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Magneto-thermo-mechanical dynamic buckling analysis of a FG-CNTs-reinforced curved microbeam with different boundary conditions using strain gradient theory

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Abstract

In this article, dynamic buckling analysis of an embedded curved microbeam reinforced by functionally graded carbon nanotubes is carried out. The structure is subjected to thermal, magnetic and harmonic mechanical loads. Timoshenko beam theory is employed to simulate the structure. Furthermore, the temperature-dependent surrounding elastic foundation is modeled by normal springs and a shear layer. Using strain gradient theory, the small scale effects are taken into account. The extended rule of mixture is employed to estimate the equivalent properties of the composite material. The governing equations and different boundary conditions are derived based on the energy method and Hamilton’s principle. Dynamic stability regions of the system are obtained using differential quadrature method. The aim of this paper is to investigate the influence of different parameters such as small scale effect, boundary conditions, elastic foundation, volume fraction and distribution types of carbon nanotubes, magnetic field, temperature and central angle of the curved microbeam on the dynamic stability region of the system. The results indicate that by increasing the volume fraction of CNTs, the frequency of the system increases and thus the dynamic stability region occurs at higher frequencies.

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References

  • Abbasnejad, B., Rezazadeh, G.: Mechanical behavior of a FGM micro-beam subjected to a nonlinear electrostatic pressure. Int. J. Mech. Mater. Des. 8, 381–392 (2012)

    Article  Google Scholar 

  • Ansari, R., Gholami, R., Sahmani, S.: Free vibration analysis of size-dependent functionally graded microbeams based on the strain gradient Timoshenko beam theory. Compos. Struct. 94, 221–228 (2011)

    Article  MATH  Google Scholar 

  • Chaudhari, V.K., Lal, A.: Nonlinear free vibration analysis of elastically supported nanotube reinforced composite beam in thermal environment. Proc. Eng. 144, 928–935 (2016)

    Article  Google Scholar 

  • Chen, X., Meguid, S.A.: On the parameters which govern the symmetric snap-through buckling behavior of an initially curved microbeam. Int. J. Solids Struct. 66, 77–87 (2015)

    Article  Google Scholar 

  • Chen, X., Meguid, S.A.: Asymmetric bifurcation of thermally and electrically actuated functionally graded material microbeam. Proc. R. Soc. A 472, 20150597 (2016)

    Article  Google Scholar 

  • Ghorbani Shenas, A., Malekzadeh, P., Ziaee, S.: Vibration analysis of pre-twisted functionally graded carbon nanotube reinforced composite beams in thermal environment. Compos. Struct. 162, 325–340 (2017)

    Article  Google Scholar 

  • Heydari Meybodi, M., Saber-Samandari, S., Sadighi, M., Bagheri, M.R.: Low-velocity impact response of a nanocomposite beam using an analytical model. Lat. Am. J. Solids Struct. 12, 333–354 (2015)

    Article  Google Scholar 

  • Ishaquddin, M., Raveendranath, P., Reddy, J.N.: Efficient coupled polynomial interpolation scheme for out-of-plane free vibration analysis of curved beams. Finite Elem. Anal. Des. 110, 58–66 (2016)

    Article  Google Scholar 

  • Jafari-Talookolaei, R.A., Abedi, M., Hajianmaleki, M.: Vibration characteristics of generally laminated composite curved beams with single through-the-width delamination. Compos. Struct. 138, 172–183 (2016)

    Article  Google Scholar 

  • Kolahchi, R.: A comparative study on the bending, vibration and buckling of viscoelastic sandwich nano-plates based on different nonlocal theories using DC, HDQ and DQ methods. Aerosp. Sci. Technol. 66, 235–248 (2017)

    Article  Google Scholar 

  • Kolahchi, R., Moniribidgoli, A.M.: Size-dependent sinusoidal beam model for dynamic instability of single-walled carbon nanotubes. Appl. Math. Mech. Engl Ed 372, 265–274 (2016)

    Article  MathSciNet  Google Scholar 

  • Kolahchi, R., Rabani Bidgoli, M., Beygipoor, Gh, Fakhar, M.H.: A nonlocal nonlinear analysis for buckling in embedded FG-SWCNT-reinforced microplates subjected to magnetic field. J. Mech. Sci. Technol. 29, 3669–3677 (2015)

    Article  Google Scholar 

  • Kolahchi, R., Hosseini, H., Esmailpour, M.: Differential cubature and quadrature-Bolotin methods for dynamic stability of embedded piezoelectric nanoplates based on visco-nonlocal-piezoelasticity theories. Compos. Struct. 157, 174–186 (2016a)

    Article  Google Scholar 

  • Kolahchi, R., Safari, M., Esmailpour, M.: Dynamic stability analysis of temperature-dependent functionally graded CNT-reinforced visco-plates resting on orthotropic elastomeric medium. Compos. Struct. 150, 255–265 (2016b)

    Article  Google Scholar 

  • Kolahchi, R., Zarei, MSh, Hajmohammad, M.H., Naddaf Oskouei, A.: Visco-nonlocal-refined Zigzag theories for dynamic buckling of laminated nanoplates using differential cubature-Bolotin methods. Thin-Wall Struct. 113, 162–169 (2017)

    Article  Google Scholar 

  • Liu, Y.P., Reddy, J.N.: A nonlocal curved beam model based on a modified couple stress theory. Int. J. Struct. Stab. Dyn. 11, 495–512 (2011)

    Article  MathSciNet  MATH  Google Scholar 

  • Luu, A.T., Kim, N.I., Lee, J.: NURBS-based isogeometric vibration analysis of generally laminated deep curved beams with variable curvature. Compos. Struct. 119, 150–165 (2015)

    Article  Google Scholar 

  • Rastgo, A., Shafie, H., Allahverdizadeh, A.: Instability of curved beams made of functionally graded material under thermal loading. Int. J. Mech. Mater. Des. 2, 117–128 (2005)

    Article  Google Scholar 

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

    Article  Google Scholar 

  • Shen, HSh, Zhang, ChL: Nonlocal beam model for nonlinear analysis of carbon nanotubes on elastomeric substrates. Comput. Mater. Sci. 50, 1022–1029 (2011)

    Article  Google Scholar 

  • Wu, J.S., Lin, F.T., Shaw, H.J.: Free in-plane vibration analysis of a curved beam arch with arbitrary various concentrated elements. Appl. Math. Model. 37, 7588–7610 (2013)

    Article  MathSciNet  Google Scholar 

  • Wu, H., Kitipornchai, S., Yang, J.: Imperfection sensitivity of thermal post-buckling behavior of functionally graded carbon nanotube-reinforced composite beams. Appl. Math. Model. 42, 735–752 (2017)

    Article  MathSciNet  Google Scholar 

  • Yang, J., Ke, L., Feng, C.H.: Dynamic buckling of thermo-electro-mechanically loaded FG-CNTRC beams. Int. J. Struct. Stab. Dyn. 15, 1540017 (2015)

    Article  MathSciNet  MATH  Google Scholar 

  • Yang, W.D., Fang, C.Q., Wang, X.: Nonlinear dynamic characteristics of FG CNTs reinforced microbeam with piezoelectric layer based on unifying stress-strain gradient framework. Compos. Part B Eng. 111, 372–386 (2017)

    Article  Google Scholar 

  • Ye, T., Jin, G., Ye, X., Wang, X.: A series solution for the vibrations of composite laminated deep curved beams with general boundaries. Compos. Struct. 127, 450–465 (2015)

    Article  Google Scholar 

  • Zhang, B., He, Y., Liu, D., Gan, Zh, Shen, L.: A novel size-dependent functionally graded curved mircobeam model based on the strain gradient elasticity theory. Compos. Struct. 106, 374–392 (2013)

    Article  Google Scholar 

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Authors and Affiliations

  1. Department of Mechanical and Aerospace Engineering, Science and Research Branch, Islamic Azad University, Tehran, Iran

    Farshid Allahkarami & Mansour Nikkhah-bahrami

  2. Vehicle Technology Research Institute, Amirkabir University of Technology, Tehran, Iran

    Maryam Ghassabzadeh Saryazdi

Authors
  1. Farshid Allahkarami
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  2. Mansour Nikkhah-bahrami
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  3. Maryam Ghassabzadeh Saryazdi
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Correspondence to Mansour Nikkhah-bahrami.

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Allahkarami, F., Nikkhah-bahrami, M. & Saryazdi, M.G. Magneto-thermo-mechanical dynamic buckling analysis of a FG-CNTs-reinforced curved microbeam with different boundary conditions using strain gradient theory. Int J Mech Mater Des 14, 243–261 (2018). https://doi.org/10.1007/s10999-017-9374-5

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