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

  • Ahmad Paknejad
  • Gholamhossein Rahimi
  • Hamed Salmani
Original
  • 95 Downloads

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.

Keywords

Smart composite plate Electromechanical system Piezoelectricity 

References

  1. 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)CrossRefGoogle Scholar
  2. 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)CrossRefGoogle Scholar
  3. 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)CrossRefGoogle Scholar
  4. 4.
    Anton, S.R., Sodano, H.A.: A review of power harvesting using piezoelectric materials (2003–2006). Smart Mater. Struct. 16, R1–R21 (2007)CrossRefGoogle Scholar
  5. 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)CrossRefGoogle Scholar
  6. 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)CrossRefGoogle Scholar
  7. 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)CrossRefGoogle Scholar
  8. 8.
    Paradiso, J.A., Starner, T.: Energy scavenging for mobile and wireless electronics. IEEE Pervasive Comput. 4, 18–27 (2005)CrossRefGoogle Scholar
  9. 9.
    Naruse, Y., et al.: Electrostatic micro power generation from low-frequency vibration such as human motion. J. Micromech. Microeng. 19, 094002 (2009)CrossRefGoogle Scholar
  10. 10.
    Chiu, Y., Tseng, V.F.G.: A capacitive vibration to electricity energy converter with integrated mechanical switches. J. Micromech. Microeng. 18, 104004 (2008)CrossRefGoogle Scholar
  11. 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)CrossRefGoogle Scholar
  12. 12.
    Beeby, S.P., et al.: A micro electromagnetic generator for vibration energy harvesting. J. Micromech. Microeng. 17, 1257–1265 (2007)CrossRefGoogle Scholar
  13. 13.
    Yang, B., et al.: Electromagnetic energy harvesting from vibrations of multiple frequencies. J. Micromech. Microeng. 19, 035001 (2009)CrossRefGoogle Scholar
  14. 14.
    Wang, L., Yuan, F.G.: Vibration energy harvesting by magnetostrictive material. Smart Mater. Struct. 17, 045009 (2008)CrossRefGoogle Scholar
  15. 15.
    Adly, A., et al.: Experimental tests of a magnetostrictive energy harvesting device toward its modeling. J. Appl. Phys. 107, 09A935 (2010)CrossRefGoogle Scholar
  16. 16.
    Tiwari, R., Kim, K.J., Kim, S.M.: Ionic polymer-metal composite as energy harvesters. Smart Struct. Syst. 4(5), 549–563 (2008)CrossRefGoogle Scholar
  17. 17.
    Yiming, L., et al.: Investigation of electrostrictive polymers for energy harvesting. IEEE Trans. Ultrason. Ferroelectr. Freq. Control 52, 2411–2417 (2005)CrossRefGoogle Scholar
  18. 18.
    Wang, Z.L., Song, J.: Piezoelectric nanogenerators based on zinc oxide nanowire arrays. Science 312, 242–246 (2006)CrossRefGoogle Scholar
  19. 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)CrossRefGoogle Scholar
  20. 20.
    Erturk, A., Inman, D.J.: A distributed parameter electromechanical model for cantilevered piezoelectric energy harvesters. J. Vib. Acoust. 130, 041002 (2008)CrossRefGoogle Scholar
  21. 21.
    Erturk, A., Inman, D.J.: Piezoelectric Energy Harvesting. Wiley, Hoboken (2011)CrossRefGoogle Scholar
  22. 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)CrossRefGoogle Scholar
  23. 23.
    Amini, Y., Emdad, H., Farid, M.: Finite element modeling of functionally graded piezoelectric harvesters. Compos. Struct. 129, 165–176 (2015)CrossRefGoogle Scholar
  24. 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)CrossRefGoogle Scholar
  25. 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)MathSciNetCrossRefGoogle Scholar
  26. 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)CrossRefGoogle Scholar
  27. 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)CrossRefGoogle Scholar
  28. 28.
    Dietl, J.M., Wickenheiser, A.M., Garcia, E.: A Timoshenko beam model for cantilevered piezoelectric energy harvesters. Smart Mater. Struct. 19, 055018 (2010)CrossRefGoogle Scholar
  29. 29.
    Yang, Y., Tang, L.: Equivalent circuit modeling of piezoelectric energy harvesters. J. Intell. Mater. Syst. Struct. 20, 2223–2235 (2009)CrossRefGoogle Scholar
  30. 30.
    Cottone, F., et al.: Piezoelectric buckled beams for random vibration energy harvesting. Smart Mater. Struct. 21, 035021 (2012)CrossRefGoogle Scholar
  31. 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)CrossRefGoogle Scholar
  32. 32.
    Friswell, M.I., Adhikari, S.: Sensor shape design for piezoelectric cantilever beams to harvest vibration energy. J. Appl. Phys. 108, 014901 (2010)CrossRefGoogle Scholar
  33. 33.
    Lallart, M., Guyomar, D.: Piezoelectric conversion and energy harvesting enhancement by initial energy injection. Appl. Phys. Lett. 97, 014104 (2010)CrossRefGoogle Scholar
  34. 34.
    Erturk, A., Inman, D.J.: Issues in mathematical modeling of piezoelectric energy harvesters. Smart Mater. Struct. 17, 065016 (2008b)CrossRefGoogle Scholar
  35. 35.
    Shahruz, S.M.: Design of mechanical band-pass filters with large frequency bands for energy scavenging. Mechatronics 16, 523–531 (2006)CrossRefGoogle Scholar
  36. 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)CrossRefGoogle Scholar
  37. 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)CrossRefGoogle Scholar
  38. 38.
    Friswell, M.I., Adhikari, S.: Sensor shape design for piezoelectric cantilever beams to harvest vibration energy. J. Appl. Phys. 108, 014901–014906 (2010)CrossRefGoogle Scholar
  39. 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)CrossRefGoogle Scholar
  40. 40.
    Lien, I.C., Shu, Y.C.: Array of piezoelectric energy harvesting by the equivalent impedance approach. Smart Mater. Struct. 21, 082001 (2012)CrossRefGoogle Scholar
  41. 41.
    Huang, S.-C., Lin, K.-A.: A novel design of a maptuning piezoelectric vibration energy harvester. Smart Mater. Struct. 21, 085014 (2012)CrossRefGoogle Scholar
  42. 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. 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)CrossRefGoogle Scholar
  44. 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)CrossRefGoogle Scholar
  45. 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)CrossRefGoogle Scholar
  46. 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. 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)CrossRefGoogle Scholar
  48. 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)CrossRefGoogle Scholar
  49. 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)CrossRefGoogle Scholar
  50. 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)CrossRefGoogle Scholar
  51. 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)CrossRefGoogle Scholar
  52. 52.
    Jones, R.M.: Mechanics of Composite Materials. Taylor & Frances Inc, Oxford (1999)Google Scholar
  53. 53.
    Gibson, R.F.: A review of recent research on mechanics of multifunctional composite materials and structures. Compos. Struct. 92(12), 2793–2810 (2010)CrossRefGoogle Scholar
  54. 54.
    Pellegrini Sergio, P., et al.: Bistable vibration energy harvesters: a review. J. Intell. Mater. Syst. Struct. 24(11), 1303–1312 (2012)CrossRefGoogle Scholar
  55. 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)CrossRefGoogle Scholar
  56. 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)CrossRefGoogle Scholar
  57. 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)CrossRefGoogle Scholar
  58. 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)Google Scholar
  59. 59.
    Arrieta, A.F., et al.: A piezoelectric bistable plate for nonlinear broadband energy harvesting. J. Appl. Phys. Lett. 97, 104102 (2010)CrossRefGoogle Scholar
  60. 60.
    Betts, D.N., et al.: Optimal configurations of bistable piezo-composites for energy harvesting. J. Appl. Phys. Lett. 100(11), 114104 (2012)CrossRefGoogle Scholar
  61. 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. 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)CrossRefGoogle Scholar
  63. 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)CrossRefGoogle Scholar
  64. 64.
    Xing, Y.F., Liu, B.: New exact solutions for free vibrations of thin orthotropic rectangular plates. Compos. Struct. 89, 567–574 (2009)CrossRefGoogle Scholar
  65. 65.
    Her, S.-C., Lin, C.-S.: Vibration analysis of composite laminate plate excited by piezoelectric actuators. Sensors 13(3), 2997–3013 (2013)CrossRefGoogle Scholar

Copyright information

© Springer-Verlag GmbH Germany, part of Springer Nature 2018

Authors and Affiliations

  • Ahmad Paknejad
    • 1
  • Gholamhossein Rahimi
    • 1
  • Hamed Salmani
    • 1
  1. 1.Department of Mechanical EngineeringTarbiat Modares UniversityTehranIran

Personalised recommendations