Q.: Energy harvesting from high-rise buildings by a piezoelectric coupled cantilever with a proof mass. Int. J. Eng. Sci. 72, 98–106 (2013)

    Article  Google Scholar 

  8. Paradiso, J.A., Starner, T.: Energy scavenging for mobile and wireless electronics. IEEE Pervasive Comput. 4, 18–27 (2005)

    Article  Google Scholar 

  9. Naruse, Y., et al.: Electrostatic micro power generation from low-frequency vibration such as human motion. J. Micromech. Microeng. 19, 094002 (2009)

    Article  Google Scholar 

  10. Chiu, Y., Tseng, V.F.G.: A capacitive vibration to electricity energy converter with integrated mechanical switches. J. Micromech. Microeng. 18, 104004 (2008)

    Article  Google Scholar 

  11. Lee, C., et al.: Theoretical comparison of the energy harvesting capability among various electrostatic mechanisms from structure aspect. Sens. Actuators A 156, 208–216 (2009)

    Article  Google Scholar 

  12. Beeby, S.P., et al.: A micro electromagnetic generator for vibration energy harvesting. J. Micromech. Microeng. 17, 1257–1265 (2007)

    Article  Google Scholar 

  13. Yang, B., et al.: Electromagnetic energy harvesting from vibrations of multiple frequencies. J. Micromech. Microeng. 19, 035001 (2009)

    Article  Google Scholar 

  14. Wang, L., Yuan, F.G.: Vibration energy harvesting by magnetostrictive material. Smart Mater. Struct. 17, 045009 (2008)

    Article  Google Scholar 

  15. Adly, A., et al.: Experimental tests of a magnetostrictive energy harvesting device toward its modeling. J. Appl. Phys. 107, 09A935 (2010)

    Article  Google Scholar 

  16. Tiwari, R., Kim, K.J., Kim, S.M.: Ionic polymer-metal composite as energy harvesters. Smart Struct. Syst. 4(5), 549–563 (2008)

    Article  Google Scholar 

  17. Yiming, L., et al.: Investigation of electrostrictive polymers for energy harvesting. IEEE Trans. Ultrason. Ferroelectr. Freq. Control 52, 2411–2417 (2005)

    Article  Google Scholar 

  18. Wang, Z.L., Song, J.: Piezoelectric nanogenerators based on zinc oxide nanowire arrays. Science 312, 242–246 (2006)

    Article  Google Scholar 

  19. Cook-Chennault, K.A., Thambi, N., Sastry, A.M.: Powering MEMS portable devices—a review of non-regenerative and regenerative power supply systems with special emphasis on piezoelectric energy harvesting systems. Smart Mater. Struct. 17, 043001 (2008)

    Article  Google Scholar 

  20. Erturk, A., Inman, D.J.: A distributed parameter electromechanical model for cantilevered piezoelectric energy harvesters. J. Vib. Acoust. 130, 041002 (2008)

    Article  Google Scholar 

  21. Erturk, A., Inman, D.J.: Piezoelectric Energy Harvesting. Wiley, Hoboken (2011)

    Book  Google Scholar 

  22. Erturk, A.: Assumed modes modeling of piezoelectric energy harvesters: Euler–Bernoulli, Rayleigh, and Timoshenko models with axial deformations. Comput. Struct. 106(107), 214–227 (2012)

    Article  Google Scholar 

  23. Amini, Y., Emdad, H., Farid, M.: Finite element modeling of functionally graded piezoelectric harvesters. Compos. Struct. 129, 165–176 (2015)

    Article  Google Scholar 

  24. Amini, Y., Fatehi, P., Heshmati, M., Parandvar, H.: Time domain and frequency domain analysis of functionally graded piezoelectric harvesters subjected to random vibration: finite element modeling. Compos. Struct. 136, 384–393 (2016)

    Article  Google Scholar 

  25. Dai, H.L., Wang, Y.K., Wang, L.: Nonlinear dynamics of cantilevered microbeams based on modified couple stress theory. Int. J. Eng. Sci. 94, 103–112 (2015)

    Article  MathSciNet  Google Scholar 

  26. Erturk, A., Inman, D.J.: An experimentally validated bimorph cantilever model for piezoelectric energy harvesting from base excitations. Smart Mater. Struct. 18, 025009 (2009)

    Article  Google Scholar 

  27. Zhao, S., Erturk, A.: Electroelastic modeling and experimental validations of piezoelectric energy harvesting from broadband random vibrations of cantilevered bimorphs. Smart Mater. Struct. 22, 015002 (2013)

    Article  Google Scholar 

  28. Dietl, J.M., Wickenheiser, A.M., Garcia, E.: A Timoshenko beam model for cantilevered piezoelectric energy harvesters. Smart Mater. Struct. 19, 055018 (2010)

    Article  Google Scholar 

  29. Yang, Y., Tang, L.: Equivalent circuit modeling of piezoelectric energy harvesters. J. Intell. Mater. Syst. Struct. 20, 2223–2235 (2009)

    Article  Google Scholar 

  30. Cottone, F., et al.: Piezoelectric buckled beams for random vibration energy harvesting. Smart Mater. Struct. 21, 035021 (2012)

    Article  Google Scholar 

  31. Friswell, M.I., et al.: Nonlinear piezoelectric vibration energy harvesting from a vertical cantilever beam with tip mass. J. Intell. Mater. Syst. Struct. 23, 1505–1521 (2012)

    Article  Google Scholar 

  32. Friswell, M.I., Adhikari, S.: Sensor shape design for piezoelectric cantilever beams to harvest vibration energy. J. Appl. Phys. 108, 014901 (2010)

    Article  Google Scholar 

  33. Lallart, M., Guyomar, D.: Piezoelectric conversion and energy harvesting enhancement by initial energy injection. Appl. Phys. Lett. 97, 014104 (2010)

    Article  Google Scholar 

  34. Erturk, A., Inman, D.J.: Issues in mathematical modeling of piezoelectric energy harvesters. Smart Mater. Struct. 17, 065016 (2008b)

    Article  Google Scholar 

  35. Shahruz, S.M.: Design of mechanical band-pass filters with large frequency bands for energy scavenging. Mechatronics 16, 523–531 (2006)

    Article  Google Scholar 

  36. Song, H.J., Choi, Y.-T., Purekar, A.S., et al.: Performance evaluation of multi-tier energy harvesters using macrofiber composite patches. J. Intell. Mater. Syst. Struct. 20, 2077–2088 (2009)

    Article  Google Scholar 

  37. Erturk, A., Renno, J.M., Inman, D.J.: Modeling of piezoelectric energy harvesting from an L-shaped beammass structure with an application to UAVs. J. Intell. Mater. Syst. Struct. 20, 529–544 (2009b)

    Article  Google Scholar 

  38. Friswell, M.I., Adhikari, S.: Sensor shape design for piezoelectric cantilever beams to harvest vibration energy. J. Appl. Phys. 108, 014901–014906 (2010)

    Article  Google Scholar 

  39. Huan, X., Yuantai, H., Qing-Ming, W.: Broadband piezoelectric energy harvesting devices using multiple bimorphs with different operating frequencies. IEEE Trans. Ultrason. Ferroelectr. Freq. Control 55, 2104–2108 (2008)

    Article  Google Scholar 

  40. Lien, I.C., Shu, Y.C.: Array of piezoelectric energy harvesting by the equivalent impedance approach. Smart Mater. Struct. 21, 082001 (2012)

    Article  Google Scholar 

  41. Huang, S.-C., Lin, K.-A.: A novel design of a maptuning piezoelectric vibration energy harvester. Smart Mater. Struct. 21, 085014 (2012)

    Article  Google Scholar 

  42. Salmani, H., Rahimi, G.H., Hosseini Kordkheili, S.A.: An exact analytical solution to exponentially tapered piezoelectric energy harvester. Shock Vib. (2015). https://doi.org/10.1155/2015/426876

  43. Paknejad, A., Rahimi, G.H., Farrokhabadi, A., Khatibi, M.M.: Analytical solution of piezoelectric energy harvester patch for various thin multilayer composite beams. Compos. Struct. 154, 694–706 (2016)

    Article  Google Scholar 

  44. Bayik, B., Aghakhani, A., Basdogan, I., Erturk, A.: Equivalent circuit modeling of a piezo-patch energy harvester on a thin plate with AC–DC conversion. Smart Mater. Struct. 25(5), 055015 (2016)

    Article  Google Scholar 

  45. Aridogan, U., Basdogan, I., Erturk, A.: Analytical modeling and experimental validation of a structurally integrated piezoelectric energy harvester on a thin plate. Smart Mater. Struct. 23, 045039 (2014)

    Article  Google Scholar 

  46. Aridogan, U., Basdogan, I., Erturk, A.: Random vibration energy harvesting on thin plates using multiple piezopatches. J. Intell. Mater. Syst. Struct. (2016). https://doi.org/10.1177/1045389X16635846

    Google Scholar 

  47. Erturk, A.: Piezoelectric energy harvesting for civil infrastructure system applications: moving loads and surface strain fluctuations. J. Intell. Mater. Syst. Struct. 22, 1959–1973 (2011)

    Article  Google Scholar 

  48. Aridogan, U., Basdogan, I., Erturk, A.: Multiple patch-based broadband piezoelectric energy harvesting on plate-based structures. J. Intell. Mater. Syst. Struct. 25, 1664–1680 (2014)

    Article  Google Scholar 

  49. De Marqui, C., Erturk, A., Inman, D.J.: Piezoaeroelastic modeling and analysis of a generator wing with continuous and segmented electrodes. J. Intell. Mater. Syst. Struct. 21, 983–993 (2010)

    Article  Google Scholar 

  50. De Marqui, C., et al.: Modeling and analysis of piezoelectric energy harvesting from aeroelastic vibrations using the doublet-lattice method. J. Vib. Acoust. Trans. ASME 133, 011003 (2011)

    Article  Google Scholar 

  51. Rupp, C.J., et al.: Design of piezoelectric energy harvesting systems: a topology optimization approach based on multilayer plates and shells. J. Intell. Mater. Syst. Struct. 20, 1923–1939 (2009)

    Article  Google Scholar 

  52. Jones, R.M.: Mechanics of Composite Materials. Taylor & Frances Inc, Oxford (1999)

    Google Scholar 

  53. Gibson, R.F.: A review of recent research on mechanics of multifunctional composite materials and structures. Compos. Struct. 92(12), 2793–2810 (2010)

    Article  Google Scholar 

  54. Pellegrini Sergio, P., et al.: Bistable vibration energy harvesters: a review. J. Intell. Mater. Syst. Struct. 24(11), 1303–1312 (2012)

    Article  Google Scholar 

  55. Harne, R.L., Wang, K.W.: A review of the recent research on vibration energy harvesting via bistable systems. J. Smart Mater. Struct. 2013(22), 023001 (2013)

    Article  Google Scholar 

  56. Brampton Christopher, J., et al.: Sensitivity of bistable laminates to uncertainties in material properties, geometry and environmental conditions. J. Compos. Struct. 102, 276–286 (2013)

    Article  Google Scholar 

  57. Jong-Gu, L., et al.: Effect of initial tool-plate curvature on snap-through load of unsymmetric laminated cross-ply bistable composites. J. Compos. Struct. 122, 82–91 (2015)

    Article  Google Scholar 

  58. Mehdi, Tavakkoli S., et al.: An analytical study on piezoelectric-bistable laminates with arbitrary shapes for energy harvesting. In: 7th ECCOMAS Thematic Conference on Smart Structures and Materials (2015)

  59. Arrieta, A.F., et al.: A piezoelectric bistable plate for nonlinear broadband energy harvesting. J. Appl. Phys. Lett. 97, 104102 (2010)

    Article  Google Scholar 

  60. Betts, D.N., et al.: Optimal configurations of bistable piezo-composites for energy harvesting. J. Appl. Phys. Lett. 100(11), 114104 (2012)

    Article  Google Scholar 

  61. Betts, D.N., et al.: Preliminary study of optimum piezoelectric cross-ply composites for energy harvesting. J. Smart Mater. Res. (2012). https://doi.org/10.1155/2012/621364

    Google Scholar 

  62. Syta, A., Bowen, C.R., Kim, H.A., Rysak, A., Litak, G.: Experimental analysis of the dynamical response of energy harvesting devices based on bistable laminated plates. Meccanica 50(8), 1961–1970 (2015)

    Article  Google Scholar 

  63. Betts, D.N., Bowen, C.R., Kim, H.A., Gathercole, N., Clarke, C.T., Inman, D.J.: Nonlinear dynamics of a bistable piezoelectric-composite energy harvester for broadband application. Eur. Phys. J. Spec. Top. 222(7), 1553–1562 (2013)

    Article  Google Scholar 

  64. Xing, Y.F., Liu, B.: New exact solutions for free vibrations of thin orthotropic rectangular plates. Compos. Struct. 89, 567–574 (2009)

    Article  Google Scholar 

  65. Her, S.-C., Lin, C.-S.: Vibration analysis of composite laminate plate excited by piezoelectric actuators. Sensors 13(3), 2997–3013 (2013)

    Article  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Department of Mechanical Engineering, Tarbiat Modares University, Tehran, 14115-111, Iran

    Ahmad Paknejad, Gholamhossein Rahimi & Hamed Salmani

Authors
  1. Ahmad Paknejad
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Gholamhossein Rahimi
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Hamed Salmani
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Gholamhossein Rahimi.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Paknejad, A., Rahimi, G. & Salmani, H. Analytical solution and numerical validation of piezoelectric energy harvester patch for various thin multilayer composite plates. Arch Appl Mech 88, 1139–1161 (2018). https://doi.org/10.1007/s00419-018-1363-0

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s00419-018-1363-0

Keywords

Search

Navigation