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Nonlinear free vibration of temperature-dependent sandwich beams with carbon nanotube-reinforced face sheets

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Abstract

In this research, large amplitude free vibrations of a sandwich beam with stiff core and carbon nanotube (CNT)-reinforced face sheets are analysed. The distribution of CNTs across the thickness of the face sheets may be uniform or functionally graded. The equivalent single- layer theory of Timoshenko is used to construct the Hamiltonian of the beam under the von Kármán type of geometrical nonlinearity assumptions. A uniform temperature field through the beam is also included in the formulation. The Ritz method with polynomial basis functions is used to discrete the equations of motion and establish the matrix representation of the governing equations. A nonlinear eigenvalue problem is obtained and solved using a standard continuation procedure. After validating the developed solution method and formulation, parametric studies are conducted to examine the influences of thermal environment, core thickness-to-face sheet thickness ratio, boundary conditions, amplitude of vibrations, CNTs volume fraction and their distribution pattern. It is concluded that an increase in the volume fraction of CNTs results in higher fundamental frequency and decreases the nonlinear-to-linear frequency ratio.

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References

  1. Liew K.M., Lei Z.X., Zhang L.W.: Mechanical analysis of functionally graded carbon nanotube reinforced composites: a review. Compos. Struct. 120, 90–97 (2015)

    Article  MathSciNet  Google Scholar 

  2. Kundalwal S.I., Meguid S.A.: Effect of carbon nanotube waviness on active damping of laminated hybrid composite shells. Acta Mech. 226, 2035–2052 (2015)

    Article  MathSciNet  MATH  Google Scholar 

  3. Ngabonziza Y., Li J., Barry C.F.: Electrical conductivity and mechanical properties of multiwalled carbon nanotube-reinforced polypropylene nanocomposites. Acta Mech. 220, 289–298 (2011)

    Article  MATH  Google Scholar 

  4. Moradi-Dastjerdi R., Pourasghar A., Foroutan M.: The effects of carbon nanotube orientation and aggregation on vibrational behavior of functionally graded nanocomposite cylinders by a mesh-free method. Acta Mech. 224, 2817–2832 (2013)

    Article  MathSciNet  MATH  Google Scholar 

  5. Yanase K., Moriyama S., Ju J.W.: Effects of CNT waviness on the effective elastic responses of CNT-reinforced polymer composites. Acta Mech. 224, 1351–1364 (2013)

    Article  MATH  Google Scholar 

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

    Article  Google Scholar 

  7. Lin F., Xiang Y.: Vibration of carbon nanotube reinforced composite beams based on the first and third order beam theories. Appl. Math. Model. 38, 3741–3754 (2014)

    Article  MathSciNet  Google Scholar 

  8. Lin F., Xiang Y.: Numerical analysis on nonlinear free vibration of carbon nanotube reinforcement composite beams. Int. J. Struct. Stab. Dyn. 14, 1350056 (2014)

    Article  MathSciNet  Google Scholar 

  9. Pourasghar A., Kamarian S.: Dynamic stability analysis of functionally graded nanocomposite non-uniform column reinforced by carbon nanotube. J. Vib. Control 21, 2499–2508 (2015)

    Article  Google Scholar 

  10. Rafiee M., Yang J., Kitipornchai S.: Thermal bifurcation buckling of piezoelectric carbon nanotube reinforced composite beams. Comput. Math. Appl. 66, 1147–1160 (2013)

    Article  Google Scholar 

  11. Yas M.H., Samadi N.: Free vibrations and buckling analysis of carbon nanotube-reinforced composite Timoshenko beams on elastic foundation. Int. J. Press. Vessels Pip. 98, 119–128 (2012)

    Article  Google Scholar 

  12. Ansari R., Faghih Shojaei M., Mohammadi V., Gholami R., Sadeghi F.: Nonlinear forced vibration analysis of functionally graded carbon nanotube-reinforced composite Timoshenko beams. Compos. Struct. 113, 316–327 (2014)

    Article  Google Scholar 

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

    Article  Google Scholar 

  14. Shen H.S., Xiang Y.: Nonlinear analysis of nanotube-reinforced composite beams resting on elastic foundations in thermal environments. Eng. Struct. 56, 698–708 (2013)

    Article  Google Scholar 

  15. Rafiee M., Yang J., Kitipornchai S.: Large amplitude vibration of carbon nanotube reinforced functionally graded composite beams with piezoelectric layers. Compos. Struct. 96, 716–725 (2013)

    Article  Google Scholar 

  16. Ke L.L., Yang J., Kitipornchai S.: Dynamic stability of functionally graded carbon nanotube-reinforced composite beams. Mech. Adv. Mater. Struct. 20, 28–37 (2013)

    Article  Google Scholar 

  17. Alibeigloo A., Liew K.M.: Elasticity solution of free vibration and bending behavior of functionally graded carbon nanotube-reinforced composite beam with thin piezoelectric layers using differential quadrature method. Int. J. Appl. Mech. 7, 1550002 (2015)

    Article  Google Scholar 

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

  19. Jam J.E., Kiani Y.: Low velocity impact response of functionally graded carbon nanotube reinforced composite beams in thermal environment. Compos. Struct. 132, 35–43 (2015)

    Article  Google Scholar 

  20. Mirzaei M., Kiani Y.: Snap-through phenomenon in a thermally postbuckled temperature dependent sandwich beam with FG-CNTRC face sheets. Compos. Struct. 134, 1004–1013 (2015)

    Article  Google Scholar 

  21. Wu H., Kitipornchai S., Yang J.: Free vibration and buckling analysis of sandwich beams with functionally graded carbon nanotube-reinforced composite face sheets. Int. J. Struct. Stab. Dyn. 15, 1540011 (2015)

    Article  MathSciNet  Google Scholar 

  22. Zhang L.W., Song Z.G., Liew K.M.: State-space Levy method for vibration analysis of FG-CNT composite plates subjected to in-plane loads based on higher-order shear deformation theory. Compos. Struct. 134, 989–1003 (2015)

    Article  Google Scholar 

  23. Zhang L.W., Cui W.C., Liew K.M.: Vibration analysis of functionally graded carbon nanotube reinforced composite thick plates with elastically restrained edges. Int. J. Mech. Sci. 103, 9–21 (2015)

    Article  Google Scholar 

  24. Lei Z.X., Zhang L.W., Liew K.M.: Free vibration analysis of laminated FG-CNT reinforced composite rectangular plates using the kp-Ritz method. Compos. Struct. 127, 245–259 (2015)

    Article  Google Scholar 

  25. Lei Z.X., Zhang L.W., Liew K.M.: Elastodynamic analysis of carbon nanotube-reinforced functionally graded plates. Int. J. Mech. Sci. 99, 208–217 (2015)

    Article  Google Scholar 

  26. Zhang L.W., Liew K.M.: Large deflection analysis of FG-CNT reinforced composite skew plates resting on Pasternak foundations using an element-free approach. Compos. Struct. 132, 974–983 (2015)

    Article  Google Scholar 

  27. Zhang L.W., Song Z.G., Liew K.M.: Nonlinear bending analysis of FG-CNT reinforced composite thick plates resting on Pasternak foundations using the element-free IMLS-Ritz method. Compos. Struct. 128, 165–175 (2015)

    Article  Google Scholar 

  28. Zhang L.W., Liew K.M.: Geometrically nonlinear large deformation analysis of functionally graded carbon nanotube reinforced composite straight-sided quadrilateral plates. Comput. Methods Appl. Mech. Eng. 295, 219–239 (2015)

    Article  MathSciNet  Google Scholar 

  29. Zhang L.W., Lei Z.X., Liew K.M.: Buckling analysis of FG-CNT reinforced composite thick skew plates using an element-free approach. Compos. Part B Eng. 75, 36–46 (2015)

    Article  Google Scholar 

  30. Zhang L.W., Liew K.M., Reddy J.N.: Postbuckling of carbon nanotube reinforced functionally graded plates with edges elastically restrained against translation and rotation under axial compression. Comput. Methods Appl. Mech. Eng. 298, 1–28 (2016)

    Article  MathSciNet  Google Scholar 

  31. Lei Z.X., Zhang L.W., Liew K.M., Yu J.L.: Dynamic stability analysis of carbon nanotube-reinforced functionally graded cylindrical panels using the element-free kp-Ritz method. Compos. Struct. 113, 328–338 (2014)

    Article  Google Scholar 

  32. Lei Z.X., Zhang L.W., Liew K.M.: Analysis of laminated CNT reinforced functionally graded plates using the element-free kp-Ritz method. Compos. Part B Eng. 84, 211–221 (2016)

    Article  Google Scholar 

  33. Shen H.S.: Postbuckling of nanotube-reinforced composite cylindrical shells in thermal environments, part I: axially-loaded shells. Compos. Struct. 93, 2096–2108 (2011)

    Article  Google Scholar 

  34. Shen H.S.: Thermal buckling and postbuckling behavior of functionally graded carbon nanotube-reinforced composite cylindrical shells. Compos. Part B Eng. 43, 1030–1038 (2012)

    Article  Google Scholar 

  35. Mirzaei M., Kiani Y.: Thermal buckling of temperature dependent FG-CNT reinforced composite conical shells. Aerosp. Sci. Technol. 47, 42–53 (2015)

    Article  Google Scholar 

  36. Mirzaei, M., Kiani, Y.: Thermal buckling of temperature dependent FG-CNT reinforced composite plates. Meccanica. doi:10.1007/s11012-015-0348-0

  37. Mirzaei, M., Kiani, Y.: Free vibration of functionally graded carbon nanotube reinforced composite cylindrical panels. Compos. Struct. 142, 45–56 (2016)

  38. Jam J.E., Kiani Y.: Buckling of pressurized functionally graded carbon nanotube reinforced conical shells. Compos. Struct. 125, 586–595 (2015)

    Article  Google Scholar 

  39. Zhang L.W., Lei Z.X., Liew K.M.: Buckling analysis of FG-CNT reinforced composite thick skew plates using an element-free approach. Compos. Part B Eng. 75, 36–46 (2015)

    Article  Google Scholar 

  40. Lei Z.X., Zhang L.W., Liew K.M.: Vibration analysis of CNT-reinforced functionally graded rotating cylindrical panels using the element-free kp-Ritz method. Compos. Part B Eng. 77, 291–303 (2015)

    Article  Google Scholar 

  41. Zhang L.W., Huang D., Liew K.M.: An element-free IMLS-Ritz method for numerical solution of three-dimensional wave equations. Comput. Methods Appl. Mech. Eng. 297, 116–139 (2015)

    Article  MathSciNet  Google Scholar 

  42. Zhang L.W., Zhu P., Liew K.M.: Thermal buckling of functionally graded plates using a local Kriging meshless method. Compos. Struct. 108, 472–492 (2014)

    Article  Google Scholar 

  43. Zhu P., Zhang L.W., Liew K.M.: Geometrically nonlinear thermomechanical analysis of moderately thick functionally graded plates using a local Petrov Galerkin approach with moving Kriging interpolation. Compos. Struct. 107, 298–314 (2014)

    Article  Google Scholar 

  44. Zhang L.W., Li D.M., Liew K.M.: An element-free computational framework for elastodynamic problems based on the IMLS-Ritz method. Eng. Anal. Bound. Elem. 54, 39–46 (2015)

    Article  MathSciNet  Google Scholar 

  45. Ghiasian S.E., Kiani Y., Eslami M.R.: Non-linear rapid heating of FGM beams. Int. J. Non Linear Mech. 67, 74–84 (2014)

    Article  Google Scholar 

  46. Prathap G., Varadan T.K.: The large amplitude vibration of hinged beams. Comput. Struct. 9, 219–222 (1978)

    Article  MATH  Google Scholar 

  47. Bhashyam G.R., Prathap G.: Galerkin finite element method for nonlinear beam vibrations. J. Sound Vib. 72, 191–203 (1980)

    Article  MATH  Google Scholar 

  48. Shen H.S., Xiang Y.: Postbuckling of axially compressed nanotube-reinforced composite cylindrical panels resting on elastic foundations in thermal environments. Compos. Part B Eng. 67, 50–61 (2014)

    Article  Google Scholar 

  49. Shen H.S., Xiang Y.: Postbuckling of nanotube-reinforced composite cylindrical shells under combined axial and radial mechanical loads in thermal environment. Compos. Part B Eng. 52, 311–322 (2013)

    Article  Google Scholar 

  50. Han Y., Elliott J.: Molecular dynamics simulations of the elastic properties of polymer/carbon nanotube composites. Comput. Mater. Sci. 39, 315–323 (2007)

    Article  Google Scholar 

  51. Wang Z.X., Shen H.S.: Nonlinear vibration and bending of sandwich plates with nanotube-reinforced composite face sheets. Compos. Part B Eng. 43, 411–421 (2012)

    Article  Google Scholar 

  52. Marur S.R., Prathap G.: Non-linear beam vibration problems and simplifications in finite element models. Comput. Mech. 35, 352–360 (2005)

    Article  MATH  Google Scholar 

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Authors and Affiliations

  1. Department of Mechanical Engineering, Faculty of Engineering, University of Qom, Qom, Iran

    M. Mirzaei

  2. Faculty of Engineering, Shahrekord University, Shahrekord, Iran

    Y. Kiani

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  1. M. Mirzaei
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  2. Y. Kiani
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Correspondence to Y. Kiani.

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Mirzaei, M., Kiani, Y. Nonlinear free vibration of temperature-dependent sandwich beams with carbon nanotube-reinforced face sheets. Acta Mech 227, 1869–1884 (2016). https://doi.org/10.1007/s00707-016-1593-6

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  • DOI: https://doi.org/10.1007/s00707-016-1593-6

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