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Nonlocal viscoelasticity based vibration of double viscoelastic piezoelectric nanobeam systems

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Abstract

The present work deals with the analysis of free and forced vibrations of double viscoelastic piezoelectric nanobeam systems (DVPNBSs) incorporating nonlocal viscoelasticity theory and Euler–Bernoulli beam model. The two viscoelastic piezoelectric nanobeams (VPNBs) are coupled by visco-Pasternak medium. Viscoelastic property of VPNBs is simulated by Kelvin–Voigt and Maxwell models. In order to obtain the natural frequency and frequency response of the coupled system under the harmonic excitation, an exact solution is presented. The free and forced vibrations of DVPNBS are considered in three cases namely out-of-phase vibration, in-phase vibration and vibration with one VPNB fixed. A detailed parametric study is carried out to demonstrate the influence of nonlocal parameter, visco-Pasternak constants, voltage, Kelvin–Voigt and Maxwell coefficients on the vibration characteristic of DVPNBS. Results indicate that the natural frequencies of DVPNBS are significantly influenced by nonlocal effects. In addition, effects of damping coefficient of the viscoelastic medium and internal damping of the material on the frequency of the coupled system are vice versa. Furthermore, the imposed external voltage is an effective controlling parameter for vibration of the coupled system.

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References

  1. Jalili N (2010) Piezoelectric-based vibration control from macro to micro/nano scale systems. Springer Science, New York

    Book  Google Scholar 

  2. Ke LL, Wang YS, Wang ZhD (2012) Nonlinear vibration of the piezoelectric nanobeam based on nonlocal theory. Compos Struct 6:2038–2047

    Article  Google Scholar 

  3. Tanner SM, Gray JM, Rogers CT, Bertness KA, Sanford NA (2007) High-Q GaN nanowire resonators and oscillators. Appl Phys Lett 91:203117

    Article  ADS  Google Scholar 

  4. Fei P, Yeh PH, Zhou J, Xu S, Gao YF, Song JH (2009) Piezoelectric potential gated field-effect transistor based on a free-standing ZnO wire. Nano Lett 9:3435–3439

    Article  ADS  Google Scholar 

  5. He JH, Hsin CL, Liu J, Chen LJ, Wang ZL (2007) Piezoelectric gated diode of a single ZnO nanowire. Adv Mater 19:781–784

    Article  Google Scholar 

  6. Wang Q, Li QH, Chen YJ, Wang TH, He XL, Li JP (2004) Fabrication and ethanol sensing characteristics of ZnO nanowire gas sensors. Appl Phys Lett 84:3654–3656

    Article  ADS  Google Scholar 

  7. Wang ZL, Song JH (2006) Piezoelectric nanogenerators based on zinc oxide nanowire arrays. Science 312:242–246

    Article  ADS  Google Scholar 

  8. Eringen AC (2002) Nonlocal continuum field theories. Springer, New York

    MATH  Google Scholar 

  9. lu P, Lee HP, Lu C, Zhang PQ (2006) Dynamic properties of flexural beams using a nonlocal elasticity model. J Appl Phys 99:073510

    Article  ADS  Google Scholar 

  10. Lim CW, Li CH, Yu JL (2010) Free vibration of pretensioned nanobeams based on nonlocal stress theory. J Zhejiang Univ Sci A 11:34–42

    Article  MATH  Google Scholar 

  11. Haghpanahi M, Oveisi A, Gudarzi M (2013) Vibration analysis of piezoelectric nanowires using the finite element method. Int J Basic Appl Sci 4:205–212

    Google Scholar 

  12. Aydogdu M (2009) A general nonlocal beam theory: its application to nanobeam bending, buckling and vibration. Phys E 41:1651–1655

    Article  Google Scholar 

  13. Yang J, Ke LL, Kitipornchai S (2010) Nonlinear free vibration of single-walled carbone-nanotubes using nonlocal Timoshenko beam theory. Phys E 42:1727–1735

    Article  Google Scholar 

  14. Phadikar JK, Pradhan SC (2010) Variational formulation and finite element analysis for nonlocal elastic nanobeams and nanoplates. Comput Mater Sci 49:492–499

    Article  Google Scholar 

  15. Vu HV, Ordóňez AM, Karnopp BH (2000) Vibration of a double beam system. J Sound Vib 229:807–822

    Article  ADS  MATH  Google Scholar 

  16. Gürgöze M, Erol H (2003) On lateraly vibrating beams carrying tip masses, coupled by several double spring-mass system. J Sound Vib 269:431–438

    Article  Google Scholar 

  17. Murmu T, Adhikari S (2010) Nonlocal effects in the longitudinal vibration of doubled nanorod systems. Phys E 43:415–422

    Article  Google Scholar 

  18. Murmu T, Adhikari S (2010) Nonlocal transverse vibration of double nanobeam system. J Appl Phys 108:083514

    Article  ADS  Google Scholar 

  19. Murmu T, Adhikari S (2012) Nonlocal elasticity based vibration of initially pre-stressed couple nanobeam systems. Eur J Mech A/Solids 34:52–62

    Article  MathSciNet  Google Scholar 

  20. Salehi-Khojin A, Jalili N (2008) Buckling of boron nitride nanotube reinforced piezoelectric polymeric composites subject to combined electro-thermo-mechanical loadings. Compos Sci Tech 68:1489–1501

    Article  Google Scholar 

  21. Ghorbanpour Arani A, Amir S, Shajari AR, Mozdianfard MR, Khoddami Maraghi Z, Mohammadimehr M (2011) Electro-thermal non-local vibration analysis of embedded DWBNNTs. Proc Inst Mech Eng Part C 224:745–756

    Article  Google Scholar 

  22. Ghorbanpour Arani A, Amir S, Shajari AR, Mozdianfard MR (2012) Electro-thermo-mechanical buckling of DWBNNTs embedded in bundle of CNTs using nonlocal piezoelasticity cylindrical shell theory. Compos Part B Eng 43:195–203

    Article  Google Scholar 

  23. Khodami Maraghi Z, Ghorbanpour Arani A, Kolahchi R, Amir S, Bagheri MR (2013) Nonlocal vibration and instability of embedded DWBNNT conveying viscose fluid. Compos Part B Eng 45:423–432

    Article  Google Scholar 

  24. Ghorbanpour Arani A, Kolahchi R, Khoddami Maraghi Z (2013) Nonlinear vibration and instability of embedded double-walled boron nitride nanotubes based on nonlocal cylindrical shell theory. Appl Math Model 37:7685–7707

    Article  MathSciNet  Google Scholar 

  25. Nima Mahmoodi S, Jalili N, Khadem SE (2008) An experimental investigation of nonlinear vibration and frequency response analysis of cantilever viscoelastic beams. J Sound Vib 311:1409–1419

    Article  ADS  Google Scholar 

  26. Fu YM, Zhang J (2009) Nonlinear static and dynamic responses of an electrically actuated viscoelastic microbeam. Acta Mech Sin 25:211–218

    Article  ADS  MATH  Google Scholar 

  27. Ghavanloo E, Fazelzadeh SA (2011) Flow-thermoelastic vibration and instability analysis of viscoelastic carbon nanotubes embedded in viscous fluid. Phys E 44:17–24

    Article  Google Scholar 

  28. Pouresmaeeli S, Ghavanloo E, Fazelzadeh SA (2013) Vibration analysis of viscoelastic orthotropic nanoplate resting on viscoelastic medium. Compos Struct 96:405–410

    Article  Google Scholar 

  29. Ghorbanpour Arani A, Kolahchi R, Mosallaie Barzoki AA (2011) Effect of material in-homogeneity on electro-thermo-mechanical behaviors of functionally graded piezoelectric rotating shaft. Appl Math Model 35:2771–2789

    Article  MATH  MathSciNet  Google Scholar 

  30. Ghorbanpour Arani A, Kolahchi R, Vossough H (2012) Buckling analysis and smart control of SLGS using elastically coupled PVDF nanoplate based on the nonlocal Mindlin plate theory. Phys B 407:4458–4465

    Article  ADS  Google Scholar 

  31. Riande E (2000) Polymer viscoelasticity-stress and strain in practice. Marcel Dekker, New York

    Google Scholar 

  32. Bakhtiari-Nejad F, Meidan-Sharafi M (2004) Vibration optimal control of a smart plate with input voltage constraint of piezoelectric actuators. J Vib Control 10:1749–1774

    Article  MATH  Google Scholar 

  33. Mainardi F (2010) Fractional calculus and waves in linear viscoelasticity. Imperial College Press, London

    Book  MATH  Google Scholar 

  34. Wang Q (2005) Wave propagation in carbon nanotubes via nonlocal continuum mechanics. J Appl Phys 98:124301

    Article  ADS  Google Scholar 

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Acknowledgments

The author would like to thank the reviewers for their comments and suggestions to improve the clarity of this article. The authors are grateful to University of Kashan for supporting this work by Grant No. 363443/58. They would also like to thank the Iranian Nanotechnology Development Committee for their financial support.

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Authors and Affiliations

  1. School of Mechanical Engineering, College of Engineering, University of Tehran, Tehran, Iran

    A. H. Ghorbanpour-Arani & A. Rastgoo

  2. Faculty of Mechanical Engineering, University of Kashan, Kashan, Iran

    M. M. Sharafi, R. Kolahchi & A. Ghorbanpour Arani

  3. Institute of Nanoscience and Nanotechnology, University of Kashan, Kashan, Iran

    A. Ghorbanpour Arani

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  1. A. H. Ghorbanpour-Arani
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  2. A. Rastgoo
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  4. R. Kolahchi
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Correspondence to A. Ghorbanpour Arani.

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Ghorbanpour-Arani, A.H., Rastgoo, A., Sharafi, M.M. et al. Nonlocal viscoelasticity based vibration of double viscoelastic piezoelectric nanobeam systems. Meccanica 51, 25–40 (2016). https://doi.org/10.1007/s11012-014-9991-0

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  • DOI: https://doi.org/10.1007/s11012-014-9991-0

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