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Axisymmetric vibrations of temperature-dependent functionally graded moderately thick circular plates with two-dimensional material and temperature distribution

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Abstract

In the present paper, free vibration analysis of bi-directional functionally graded circular plates subjected to two-dimensional temperature variation has been presented on the basis of first-order shear deformation theory. The mechanical properties of the plate material are assumed to be temperature-dependent and graded in thickness as well as radial direction. Using the thermal boundary conditions of the plate, the exact solution of two-dimensional heat conduction equation has been obtained by separation of variables technique. The thermoelastic equilibrium equations and equations of motion for such plate have been derived from an energy-based Hamilton’s principle. The generalized differential quadrature method has been applied to compute the numerical values for thermally induced displacements and natural frequencies. MATLAB has been used to obtain these values for clamped and simply supported plates. The influence of thermal environment together with various plate parameters such as power-law index, heterogeneity parameter and density parameter on the natural frequencies has been investigated for the first three modes. The results obtained herein for some special cases are in good agreement with those obtained by other numerical methods. Three-dimensional mode shapes for specified plates have been illustrated.

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References

  1. Koizumi M (1993) The concept of FGM. Ceram Trans Funct Grad Mater 34:3–10

    Google Scholar 

  2. Li W, Han B (2018) Research and application of functionally gradient materials. IOP Conf Ser Mater Sci Eng. https://doi.org/10.1088/1757-899x/394/2/022065

    Article  Google Scholar 

  3. Jha DK, Kant T, Singh RK (2013) A critical review of recent research on functionally graded plates. Compos Struct 96:833–849. https://doi.org/10.1016/j.compstruct.2012.09.001

    Article  Google Scholar 

  4. Mahamood RM, Akinlabi ET (1978) Functionally graded material: an overview. Trans Jpn Inst Met. 19:664–668

    Google Scholar 

  5. Nikbakht S, Kamarian S, Shakeri M (2019) A review on optimization of composite structures Part II: functionally graded materials. Compos Struct 214:83–102. https://doi.org/10.1016/j.compstruct.2019.01.105

    Article  Google Scholar 

  6. Swaminathan K, Sangeetha DM (2017) Thermal analysis of FGM plates—a critical review of various modeling techniques and solution methods. Compos Struct 160:43–60. https://doi.org/10.1016/j.compstruct.2016.10.047

    Article  Google Scholar 

  7. Reddy JN (2008) Theory and analysis of elastic plates and shells. J Appl Math Mech. https://doi.org/10.1002/zamm.200890020

    Article  Google Scholar 

  8. Nejati M, Yas MH, Eslampanah AH, Bagheriasl M (2017) Extended three-dimensional generalized differential quadrature method: the basic equations and thermal vibration analysis of functionally graded fiber orientation rectangular plates. Mech Adv Mater Struct 24:854–870. https://doi.org/10.1080/15376494.2016.1196789

    Article  Google Scholar 

  9. Adineh M, Kadkhodayan M (2017) Three-dimensional thermo-elastic analysis of multi-directional functionally graded rectangular plates on elastic foundation. Acta Mech 228:881–899. https://doi.org/10.1007/s00707-016-1743-x

    Article  MathSciNet  Google Scholar 

  10. Adineh M, Kadkhodayan M (2017) Three-dimensional thermo-elastic analysis and dynamic response of a multi-directional functionally graded skew plate on elastic foundation. Compos Part B Eng 125:227–240. https://doi.org/10.1016/j.compositesb.2017.05.070

    Article  Google Scholar 

  11. Ding S, Wu CP (2018) Optimization of material composition to minimize the thermal stresses induced in FGM plates with temperature-dependent material properties. Int J Mech Mater Des 14:527–549. https://doi.org/10.1007/s10999-017-9388-z

    Article  Google Scholar 

  12. Demirbas MD (2017) Thermal stress analysis of functionally graded plates with temperature-dependent material properties using theory of elasticity. Compos Part B Eng 131:100–124. https://doi.org/10.1016/j.compositesb.2017.08.005

    Article  Google Scholar 

  13. Demirbas MD, Ekici R, Apalak MK (2018) Thermoelastic analysis of temperature-dependent functionally graded rectangular plates using finite element and finite difference methods. Mech Adv Mater Struct. https://doi.org/10.1080/15376494.2018.1494871

    Article  Google Scholar 

  14. Manthena VR (2019) Uncoupled thermoelastic problem of a functionally graded thermosensitive rectangular plate with convective heating. Arch Appl Mech 89:1627–1639. https://doi.org/10.1007/s00419-019-01532-1

    Article  Google Scholar 

  15. Zaoui FZ, Ouinas D, Tounsi A (2019) New 2D and quasi-3D shear deformation theories for free vibration of functionally graded plates on elastic foundations. Compos Part B Eng 159:231–247. https://doi.org/10.1016/j.compositesb.2018.09.051

    Article  Google Scholar 

  16. Bellifa H, Benrahou KH, Hadji L, Houari MSA, Tounsi A (2016) Bending and free vibration analysis of functionally graded plates using a simple shear deformation theory and the concept the neutral surface position. J Braz Soc Mech Sci Eng 38:265–275. https://doi.org/10.1007/s40430-015-0354-0

    Article  Google Scholar 

  17. Brischetto S, Tornabene F, Fantuzzi N, Viola E (2016) 3D exact and 2D generalized differential quadrature models for free vibration analysis of functionally graded plates and cylinders. Meccanica 51:2059–2098. https://doi.org/10.1007/s11012-016-0361-y

    Article  MathSciNet  MATH  Google Scholar 

  18. Fahsi A, Tounsi A, Hebali H, Chikh A, Bedia EAA, Mahmoud SR (2017) A four variable refined nth-order shear deformation theory for mechanical and thermal buckling analysis of functionally graded plates. Geomech Eng 13:385–410. https://doi.org/10.12989/scs.2017.25.3.257

    Article  Google Scholar 

  19. Houari MSA, Tounsi A, Bessaim A, Mahmoud SR (2018) A new simple three-unknown sinusoidal shear deformation theory for functionally graded plates|Korea Science A new simple three-unknown sinusoidal shear deformation theory for functionally graded plates. Steel Compos Struct 22:2018

    Google Scholar 

  20. Tounsi A, Al-Dulaijan SU, Al-Osta MA, Chikh A, Al-Zahrani MM, Sharif A (2020) A four variable trigonometric integral plate theory for hygro-thermo-mechanical bending analysis of AFG ceramic–metal plates resting on a two-parameter elastic foundation. Steel Compos Struct 34:511–524

    Google Scholar 

  21. Abbasi S, Farhatnia F, Jazi SR (2014) A semi-analytical solution on static analysis of circular plate exposed to non-uniform axisymmetric transverse loading resting on Winkler elastic foundation. Arch Civ Mech Eng 14:476–488. https://doi.org/10.1016/j.acme.2013.09.007

    Article  Google Scholar 

  22. Kiani Y, Eslami MR (2013) Instability of heated circular FGM plates on a partial Winkler-type foundation. Acta Mech 224:1045–1060. https://doi.org/10.1007/s00707-012-0800-3

    Article  MathSciNet  MATH  Google Scholar 

  23. Kiani Y, Eslami MR (2013) Composites : part B An exact solution for thermal buckling of annular FGM plates on an elastic medium. Compos Part B 45:101–110. https://doi.org/10.1016/j.compositesb.2012.09.034

    Article  Google Scholar 

  24. Kiani Y, Eslami MR (2014) Geometrically non-linear rapid heating of temperature-dependent circular FGM plates. J Therm Stress 37:1495–1518. https://doi.org/10.1080/01495739.2014.937259

    Article  Google Scholar 

  25. Demirbas MD, Apalak MK (2018) Investigation of the thermo-elastic response of adhesively bonded two-dimensional functionally graded circular-plates based on theory of elasticity. Iran J Sci Technol Trans Mech Eng 42(2018):415–433. https://doi.org/10.1007/s40997-018-0261-y

    Article  Google Scholar 

  26. Lal R, Ahlawat N (2019) Buckling and vibrations of two-directional FGM Mindlin circular plates under hydrostatic peripheral loading hydrostatic peripheral loading. Mech Adv Mater Struct. https://doi.org/10.1080/15376494.2017.1341576

    Article  Google Scholar 

  27. Wu CP, Yu LT (2019) Free vibration analysis of bi-directional functionally graded annular plates using finite annular prism methods. J Mech Sci Technol 33:2267–2279. https://doi.org/10.1007/s12206-019-0428-5

    Article  Google Scholar 

  28. Javani M, Kiani Y, Eslami MR (2019) Large amplitude thermally induced vibrations of temperature dependent annular FGM plates. Compos Part B Eng 163:371–383. https://doi.org/10.1016/j.compositesb.2018.11.018

    Article  Google Scholar 

  29. Javani M, Kiani Y, Eslami MR (2019) Rapid heating vibrations of FGM annular sector plates. Eng Comput. https://doi.org/10.1007/s00366-019-00825-x

    Article  MATH  Google Scholar 

  30. Farhatnia F, Ghanbari-Mobarakeh M, Rasouli-Jazi S, Oveissi S (2017) Thermal buckling analysis of functionally graded circular plate resting on the pasternak elastic foundation via the differential transform method. Facta Univ Ser Mech Eng 15:545. https://doi.org/10.22190/FUME170104004F

    Article  Google Scholar 

  31. Bagheri H, Kiani Y, Eslami MR (2018) Asymmetric thermal buckling of temperature dependent annular FGM plates on a partial elastic foundation. Comput Math Appl 75:1566–1581. https://doi.org/10.1016/j.camwa.2017.11.021

    Article  MathSciNet  MATH  Google Scholar 

  32. Mirtalaie SH (2018) Differential quadrature free vibration analysis of functionally graded thin annular sector plates in thermal environments. J Dyn Syst Meas Control 140:101006. https://doi.org/10.1115/1.4039785

    Article  Google Scholar 

  33. Civalek Ö, Baltacıoglu AK (2019) Free vibration analysis of laminated and FGM composite annular sector plates. Compos Part B Eng 157:182–194. https://doi.org/10.1016/j.compositesb.2018.08.101

    Article  Google Scholar 

  34. Saini R, Saini S, Lal R, Singh IV (2019) Buckling and vibrations of FGM circular plates in thermal environment. Procedia Struct Integr 14:362–374. https://doi.org/10.1016/j.prostr.2019.05.045

    Article  Google Scholar 

  35. Lal R, Saini R (2019) Vibration analysis of functionally graded circular plates of variable thickness under thermal environment by generalized differential quadrature method. J Vib Control. https://doi.org/10.1177/1077546319876389

    Article  Google Scholar 

  36. Lal R, Saini R (2019) Thermal effect on radially symmetric vibrations of temperature-dependent FGM circular plates with nonlinear thickness variation. Mater Res Express 6:0865. https://doi.org/10.1088/2053-1591/ab24ee

    Article  Google Scholar 

  37. Lal R, Saini R (2019) On the high-temperature free vibration analysis of elastically supported functionally graded material plates under mechanical in-plane force via GDQR. J Dyn Syst Meas Control 141:101003. https://doi.org/10.1115/1.4043489

    Article  Google Scholar 

  38. Lal R, Saini R (2019) On radially symmetric vibrations of functionally graded non-uniform circular plate including non-linear temperature rise. Eur J Mech A/Solids 77:103796. https://doi.org/10.1016/j.euromechsol.2019.103796

    Article  MathSciNet  MATH  Google Scholar 

  39. Lal R, Saini R (2020) Vibration analysis of FGM circular plates under non-linear temperature variation using generalized differential quadrature rule. Appl Acoust 158:107027. https://doi.org/10.1016/j.apacoust.2019.107027

    Article  Google Scholar 

  40. Abrate S (2008) Functionally graded plates behave like homogeneous plates. Compos Part B Eng 39:151–158. https://doi.org/10.1016/j.compositesb.2007.02.026

    Article  Google Scholar 

  41. Fallah F, Nosier A (2015) Thermo-mechanical behavior of functionally graded circular sector plates. Acta Mech 226:37–54. https://doi.org/10.1007/s00707-014-1140-2

    Article  MathSciNet  MATH  Google Scholar 

  42. Zhang DG, Zhou HM (2015) Nonlinear bending analysis of FGM circular plates based on physical neutral surface and higher-order shear deformation theory. Aerosp Sci Technol 41:90–98. https://doi.org/10.1016/j.ast.2014.12.016

    Article  Google Scholar 

  43. Malekzadeh P, Haghighi MRG, Atashi MM (2011) Free vibration analysis of elastically supported functionally graded annular plates subjected to thermal environment. Meccanica 46:893–913. https://doi.org/10.1007/s11012-010-9345-5

    Article  MathSciNet  MATH  Google Scholar 

  44. Alibeigloo A (2012) Three-dimensional semi-analytical thermo-elasticity solution for a functionally graded solid and an annular circular plate. J Therm Stress 35:653–676. https://doi.org/10.1080/01495739.2012.688663

    Article  Google Scholar 

  45. Wang X (2015) Differential quadrature and differential quadrature based element. Methods. https://doi.org/10.1016/c2014-0-03612-x

    Article  MATH  Google Scholar 

  46. Gupta US, Lal R, Sharma S (2007) Vibration of non-homogeneous circular Mindlin plates with variable thickness. J Sound Vib 302:1–17. https://doi.org/10.1016/j.jsv.2006.07.005

    Article  Google Scholar 

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Acknowledgements

The authors wish to express their sincere thanks to the learned reviewers for their constructive comments and valuable suggestions in improving the paper. The financial support provided by Ministry of Human Resource Development, India, Grant No. MHRD-02-23-200-44 is gratefully acknowledged by Rahul Saini, to carrying this research work which is a part of his Ph.D. work at Indian Institute of Technology Roorkee, Roorkee, India.

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  1. Department of Mathematics, Indian Institute of Technology Roorkee, Roorkee, India

    Rahul Saini & Roshan Lal

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Saini, R., Lal, R. Axisymmetric vibrations of temperature-dependent functionally graded moderately thick circular plates with two-dimensional material and temperature distribution. Engineering with Computers 38, 437–452 (2022). https://doi.org/10.1007/s00366-020-01056-1

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