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Flexural Wave Propagation Analysis of Embedded S-FGM Nanobeams Under Longitudinal Magnetic Field Based on Nonlocal Strain Gradient Theory

  • Research Article - Mechanical Engineering
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Abstract

This paper investigates wave propagation of size-dependent functionally graded (FG) nanobeams resting on elastic foundation subjected to axial magnetic field based on the nonlocal strain gradient theory and Euler–Bernoulli beam model by using an analytical approach. The nonlocal beam model has a length scale parameter and captures the size influences. Material properties are spatially graded according to sigmoid distribution. A derivation of the governing equations for the wave propagation analysis of nanoscale S-FGM beams is conducted. Then, the dispersion relations between wave frequency and phase velocity with the wave number is investigated. It is found that wave propagation characteristics of nonlocal S-FGM beams are influenced by various parameters including length scale parameter, material graduation, elastic foundation parameters and magnetic field intensity.

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References

  1. Akbarzadeh, A.H.; Abedini, A.; Chen, Z.T.: Effect of micromechanical models on structural responses of functionally graded plates. Compos. Struct. 119, 598–609 (2015)

    Article  Google Scholar 

  2. Han, S.C.; Lomboy, G.R.; Kim, K.D.: Mechanical vibration and buckling analysis of FGM plates and shells using a four-node quasi-conforming shell element. Int. J. Struct. Stab. Dyn. 8(02), 203–229 (2008)

    Article  Google Scholar 

  3. Ben-Oumrane, S.; Abedlouahed, T.; Ismail, M.; Mohamed, B.B.; Mustapha, M.; El Abbas, A.B.: A theoretical analysis of flexional bending of Al/Al\(_2\)O\(_3\) S-FGM thick beams. Comput. Mater. Sci. 44(4), 1344–1350 (2009)

    Article  Google Scholar 

  4. Atmane, H.A.; Tounsi, A.; Ziane, N.; Mechab, I.: Mathematical solution for free vibration of sigmoid functionally graded beams with varying cross-section. Steel Compos. Struct. 11(6), 489–504 (2011)

    Article  Google Scholar 

  5. Lee, W.H.; Han, S.C.; Park, W.T.: A refined higher order shear and normal deformation theory for E-, P-, and S-FGM plates on Pasternak elastic foundation. Compos. Struct. 122, 330–342 (2015)

    Article  Google Scholar 

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

    Article  MathSciNet  MATH  Google Scholar 

  7. Eringen, A.C.: On differential equations of nonlocal elasticity and solutions of screw dislocation and surface waves. J. Appl. Phys. 54(9), 4703–4710 (1983)

    Article  Google Scholar 

  8. Yang, F.A.C.M.; Chong, A.C.M.; Lam, D.C.C.; Tong, P.: Couple stress based strain gradient theory for elasticity. Int. J. Solid. Struct. 39(10), 2731–2743 (2002)

    Article  MATH  Google Scholar 

  9. Ruoff, R.S.; Qian, D.; Liu, W.K.: Mechanical properties of carbon nanotubes: theoretical predictions and experimental measurements. C. R. Phys. 4(9), 993–1008 (2003)

    Article  Google Scholar 

  10. Ke, C.H.; Pugno, N.; Peng, B.; Espinosa, H.D.: Experiments and modeling of carbon nanotube-based NEMS devices. J. Mech. Phys. Solids 53(6), 1314–1333 (2005)

    Article  MATH  Google Scholar 

  11. Patti, A.; Barretta, R.; de Sciarra, F.M.; Mensitieri, G.; Menna, C.; Russo, P.: Flexural properties of multi-wall carbon nanotube/polypropylene composites: experimental investigation and nonlocal modeling. Compos. Struct. 131, 282–289 (2015)

    Article  Google Scholar 

  12. Narendar, S.; Gopalakrishnan, S.: Nonlocal scale effects on wave propagation in multi-walled carbon nanotubes. Comput. Mater. Sci. 47(2), 526–538 (2009)

    Article  Google Scholar 

  13. Wang, L.: Wave propagation of fluid-conveying single-walled carbon nanotubes via gradient elasticity theory. Comput. Mater. Sci. 49(4), 761–766 (2010)

    Article  Google Scholar 

  14. Yang, Y.; Zhang, L.; Lim, C.W.: Wave propagation in double-walled carbon nanotubes on a novel analytically nonlocal Timoshenko-beam model. J. Sound Vib. 330(8), 1704–1717 (2011)

    Article  Google Scholar 

  15. Assadi, A.; Farshi, B.: Size-dependent longitudinal and transverse wave propagation in embedded nanotubes with consideration of surface effects. Acta Mech. 222(1–2), 27–39 (2011)

    Article  MATH  Google Scholar 

  16. Narendar, S.; Gupta, S.S.; Gopalakrishnan, S.: Wave propagation in single-walled carbon nanotube under longitudinal magnetic field using nonlocal Euler-Bernoulli beam theory. Appl. Math. Model. 36(9), 4529–4538 (2012)

    Article  MathSciNet  MATH  Google Scholar 

  17. Akgöz, B.; Civalek, Ö.: Longitudinal vibration analysis for microbars based on strain gradient elasticity theory. J. Vib. Control 20(4), 606–616 (2014)

    Article  MathSciNet  Google Scholar 

  18. Aydogdu, M.: Longitudinal wave propagation in multiwalled carbon nanotubes. Compos. Struct. 107, 578–584 (2014)

    Article  Google Scholar 

  19. Arani, A.G.; Kolahchi, R.; Mortazavi, S.A.: Nonlocal piezoelasticity based wave propagation of bonded double-piezoelectric nanobeam-systems. Int. J. Mech. Mater. Des. 10(2), 179–191 (2014)

    Article  Google Scholar 

  20. Filiz, S.; Aydogdu, M.: Wave propagation analysis of embedded (coupled) functionally graded nanotubes conveying fluid. Compos. Struct. 132, 1260–1273 (2015)

    Article  Google Scholar 

  21. Eltaher, M.A.; Khater, M.E.; Emam, S.A.: A review on nonlocal elastic models for bending, buckling, vibrations, and wave propagation of nanoscale beams. Appl. Math. Model. 40(5), 4109–4128 (2015)

    MathSciNet  Google Scholar 

  22. Li, L.; Hu, Y.; Ling, L.: Wave propagation in viscoelastic single-walled carbon nanotubes with surface effect under magnetic field based on nonlocal strain gradient theory. Phys. E 75, 118–124 (2016)

    Article  Google Scholar 

  23. Barati, M.R.; Zenkour, A.M.; Shahverdi, H.: Thermo-mechanical buckling analysis of embedded nanosize FG plates in thermal environments via an inverse cotangential theory. Compos. Struct. 141, 203–212 (2016)

    Article  Google Scholar 

  24. Eltaher, M.A.; Emam, S.A.; Mahmoud, F.F.: Free vibration analysis of functionally graded size-dependent nanobeams. Appl. Math. Comput. 218(14), 7406–7420 (2012)

    MathSciNet  MATH  Google Scholar 

  25. Akgöz, B.; Civalek, Ö.: Thermo-mechanical buckling behavior of functionally graded microbeams embedded in elastic medium. Int. J. Eng. Sci. 85, 90–104 (2014)

    Article  Google Scholar 

  26. Niknam, H.; Aghdam, M.M.: A semi analytical approach for large amplitude free vibration and buckling of nonlocal FG beams resting on elastic foundation. Compos. Struct. 119, 452–462 (2015)

    Article  Google Scholar 

  27. Ebrahimi, F.; Salari, E.: Effect of various thermal loadings on buckling and vibrational characteristics of nonlocal temperature-dependent FG nanobeams. Mech. Adv. Mater. Struct. 23(12), 1379–1397 (2016)

    Article  Google Scholar 

  28. Ebrahimi, F.; Salari, E.: Thermo-mechanical vibration analysis of nonlocal temperature-dependent FG nanobeams with various boundary conditions. Compos. Part B Eng. 78, 272–290 (2015)

    Article  Google Scholar 

  29. Tounsi, A.; Zemri, A.; Houari, M.S.A.; Bousahla, A.A.: A mechanical response of functionally graded nanoscale beam: an assessment of a refined nonlocal shear deformation theory beam theory. Struct. Eng. Mech. 54(4), 693 (2015)

    Article  Google Scholar 

  30. Ebrahimi, F.; Barati, M.R.: A nonlocal higher-order shear deformation beam theory for vibration analysis of size-dependent functionally graded nanobeams. Arab. J. Sci. Eng. 41(5), 1679–1690 (2016)

    Article  MathSciNet  Google Scholar 

  31. Ebrahimi, F.; Salari, E.: Size-dependent thermo-electrical buckling analysis of functionally graded piezoelectric nanobeams. Smart Mater. Struct. 24(12), 125007 (2015)

    Article  Google Scholar 

  32. Khorshidi, M.A.; Shariati, M.: Free vibration analysis of sigmoid functionally graded nanobeams based on a modified couple stress theory with general shear deformation theory. J. Braz. Soc. Mech. Sci. Eng. 1–13 (2015)

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

    Article  Google Scholar 

  34. Li, L., Hu, Y., Ling, L.: Flexural wave propagation in small-scaled functionally graded beams via a nonlocal strain gradient theory. Compos. Struct. 133, 1079–1092 (2015)

    Article  Google Scholar 

  35. Zhang, Y.W.; Chen, J.; Zeng, W.; Teng, Y.Y.; Fang, B.; Zang, J.: Surface and thermal effects of the flexural wave propagation of piezoelectric functionally graded nanobeam using nonlocal elasticity. Comput. Mater. Sci. 97, 222–226 (2015)

    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 & Mohammad Reza Barati

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  1. Farzad Ebrahimi
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  2. Mohammad Reza Barati
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Correspondence to Farzad Ebrahimi.

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Ebrahimi, F., Barati, M.R. Flexural Wave Propagation Analysis of Embedded S-FGM Nanobeams Under Longitudinal Magnetic Field Based on Nonlocal Strain Gradient Theory. Arab J Sci Eng 42, 1715–1726 (2017). https://doi.org/10.1007/s13369-016-2266-4

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  • DOI: https://doi.org/10.1007/s13369-016-2266-4

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