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Magneto-electro-elastic analysis of piezoelectric–flexoelectric nanobeams rested on silica aerogel foundation

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Abstract

This article explores that the study on bending of magneto-electric-elastic nanobeams relies on nonlocal elasticity theory. The Vlasov’s model foundation utilizes the silica aerogel foundation. The guiding expressions of nonlocal nanobeams in the considered framework are used extensively and where parabolic third-order beam theory is achieved after using Hamilton’s principle. Parametric work is introduced to scrutinize the influence of the magneto-electro-mechanical loadings, nonlocal parameter, and aspect ratio on the deflection characteristics of nanobeams. It is noticed that the boundary conditions, nonlocal parameter, and beam geometrical parameters have significant effects on dimensionless deflection of nanoscale beams.

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References

  1. van den Boomgard J, Terrell DR, Born RAJ et al (1974) An in situ grown eutectic magnetoelectric composite material. J Mater Sci 9:1705–1709

    Article  Google Scholar 

  2. Zheng H, Wang J, Lofland SE et al (2004) Multiferroic BaTiO3–CoFe2O4 nanostructures. Science 303:661–663

    Article  Google Scholar 

  3. Martin LW, Crane SP, Chu YH et al (2008) Multiferroics and magnetoelectrics: thin films and nanostructures. J Phys Condens Matter 20:434220

    Article  Google Scholar 

  4. Wang Y, Hu JM, Lin YH et al (2010) Multiferroic magnetoelectric composite nanostructures. NPG Asia Mater 2:61–68

    Article  Google Scholar 

  5. Prashanthi K, Shaibani PM, Sohrabi A et al (2012) Nanoscale magnetoelectric coupling in multiferroic BiFeO3 nanowires. Phys Status Solidi R 6:244–246

    Article  Google Scholar 

  6. Eringen A (1968) Mechanics of micromorphic continua. In: Kroner E (ed) Mechanics of generalized continua. Springer, New York, pp 18–35

    Chapter  Google Scholar 

  7. Eringen A (1972) Nonlocal polar elastic continua. Int J Eng Sci 10:1–16

    Article  MathSciNet  Google Scholar 

  8. Eringen A (1976) Nonlocal micropolar field theory. In: Eringen AC (ed) Continuum physics. Academic Press, New York

    Google Scholar 

  9. Eringen A (2002) Nonlocal continuum field theories. Springer, New York

    MATH  Google Scholar 

  10. Eringen A (2006) Nonlocal continuum mechanics based on distributions. Int J Eng Sci 44(3):141–147

    Article  MathSciNet  Google Scholar 

  11. Eringen A, Edelen D (1972) On nonlocal elasticity. Int J Eng Sci 10:233–248

    Article  MathSciNet  Google Scholar 

  12. Zenkour AM, Sobhy M (2013) Nonlocal elasticity theory for thermal buckling of nanoplates lying on Winkler–Pasternak elastic substrate medium. Physica E 53:251–259

    Article  Google Scholar 

  13. Peddieson J, Buchanan GR, McNitt RP (2003) Application of nonlocal continuum models to nanotechnology. Int J Eng Sci 41:305–312

    Article  Google Scholar 

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

    Article  Google Scholar 

  15. Civalek O, Demir C (2011) Bending analysis of microtubules using nonlocal Euler–Bernoulli beam theory. Appl Math Model 35:2053–2067

    Article  MathSciNet  Google Scholar 

  16. Wang CM, Kitipornchai S, Lim CW, Eisenberger M (2008) Beam bending solutions based on nonlocal Timoshenko beam theory. J Eng Mech 134:475–481

    Article  Google Scholar 

  17. Murmu T, Pradhan SC (2009) Buckling analysis of a single-walled carbon nanotube embedded in an elastic medium based on nonlocal elasticity and Timoshenko beam theory and using DQM. Physica E 41(7):1232–1239

    Article  Google Scholar 

  18. Yang J, Ke LL, Kitipornchai S (2010) Nonlinear free vibration of single-walled carbon nanotubes using nonlocal Timoshenko beam theory. Physica E 42(5):1727–1735

    Article  Google Scholar 

  19. Ebrahimi F, Barati MR (2016) Dynamic modeling of a thermo–piezo-electrically actuated nanosize beam subjected to a magnetic field. Appl Phys A 122(4):1–18

    Article  Google Scholar 

  20. Ebrahimi F, Barati MR (2016) Electromechanical buckling behavior of smart piezoelectrically actuated higher-order size-dependent graded nanoscale beams in thermal environment. Int J Smart Nano Mater 7:1–22

    Article  Google Scholar 

  21. Ebrahimi F, Barati MR (2016) An exact solution for buckling analysis of embedded piezoelectro-magnetically actuated nanoscale beams. Adv Nano Res 4(2):65–84

    Article  Google Scholar 

  22. Roque CMC, Ferreira AJM, Reddy JN (2011) Analysis of Timoshenko nanobeams with a nonlocal formulation and meshless method. Int J Eng Sci 49(9):976–984

    Article  Google Scholar 

  23. Arefi M, Zenkour AM (2016) A simplified shear and normal deformations nonlocal theory for bending of functionally graded piezomagnetic sandwich nanobeams in magneto-thermo-electric environment. J Sandwich Struct Mater 18(5):624–651

    Article  Google Scholar 

  24. Şimşek M, Yurtcu HH (2013) Analytical solutions for bending and buckling of functionally graded nanobeams based on the nonlocal Timoshenko beam theory. Compos Struct 97:378–386

    Article  Google Scholar 

  25. Ghorbanpour Arani A, Zamani MH (2017) Investigation of electric field effect on size-dependent bending analysis of functionally graded porous shear and normal deformable sandwich nanoplate on silica Aerogel foundation. J Sandwich Struct Mater 21:2700–2734

    Article  Google Scholar 

  26. Ke LL, Wang YS, Yang J, Kitipornchai S (2014) Free vibration of size-dependent magneto-electro-elastic nanoplates based on the nonlocal theory. Acta Mech Sin 30(4):516–525

    Article  MathSciNet  Google Scholar 

  27. Sobhy M (2013) Buckling and free vibration of exponentially graded sandwich plates resting on elastic foundations under various boundary conditions. Compos Struct 99:76–87

    Article  Google Scholar 

  28. Ramirez F, Heyliger PR, Pan E (2006) Discrete layer solution to free vibrations of functionally graded magneto-electro-elastic plates. Mech Adv Mater Struct 13(3):249–266

    Article  Google Scholar 

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Authors and Affiliations

  1. Department of Mechanical Engineering, Faculty of Engineering, Imam Khomeini International University, Qazvin, Iran

    Farzad Ebrahimi & Mahsa Karimiasl

  2. Department of Mathematics, Madanapalle Institute of Technology and Science, Madanapalle, Andhra Pradesh, 517325, India

    Abhinav Singhal

Authors
  1. Farzad Ebrahimi
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  2. Mahsa Karimiasl
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  3. Abhinav Singhal
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Correspondence to Farzad Ebrahimi.

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Ebrahimi, F., Karimiasl, M. & Singhal, A. Magneto-electro-elastic analysis of piezoelectric–flexoelectric nanobeams rested on silica aerogel foundation. Engineering with Computers 37, 1007–1014 (2021). https://doi.org/10.1007/s00366-019-00869-z

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  • DOI: https://doi.org/10.1007/s00366-019-00869-z

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