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An electromechanical finite element model for new CNTs-reinforced harvesters subjected to harmonic and random base excitations

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Abstract

Conventional piezoelectric energy harvesters are cantilever beams made of homogenous substructure and piezoelectric layers that produce alternating voltage due to their vibrations. Recently, a class of new emerging composite materials, the carbon nanotubes (CNTs)-reinforced composite, has been proposed making use of CNTs as the reinforcements in a functionally graded (FG) pattern. Harvesters made of functionally graded CNTs-reinforced substructure materials have not been studied in the energy harvesting literature, yet. Thus, in this study, functionally graded piezoelectric CNTs-reinforced harvesters as new energy harvesters subjected to harmonic and random vibrations are analyzed. The harvester is assumed to be comprised of piezoelectric and FG-CNTs-reinforced substructure layers. Five types of CNTs distributions through the substructure thickness direction are considered. The generalized Hamilton’s principle for electromechanical materials based on Euler–Bernoulli beam assumption is adopted in the derivation of governing equations. The finite element formulation of the equations is also presented. Time and frequency domain analyses of the finite element equations are performed. The output power from the CNTs-reinforced harvesters subjected to random and harmonic base excitations is calculated. The harvested energy of the CNTs-reinforced harvesters is compared, and it is concluded that the CNTs distribution has a significant effect on the deflection, produced voltage and harvested power.

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References

  1. Ajayan PM, Stephan O, Colliex C, Trauth D (1994) Aligned carbon nanotube arrays formed by cutting a polymer resin-nanotube composite. Science 265:1212–1214

  2. Ajitsaria J, Choe SY, Shen D, Kim DJ (2007) Modeling and analysis of a bimorph piezoelectric cantilever beam for voltage generation. Smart Mater Struct 16:447–454

  3. Alibeigloo A (2014) Three-dimensional thermoelasticity solution of functionally graded carbon nanotube reinforced composite plate embedded in piezoelectric sensor and actuator layers. Compos Struct 118:482–495

  4. Amini Y, Emdad H, Farid M (2014) An accurate model for numerical prediction of piezoelectric energy harvesting from fluid structure interaction problems. Smart Mater Structu 23:095034

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

  6. Andrews R, Jacques D, Minot M, Rantell T (2002) Fabrication of carbon multiwall nanotube/polymer composites by shear mixing. Macromol Mater Eng 287:395–403

  7. Cadek M (2002) Morphological and mechanical properties of carbon-nanotube reinforced semicrystalline and amorphous polymer composites. Appl Phys Lett 81:5123

  8. Crandall SH (1968) Dynamics of mechanical and electromechanical systems. McGraw-Hill, New York

  9. Duan WH, Quek ST, Wang Q (2005) Free vibration analysis of piezoelectric coupled thin and thick annular plate. J Sound Vib 281:119–139

  10. Dym CL, Shames IH (2013) Solid mechanics: a variational approach, augmented edn. Springer, Berlin

  11. Erturk A, Inman DJ (2008) A distributed parameter electromechanical model for cantilevered piezoelectric energy harvesters. J Vib Acoust 130:041002-1

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

  13. Erturk A, Inman DJ (2011) Piezoelectric energy harvesting. Wiley, Hoboken

  14. Griebel M, Hamaekers J (2004) Molecular dynamics simulations of the elastic moduli of polymer-carbon nanotube composites. Comput Methods Appl Mech Eng 193:1773–1788

  15. Heshmati M, Yas MH (2013a) Free vibration analysis of functionally graded CNT-reinforced nanocomposite beam using Eshelby–Mori–Tanaka approach. J Mech Sci Technol 27(11):3403–3408

  16. Heshmati M, Yas MH (2013b) Vibrations of non-uniform functionally graded MWCNTs-polystyrene nanocomposite beams under action of moving load. Mater Des 46:206–218

  17. Heshmati M, Yas MH (2013c) Dynamic analysis of functionally graded multi-walled carbon nanotube-polystyrene nanocomposite beams subjected to multi-moving loads. Mater Des 49:894–904

  18. Heshmati M, Yas MH, Daneshmand F (2015) A comprehensive study on the vibrational behavior of CNT-reinforced composite beams. Compos Struct 125:434–448

  19. Jalali SK, Heshmati M (2016) Buckling analysis of circular sandwich plates with tapered cores and functionally graded carbon nanotubes-reinforced composite face sheets. Thin Walled Struct 100:14–24

  20. Karami B, Shahsavari D, Janghorban M (2017) Wave propagation analysis in functionally graded (FG) nanoplates under in-plane magnetic field based on nonlocal strain gradient theory and four variable refined plate theory. Mech Adv Mater Struct. https://doi.org/10.1080/15376494.2017.1323143

  21. Karami B, Janghorban M, Li L (2018) On guided wave propagation in fully clamped porous functionally graded nanoplates. Acta Astronaut 143:380–390

  22. Ke LL, Yang J, Kitipornchai S (2010) Nonlinear free vibration of functionally graded carbon nanotube-reinforced composite beams. Compos Struct 92:676–683

  23. Lau AKT, Hui D (2002) The revolutionary creation of new advanced materials-carbon nanotube composites. Compos Part B 33:263–277

  24. Lei ZX, Liew KM, Yu JL (2013a) Buckling analysis of functionally graded carbon nanotube-reinforced composite plates using the element-free kp-Ritz method. Compos Struct 98:160–168

  25. Lei ZX, Liew KM, Yu JL (2013b) Free vibration analysis of functionally graded carbon nanotube-reinforced composite plates using the element-free kp-Ritz method in thermal environment. Compos Struct 106:128–138

  26. Liao Y, Sodano HA (2008) Model of a single mode energy harvester and properties for optimal power generation. Smart Mater Struct 17:065026

  27. Loos MR, Manas-Zloczower I (2012) Reinforcement efficiency of carbon nanotubes–myth and reality. Macromol Theory Simul 21:130–137

  28. Lutes LD, Sarkani S (2004) Chapter 8—matrix analysis of linear systems. In: Sarkani LDL (ed) Random vibrations. Butterworth-Heinemann, Burlington, pp 307–350

  29. Nami MR, Janghorban M (2015) Free vibration of thick functionally graded carbon nanotube-reinforced rectangular composite plates based on three-dimensional elasticity theory via differential quadrature method. Adv Compos Mater. https://doi.org/10.1080/09243046.2014.901472

  30. Nami MR, Janghorban M, Damadam M (2015) Thermal buckling analysis of functionally graded rectangular nanoplates based on nonlocal third-order shear deformation theory. Aerosp Sci Technol 41:7–15

  31. Newland DE (2012) An introduction to random vibrations, spectral & wavelet analysis, 3rd edn. Dover Publications, Mineola

  32. Odegard GM, Gates TS, Wise KE, Park C, Siochi EJ (2003) Constitutive modeling of nanotube-reinforced polymer composites. Compos Sci Technol 63:1671–1687

  33. Omidi M, Rokni HDT, Milani AS, Seethaler RJ, Arasteh R (2010) Prediction of the mechanical characteristics of multi-walled carbon nanotube/epoxy composites using a new form of the rule of mixtures. Carbon 48:3218–3228

  34. Reddy JN (2002) Energy principles and variational methods in applied mechanics. Wiley, New York

  35. Reddy J (2005) An introduction to the finite element method. McGraw-Hill Education, New York

  36. Shen HS (2009) Nonlinear bending of functionally graded carbon nanotube reinforced composite plates in thermal environments. Compos Struct 91:9–19

  37. Vatanabe SL, Paulino GH, Silva ECN (2013) Design of functionally graded piezocomposites using topology optimization and homogenization—toward effective energy harvesting materials. Comput Methods Appl Mech Eng 266:205–218

  38. Wang Q, Quek ST (2000) On dispersion relations in piezoelectric coupled beams. AIAA J 38:2357–2361

  39. Wang Q, Quek ST (2002) A model for the analysis of beam embedded with piezoelectric layers. J Intell Syst Struct 13:61–70

  40. Wang Q, Wu N (2012) Optimal design of piezoelectric coupled beam for power harvesting. Smart Mater Struct 21:085013

  41. Wang Q, Quek ST, Sun CT, Liu X (2001) Analysis of piezoelectric coupled circular plate. Smart Mater Struct 10:229–239

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

  43. Yas MH, Heshmati M (2012) Dynamic analysis of functionally graded nanocomposite beams reinforced by randomly oriented carbon nanotube under the action of moving load. Appl Math Model 36:1371–1394

  44. Yas MH, Pourasghar A, Kamarian S, Heshmati M (2013) Three-dimensional free vibration analysis of functionally graded nanocomposite cylindrical panels reinforced by carbon nanotube. Mater Des 49:583–590

  45. Zhang LW, Lei ZX, Liew KM, Yu JL (2014) Static and dynamic of carbon nanotube reinforced functionally graded cylindrical panels. Compos Struct 111:205–212

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

  47. Zhu P, Lei ZX, Liew KM (2012) Static and free vibration analyses of carbon nanotube- reinforced composite plates using finite element method with first order shear deformation plate theory. Compos Struct 94:1450–1460

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Correspondence to M. Heshmati.

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Heshmati, M., Amini, Y. An electromechanical finite element model for new CNTs-reinforced harvesters subjected to harmonic and random base excitations. Iran J Sci Technol Trans Mech Eng 44, 163–181 (2020). https://doi.org/10.1007/s40997-018-0254-x

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Keywords

  • Nanostructures
  • Vibration
  • Piezoelectric
  • Energy harvesting
  • CNTs-reinforced harvesters