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Hygrothermal Effects on the Free Vibration Behavior of Composite Plate Using nth-Order Shear Deformation Theory: a Micromechanical Approach

  • Abdelmalek Abdelmalek
  • Mokhtar BouazzaEmail author
  • Mohamed Zidour
  • Noureddine Benseddiq
Research Paper
  • 60 Downloads

Abstract

The free vibration behavior of isotropic and orthotropic composite plates under the hygrothermal environment is investigated in this article. The composite material properties are considered to be the function of temperature and moisture concentration, and the effective properties are evaluated using the micromechanics approach. The plate model is developed mathematically using refined nth-order shear deformation theory. The theory takes account of transverse shear effects and parabolic distribution of the transverse shear strains through the thickness of the plate; hence, it is unnecessary to use shear correction factors. Numerical results obtained by the present theory are compared with those in the literature.

Keywords

Orthotropic plates Vibrations Refined nth-order shear deformation theory Hygrothermal effects Micromechanics model 

References

  1. Adams DF, Miller AK (1977) Hygrothermal microstresses in a unidirectional composite exhibiting inelastic materials behaviour. J Compos Mater 11:285–299Google Scholar
  2. Adda-Bedia ELA, Bouazza M, Tounsi A, Benzair A, Maacho M (2008) Prediction of stiffness degradation in hygrothermal aged [0 m/90n]S composite laminates with transverse cracking. J Mater Process Technol 199:199–205Google Scholar
  3. Ahmadian MT, Sherafati M (2002) Zangeneh. Vibration analysis of orthotropic rectangular plates using superelements. Comput Methods Appl Mech Eng 191:2069–2075zbMATHGoogle Scholar
  4. Ait Amar Meziane M, Abdelaziz HH, Tounsi A (2014) An efficient and simple refined theory for buckling and free vibration of exponentially graded sandwich plates under various boundary conditions. J Sandwich Struct Mater 16(3):293–318Google Scholar
  5. Belabed Z, Houari MSA, Tounsi A, Mahmoud SR, Anwar Bég O (2014) An efficient and simple higher order shear and normal deformation theory for functionally graded material (FGM) plates. Compos B 60:274–283Google Scholar
  6. Benkeddad A, Grediac M, Vautrin A (1995) On the transient hygroscopic stresses in laminated composite plates. Compos Struct 30(2):201–205Google Scholar
  7. Benkeddad A, Grediac M, Vautrin A (1996) Computation of transient hygroscopic stresses in laminated composite plates. Compos Sci Technol 56:869–876Google Scholar
  8. Bennoun M, Houari MSA, Tounsi A (2016) A novel five variable refined plate theory for vibration analysis of functionally graded sandwich plates. Mech Adv Mater Struct 23(4):423–431Google Scholar
  9. Bouazza M, Benseddiq N (2015) Analytical modeling for the thermoelastic buckling behavior of functionally graded rectangular plates using hyperbolic shear deformation theory under thermal loadings. Multidiscip Model Mater Struct 11(4):558–578.  https://doi.org/10.1108/MMMS-02-2015-0008 Google Scholar
  10. Bouazza M, Lairedj A, Benseddiq N, Khalki S (2016) A refined hyperbolic shear deformation theory for thermal buckling analysis of cross-ply laminated plates. Mech Res Commun 73:117–126Google Scholar
  11. Bourada M, Kaci A, Houari MSA, Tounsi A (2015) A new simple shear and normal deformations theory for functionally graded beams. Steel and Compos Struct 18(2):409–423Google Scholar
  12. Bowles DE, Tompkins SS (1989) Prediction of coefficients of thermal expansion for unidirectional composites. J Compos Mater 23:370–381Google Scholar
  13. Chen S, Liu Z, Zhang Z (1992) Random vibration analysis for larger scale structures with random parameters. Comput Struct 43:247–254Google Scholar
  14. Hahn HT, Kim RY (1978) Swelling of composite laminates. Adv Compos Mater Environ Eff ASTM STP 658:98–120Google Scholar
  15. Hassaine Daouadji T, Hadj Henni A, Tounsi A, Adda Bedia EA (2012) A new hyperbolic shear deformation theory for bending analysis of functionally graded plates. Model Simul Eng 159806:10Google Scholar
  16. Hebali H, Tounsi A, Houari MSA, Bessaim A, Adda Bedia EA (2014) A new quasi-3D hyperbolic shear deformation theory for the static and free vibration analysis of functionally graded plates. ASCE J Eng Mech 140:374–383Google Scholar
  17. Jones RM (1975) Mechanics of composite materials. Hemisphere Publishing Corporation, WashingtonGoogle Scholar
  18. Kar VR, Panda SK (2015) Thermoelastic analysis of functionally graded doubly curved shell panels using nonlinear finite element method. Compos Struct 129:202–212Google Scholar
  19. Kar VR, Mahapatra TR, Panda SK (2015) Nonlinear flexural analysis of laminated composite flat panel under hygro-thermo-mechanical loading. Steel and Compos Struct An Int J 19(4):1011–1033zbMATHGoogle Scholar
  20. Katariya PV, Panda SK (2016) Thermal buckling and vibration analysis of laminated composite curved shell panel. Aircr Eng Aerosp Technol An Int J 88(1):97–107Google Scholar
  21. Kim HW, Grayson MA, Nairn JA (1995) The effects of hygrothermal aging on the microcracking properties of some carbon fiber/polyimide laminates. Adv Compos Lett 4:185–188Google Scholar
  22. Kim SE, Thai HT, Lee J (2009) Buckling analysis of plates using the two variable refined plate theory. Thin Wall Struct 47(4):455–462Google Scholar
  23. Koko TS, Olson MD (1992) Vibration analysis of stiffened plates by super elements. J Sound Vib 1581:149–167zbMATHGoogle Scholar
  24. Librescu L, Khdeir AA, Reddy JN (1990) Further results concerning the dynamic response of shear deformable elastic orthotropic plates. ZAMM 70:23–33MathSciNetzbMATHGoogle Scholar
  25. Liu S (1991) A vibration analysis of composite laminated plates. Finite Elem Anal Des 9:295–307zbMATHGoogle Scholar
  26. Mahapatra TR, Panda SK (2015a) Thermoelastic vibration analysis of laminated doubly curved shallow panels using non-linear FEM. J Therm Stresses 38:39–68Google Scholar
  27. Mahapatra TR, Panda SK (2015b) Effects of hygrothermal conditions on free vibration behaviour of laminated composite structures. IOP Conf Ser Mater Sci Eng.  https://doi.org/10.1088/1757-899X/75/1/012017 Google Scholar
  28. Mahapatra TR, Panda SK (2016) Nonlinear free vibration analysis of laminated composite spherical shell panel under elevated hygrothermal environment: amicromechanical approach. Aerosp Sci Technol 49:276–288Google Scholar
  29. Mahapatra TR, Kar VR, Panda SK (2015) Nonlinear free vibration analysis of laminated composite doubly curved shell panel in hygrothermal environment. J Sandwich Struct Mater 17(5):511–545Google Scholar
  30. Mahapatra TR, Panda SK, Kar VR (2016a) Nonlinear flexural analysis of laminated composite panel under hygro-thermo-mechanical loading—A micromechanical approach. Int J Comput Methods 13(3):1650015MathSciNetzbMATHGoogle Scholar
  31. Mahapatra TR, Panda Subrata K, Kar Vishesh R (2016b) Nonlinear hygro-thermo-elastic vibration analysis of doubly curved composite shell panel using finite element micromechanical model. Mech Adv Mater Struct 23(11):1343–1359.  https://doi.org/10.1080/15376494.2015.1085606 Google Scholar
  32. Mahapatra TR, Panda SK, Kar VR (2016c) Geometrically nonlinear flexural analysis of hygro-thermoelastic laminated composite doubly curved shell panel. Int J Mech Mater Des 12:153–171Google Scholar
  33. Mahapatra TR, Kar VR, Panda SK (2016d) Large amplitude vibration analysis of laminated composite spherical panels under hygrothermal environment. Int J Struct Stab Dyn 16:1450105MathSciNetzbMATHGoogle Scholar
  34. Mahapatra R, Panda SK, Dash S (2016e) Effect of hygrothermal environment on the nonlinear free vibration responses of laminated composite plates: a nonlinear Finite element micromechanical approach. IOP Conf Ser Mater Sci Eng 149:012151Google Scholar
  35. Mahi A, Adda Bedia EA, Tounsi A (2015) A new hyperbolic shear deformation theory for bending and free vibration analysis of isotropic, functionally graded, sandwich and laminated composite plates. Appl Math Model 39:2489–2508MathSciNetGoogle Scholar
  36. Mindlin RD, Schacknow A, Deresiewicz H (1956) Flexural vibrations of rectangular plates. J Appl Mech 23:431–436MathSciNetzbMATHGoogle Scholar
  37. Naidu NVS, Sinha PK (2007) Nonlinear free vibration analysis of laminated compos-ite shells in hygrothermal environments. Compos Struct 77:475–483Google Scholar
  38. Narendar S (2011) Buckling analysis of micro-/nano-scale plates based on two variable refined plate theory incorporating nonlocal scale effects. Compos Struct 93:3093–3103Google Scholar
  39. Panda SK, Mahapatra TR (2014) Nonlinear finite element analysis of laminated composite spherical shell vibration under uniform thermal loading. Meccanica 49:191–213MathSciNetzbMATHGoogle Scholar
  40. Panda SK, Katariya PV (2015) Stability and free vibration behaviour of laminated composite panels under thermo-mechanical loading. Int J Appl Comput Math 1:475–490MathSciNetzbMATHGoogle Scholar
  41. Piscopo V (2010) Refined buckling analysis of rectangular plates under uniaxial and biaxial compression. World Acad Sci Eng Technol 46:554–561Google Scholar
  42. Reddy JN (1979) Free vibration of antisymmetric angle-ply laminated including transverse shear deformation by the finite element method. J Sound Vib 66(4):565–576zbMATHGoogle Scholar
  43. Reddy JN (1984a) A simple higher-order theory for laminated composite plates. J Appl Mech 51:745–752zbMATHGoogle Scholar
  44. Reddy JN (1984b) A refined nonlinear theory of plates with transverse shear deformation. Int J Solids Struct 20:881–896zbMATHGoogle Scholar
  45. Reddy JN (1997) Mechanics of laminated composite plates: theory and analysis. CRC Press, Boca RatonzbMATHGoogle Scholar
  46. Shen HS (2001a) The effects of hygrothermal conditions on the postbuckling of shear deformable laminated cylindrical shells. Int J Solids Struct 38:6357–6380zbMATHGoogle Scholar
  47. Shen HS (2001b) Hygrothermal effects on the postbuckling of shear deformable laminated plates. Int J Mech Sci 43:1259–1281zbMATHGoogle Scholar
  48. Shen HS (2002) Hygrothermal effects on the postbuckling of axially loaded shear deformable laminated cylindrical panels. Compos Struct 56(1):73–85Google Scholar
  49. Shen CH, Springer GS (1981) Environmental effects in the elastic moduli of composite material. In: Springer GS (ed) Environmental effects on composite materials. Technomic Publishing Company Inc, Westport, pp 94–108Google Scholar
  50. Shimpi RP (2002) Refined plate theory and its variants. AIAA J 40(1):137–146Google Scholar
  51. Shimpi RP, Patel HG (2006a) A two variable refined plate theory for orthotropic plate analysis. Int J Solids Struct 43:6783–6799zbMATHGoogle Scholar
  52. Shimpi RP, Patel HG (2006b) Free vibrations of plate using two variable refined plate theory. J Sound Vib 296:979–999Google Scholar
  53. Srinivas S, Rao AK (1970) Bending, vibration and buckling of simply supported thick orthotropic rectangular plates and laminates. Int J Solids Struct 6:1464–1481zbMATHGoogle Scholar
  54. Srinivas S, Joga rao CV, Rao AK (1970) An exact analysis for vibration of simply supported homogeneous and laminated thick rectangular plates. J Sound Vib 12(2):187–199zbMATHGoogle Scholar
  55. Thai HT (2012) A nonlocal beam theory for bending, buckling, and vibration of nanobeams. Int J Eng Sci 52:56–64MathSciNetzbMATHGoogle Scholar
  56. Thai HT, Kim SE (2010) Free vibration of laminated composite plates using two variable refined plate theory. Int J Mech Sci 52:626–633Google Scholar
  57. Thai HT, Choi DH (2012) An efficient and simple refined theory for buckling analysis of functionally graded plates. Appl Math Model 36:1008–1022MathSciNetzbMATHGoogle Scholar
  58. Tounsi A, Adda-Bedia EA (2003) Some observations on the evolution of transversal hygroscopic stresses in laminated composites plates: effect of anisotropy. Compos Struct 59:445–454Google Scholar
  59. Tounsi A, Bouazza M, Adda-Bedia ELA (2005a) Computation of transient hygroscopique stresses in unidirectional laminated composite plates with cyclic and asymmetrical environmental conditions. J Mech Mate Des 1:271–286Google Scholar
  60. Tounsi A, Bouazza M, Meftah SA, Adda-Bedia ELA (2005b) On the transient hygroscopic stresses in polymer matrix laminated composites plates with cyclic and unsymmetric environmental conditions. Int J Polym Polym Compos Rapra Technol LTD (UK) 13(5):489–504Google Scholar
  61. Tsai SW (1988) Composite design. Think composites, DaytonGoogle Scholar
  62. Upadhyay PC, Lyons JS (2000) Effect of hygrothermal environment on the bending of PMC laminates under large deflection. J Reinf Plast Compos 19(6):465–491Google Scholar
  63. Xiang Song, Kang Gui-wen (2013a) A nth-order shear deformation theory for the bending analysis on the functionally graded plates. Eur J Mech A/Solids 37:336–343MathSciNetzbMATHGoogle Scholar
  64. Xiang S, Kang GW (2013b) A nth-order shear deformation theory for the bending analysis on the functionally graded plates. Eur J Mech A/Solid 37:336–343zbMATHGoogle Scholar
  65. Xiang S, Jin YX, Bi ZY, Jiang SX, Yang MS (2011a) A n-order shear deformation theory for free vibration of functionally graded and composite sandwich plates. Compos Struct 93:2826–2832Google Scholar
  66. Xiang S, Jiang SX, Bi ZY, Jin YX, Yang MS (2011b) A nth-order meshless generalization of Reddy’s third-order shear deformation theory for the free vibration on laminated composite plates. Compos Struct 93:299–307Google Scholar
  67. Xiang S, Kang GW, Xing B (2012) A nth-order shear deformation theory for the free vibration analysis on the isotropic plates. Meccanica 47:1913–1921MathSciNetzbMATHGoogle Scholar
  68. Xiang S, Kang GW, Yang MS, Zhao Y (2013) Natural frequencies of sandwich plate with functionally graded face and homogeneous core. Compos Struct 96:226–231Google Scholar
  69. Zenkour AM (2001) Buclding and free vibration of elastic plates using simple and mixed shear deformation theories. Acta Mech 146:183–197zbMATHGoogle Scholar
  70. Zenkour AM (2011) Bending of orthotropic plates resting on Pasternak’s foundations using mixed shear deformation theory. Acta Mech Sin 27(6):956–962MathSciNetzbMATHGoogle Scholar

Copyright information

© Shiraz University 2017

Authors and Affiliations

  • Abdelmalek Abdelmalek
    • 1
  • Mokhtar Bouazza
    • 2
    • 3
    Email author
  • Mohamed Zidour
    • 3
    • 4
  • Noureddine Benseddiq
    • 5
  1. 1.Department of Mechanical EngineeringUniversity of BecharBecharAlgeria
  2. 2.Department of Civil EngineeringUniversity of BecharBecharAlgeria
  3. 3.Laboratory of Materials and Hydrology (LMH)University of Sidi Bel AbbesSidi Bel AbbesAlgeria
  4. 4.Department of Civil EngineeringUniversity of Ibn KhaldounTiaretAlgeria
  5. 5.Mechanics Laboratory of Lille, CNRS UMR 8107University of Lille 1LilleFrance

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