Skip to main content
SpringerLink
Log in

Effects of elastic foundation on the large-amplitude vibration analysis of functionally graded GPL-RC annular sector plates

  • Original Article
  • Published:
Engineering with Computers Aims and scope Submit manuscript

Abstract

The main purpose of this research is to investigate the impacts of the two-parameter elastic medium on the geometrically nonlinear free vibration of nanocomposite annular sector plates reinforced with graphene platelets. The modified Halpin–Tsai micromechanical model is implemented to determine the overall mechanical properties. With the aid of Hamilton’s principle and in according the first-order shear deformation plate theory in conjunction with geometric nonlinearity effects, the nonlinear sets of motion equations are derived for functionally graded nanocomposite annular sector plates. The 2D generalized differential quadrature GDQ method, the harmonic balance method and Newton–Raphson iteration technique are utilized to numerically solve the problem and obtain the nonlinear vibration response. Multiple comparative investigations are provided to express the efficiency of the model. The impacts of involved geometrical and material factors are also examined on the nonlinear vibration behavior of functionally graded nanocomposite annular sector plates.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Fig.1
Fig. 2
Fig. 3
Fig. 4
Fig. 5
Fig. 6
Fig. 7
Fig. 8
Fig. 9
Fig. 10
Fig. 11

Similar content being viewed by others

References

  1. Rafiee MA, Rafiee J, Wang Z, Song H, Yu ZZ, Koratkar N (2009) Enhanced mechanical properties of nanocomposites at low graphene content. ACS Nano 3(12):3884–3890

    Google Scholar 

  2. Rahman R, Haque A (2013) Molecular modeling of crosslinked graphene–epoxy nanocomposites for characterization of elastic constants and interfacial properties. Compos B Eng 54:353–364

    Google Scholar 

  3. Shen HS (2009) Nonlinear bending of functionally graded carbon nanotube-reinforced composite plates in thermal environments. Compos Struct 91(1):9–19

    Google Scholar 

  4. Song M, Kitipornchai S, Yang J (2017) Free and forced vibrations of functionally graded polymer composite plates reinforced with graphene nanoplatelets. Compos Struct 159:579–588

    Google Scholar 

  5. Shen HS, Xiang Y, Lin F (2017) Nonlinear bending of functionally graded graphene-reinforced composite laminated plates resting on elastic foundations in thermal environments. Compos Struct 170:80–90

    Google Scholar 

  6. Civalek Ö (2017) Free vibration of carbon nanotubes reinforced (CNTR) and functionally graded shells and plates based on FSDT via discrete singular convolution method. Compos B Eng 111:45–59

    Google Scholar 

  7. Yang B, Kitipornchai S, Yang YF, Yang J (2017) 3D thermo-mechanical bending solution of functionally graded graphene reinforced circular and annular plates. Appl Math Model 49:69–86

    MathSciNet  MATH  Google Scholar 

  8. Sahmani S, Fattahi AM, Ahmed NA (2019) Analytical treatment on the nonlocal strain gradient vibrational response of postbuckled functionally graded porous micro-/nanoplates reinforced with GPL. Eng Comput. https://doi.org/10.1007/s00366-019-00782-5

    Article  Google Scholar 

  9. Ansari R, Torabi J, Hassani R (2018) In-plane and shear buckling analysis of FG-CNTRC annular sector plates based on the third-order shear deformation theory using a numerical approach. Comput Math Appl 75(2):486–502

    MathSciNet  MATH  Google Scholar 

  10. Ebrahimi F, Dabbagh A (2019) An analytical solution for static stability of multi-scale hybrid nanocomposite plates. Eng Comput. https://doi.org/10.1007/s00366-019-00840-y

    Article  Google Scholar 

  11. Wu Q, Chen H, Gao W (2019) Nonlocal strain gradient forced vibrations of FG-GPLRC nanocomposite microbeams. Eng Comput. https://doi.org/10.1007/s00366-019-00794-1

    Article  Google Scholar 

  12. Sahmani S, Fattahi AM, Ahmed NA (2019) Analytical mathematical solution for vibrational response of postbuckled laminated FG-GPLRC nonlocal strain gradient micro-/nanobeams. Eng Comput 35(4):1173–1189

    Google Scholar 

  13. Gholami R, Ansari R (2018) Nonlinear harmonically excited vibration of third-order shear deformable functionally graded graphene platelet-reinforced composite rectangular plates. Eng Struct 156:197–209

    Google Scholar 

  14. Mallek H, Jrad H, Wali M, Dammak F (2019) Nonlinear dynamic analysis of piezoelectric-bonded FG-CNTR composite structures using an improved FSDT theory. Eng Comput. https://doi.org/10.1007/s00366-019-00891-1

    Article  MATH  Google Scholar 

  15. Fallah A, Aghdam MM (2011) Nonlinear free vibration and post-buckling analysis of functionally graded beams on nonlinear elastic foundation. Eur J Mech A Solids 30(4):571–583

    MATH  Google Scholar 

  16. Sahmani S, Aghdam MM, Rabczuk T (2018) Nonlinear bending of functionally graded porous micro/nano-beams reinforced with graphene platelets based upon nonlocal strain gradient theory. Compos Struct 186:68–78

    Google Scholar 

  17. Ansari R, Torabi J (2019) Semi-analytical postbuckling analysis of polymer nanocomposite cylindrical shells reinforced with functionally graded graphene platelets. Thin-Walled Struct 144:106248

    Google Scholar 

  18. Karimiasl M, Ebrahimi F, Mahesh V (2019) Postbuckling analysis of piezoelectric multiscale sandwich composite doubly curved porous shallow shells via Homotopy Perturbation Method. Eng Comput. https://doi.org/10.1007/s00366-019-00841-x

    Article  Google Scholar 

  19. Wang ZX, Shen HS (2011) Nonlinear vibration of nanotube-reinforced composite plates in thermal environments. Comput Mater Sci 50(8):2319–2330

    Google Scholar 

  20. Shen HS, Xiang Y, Lin F (2017) Nonlinear vibration of functionally graded graphene-reinforced composite laminated plates in thermal environments. Comput Methods Appl Mech Eng 319:175–193

    MathSciNet  MATH  Google Scholar 

  21. Lei ZX, Liew KM, Yu JL (2013) Free vibration analysis of functionally graded carbon nanotube-reinforced composite plates using the element-free kp-Ritz method in thermal environment. Compos Struct 106:128–138

    Google Scholar 

  22. Malekzadeh P, Zarei AR (2014) Free vibration of quadrilateral laminated plates with carbon nanotube reinforced composite layers. Thin-Walled Struct 82:221–232

    Google Scholar 

  23. Gao K, Gao W, Chen D, Yang J (2018) Nonlinear free vibration of functionally graded graphene platelets reinforced porous nanocomposite plates resting on elastic foundation. Compos Struct 204:831–846

    Google Scholar 

  24. Reddy RMR, Karunasena W, Lokuge W (2018) Free vibration of functionally graded-GPL reinforced composite plates with different boundary conditions. Aerosp Sci Technol 78:147–156

    Google Scholar 

  25. Zhao Z, Feng C, Wang Y, Yang J (2017) Bending and vibration analysis of functionally graded trapezoidal nanocomposite plates reinforced with graphene nanoplatelets (GPLs). Compos Struct 180:799–808

    Google Scholar 

  26. Wu H, Yang J, Kitipornchai S (2018) Parametric instability of thermo-mechanically loaded functionally graded graphene reinforced nanocomposite plates. Int J Mech Sci 135:431–440

    Google Scholar 

  27. Fantuzzi N, Tornabene F, Bacciocchi M, Dimitri R (2017) Free vibration analysis of arbitrarily shaped functionally graded carbon nanotube-reinforced plates. Compos B Eng 115:384–408

    Google Scholar 

  28. Ansari R, Torabi J, Shojaei MF (2017) Buckling and vibration analysis of embedded functionally graded carbon nanotube-reinforced composite annular sector plates under thermal loading. Compos B Eng 109:197–213

    Google Scholar 

  29. Ansari R, Torabi J, Hasrati E (2018) Axisymmetric nonlinear vibration analysis of sandwich annular plates with FG-CNTRC face sheets based on the higher-order shear deformation plate theory. Aerosp Sci Technol 77:306–319

    Google Scholar 

  30. Mohammadzadeh-Keleshteri M, Asadi H, Aghdam MM (2017) Geometrical nonlinear free vibration responses of FG-CNT reinforced composite annular sector plates integrated with piezoelectric layers. Compos Struct 171:100–112

    Google Scholar 

  31. Zhong R, Wang Q, Tang J, Shuai C, Qin B (2018) Vibration analysis of functionally graded carbon nanotube reinforced composites (FG-CNTRC) circular, annular and sector plates. Compos Struct 194:49–67

    Google Scholar 

  32. Gholami R, Ansari R (2018) Geometrically nonlinear resonance of higher-order shear deformable functionally graded carbon-nanotube-reinforced composite annular sector plates excited by harmonic transverse loading. Eur Phys J Plus 133(2):56

    Google Scholar 

  33. Shen HS (2016) Functionally graded materials: nonlinear analysis of plates and shells. CRC Press, Boca Raton

    Google Scholar 

  34. Bagherizadeh E, Kiani Y, Eslami MR (2011) Mechanical buckling of functionally graded material cylindrical shells surrounded by Pasternak elastic foundation. Compos Struct 93(11):3063–3071

    Google Scholar 

  35. Zhang J, Li S (2010) Dynamic buckling of FGM truncated conical shells subjected to non-uniform normal impact load. Compos Struct 92(12):2979–2983

    Google Scholar 

  36. Oñate E (2013) Structural analysis with the finite element method Linear statics: volume 2: beams, plates and shells. Springer, Berlin

    MATH  Google Scholar 

  37. Katariya PV, Hirwani CK, Panda SK (2019) Geometrically nonlinear deflection and stress analysis of skew sandwich shell panel using higher-order theory. Eng Comput 35(2):467–485

    Google Scholar 

  38. Demir Ç, Civalek Ö (2017) A new nonlocal FEM via Hermitian cubic shape functions for thermal vibration of nano beams surrounded by an elastic matrix. Compos Struct 168:872–884

    Google Scholar 

  39. Katariya PV, Panda SK (2019) Numerical evaluation of transient deflection and frequency responses of sandwich shell structure using higher order theory and different mechanical loadings. Eng Comput 35(3):1009–1026

    Google Scholar 

  40. Torabi J, Ansari R (2018) A higher-order isoparametric superelement for free vibration analysis of functionally graded shells of revolution. Thin-Walled Struct 133:169–179

    Google Scholar 

  41. Jrad H, Mars J, Wali M, Dammak F (2019) Geometrically nonlinear analysis of elastoplastic behavior of functionally graded shells. Eng Comput 35(3):833–847

    Google Scholar 

  42. Cottrell JA, Hughes TJR, Reali A (2007) Studies of refinement and continuity in isogeometric structural analysis. Comput Methods Appl Mech Eng 196(41–44):4160–4183

    MATH  Google Scholar 

  43. Mishra BP, Barik M (2019) NURBS-augmented finite element method for stability analysis of arbitrary thin plates. Eng Comput 35(2):351–362

    Google Scholar 

  44. Nguyen LB, Thai CH, Nguyen-Xuan H (2016) A generalized unconstrained theory and isogeometric finite element analysis based on Bézier extraction for laminated composite plates. Eng Comput 32(3):457–475

    Google Scholar 

  45. Civalek Ö (2008) Vibration analysis of conical panels using the method of discrete singular convolution. Commun Numer Methods Eng 24(3):169–181

    MathSciNet  MATH  Google Scholar 

  46. Civalek O (2006) Free vibration analysis of composite conical shells using the discrete singular convolution algorithm. Steel Composite Struct 6(4):353

    Google Scholar 

  47. Civalek O (2007) Linear vibration analysis of isotropic conical shells by discrete singular convolution (DSC). Struct Eng Mech 25(1):127–130

    MathSciNet  MATH  Google Scholar 

  48. Civalek Ö, Acar MH (2007) Discrete singular convolution method for the analysis of Mindlin plates on elastic foundations. Int J Press Vessels Pip 84(9):527–535

    Google Scholar 

  49. Civalek O, Yavas A (2006) Large deflection static analysis of rectangular plates on two parameter elastic foundations. Int J Sci Technol 1(1):43–50

    Google Scholar 

  50. Akgoz B, Civalek O (2011) Nonlinear vibration analysis of laminated plates resting on nonlinear two-parameters elastic foundations. Steel Compos Struct 11(5):403–421

    Google Scholar 

  51. Shu C (2012) Differential quadrature and its application in engineering. Springer, Berlin

    Google Scholar 

  52. Tornabene F, Viola E (2008) 2-D solution for free vibrations of parabolic shells using generalized differential quadrature method. Eur J Mech A Solids 27(6):1001–1025

    MATH  Google Scholar 

  53. Ansari R, Torabi J (2016) Numerical study on the free vibration of carbon nanocones resting on elastic foundation using nonlocal shell model. Appl Phys A 122(12):1073

    Google Scholar 

  54. Deuflhard P (2011) Newton methods for nonlinear problems: affine invariance and adaptive algorithms, vol 35. Springer, Berlin

    MATH  Google Scholar 

  55. Ben-Israel A (1966) A Newton-Raphson method for the solution of systems of equations. J Math Anal Appl 15(2):243–252

    MathSciNet  MATH  Google Scholar 

  56. Hejripour F, Saidi AR (2012) Nonlinear free vibration analysis of annular sector plates using differential quadrature method. Proc Inst Mech Eng Part C J Mech Eng Sci 226(2):485–497

    Google Scholar 

Download references

Author information

Authors and Affiliations

  1. School of Forestry, Henan Agricultural University, Zhengzhou, 450002, China

    Muhammad Aqeel Ashraf & Dangquan Zhang

  2. Department of Geology Faculty of Science, University of Malaya, 50603, Kuala Lumpur, Malaysia

    Muhammad Aqeel Ashraf

  3. School of Management, Henan University of Technology, Zhengzhou, 450001, China

    Zhenling Liu

  4. Institute of Research and Development, Duy Tan University, Da Nang, 550000, Vietnam

    Binh Thai Pham

Authors
  1. Muhammad Aqeel Ashraf
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Zhenling Liu
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Dangquan Zhang
    View author publications

    You can also search for this author in PubMed Google Scholar

  4. Binh Thai Pham
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding authors

Correspondence to Dangquan Zhang or Binh Thai Pham.

Additional information

Publisher's Note

Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Ashraf, M.A., Liu, Z., Zhang, D. et al. Effects of elastic foundation on the large-amplitude vibration analysis of functionally graded GPL-RC annular sector plates. Engineering with Computers 38, 325–345 (2022). https://doi.org/10.1007/s00366-020-01068-x

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s00366-020-01068-x

Keywords

Search

Navigation