Journal of Computational Applied Mechanics

Vibration of inhomogeneous fibrous laminated plates using an efficient and simple polynomial refined theory

Document Type : Research Paper

Authors

1 Department of Civil Engineering, University TahriMohamedof Bechar, Bechar 08000, Algeria

2 Laboratory of Materials and Hydrology (LMH), University of Sidi Bel Abbes, Sidi Bel Abbes 2200, Algeria

3 Department of Mathematics, Faculty of Science, Kafrelsheikh University, Kafrelsheikh 33516, Egypt

Abstract

In this article, a reliable model for the vibration of cross-ply and angle-ply laminated plates that own inhomogeneous elastic properties is considered. The methodology includes a theoretical study of free vibration behavior of composite plates with the inhomogeneous fibrous distribution of the volume fraction using a sinusoidal model by the use of the advanced refined theory of shear deformation of nth-higher-order. The micromechanical typical is proposed to represent the elastic and physical properties of the inhomogeneous laminated composite plate. The effects of inhomogeneity, lamination schemes, aspect ratio, and the number and order of layers on dimensionless vibration frequencies are investigated.

Keywords

  1. Martin, A.F. and A.W. Leissa, Application of the Ritz method to plane elasticity problems for composite sheets with variable fibre spacing. International Journal for Numerical Methods in Engineering, 1989. 28: p. 1813–1825.
  2. Leissa, A.W. and A.F. Martin, Vibration and buckling of rectangular composite plates with variable fiber spacing. Composite Structures, 1990. 14: p. 339–57.
  3. Pandey, M.D. and A.N. Sherbourne, Stability analysis of inhomogeneous, fibrous composite plates. International Journal of Solids and Structures, 1993. 30(1): p. 37–60.
  4. Pandey, M.D. and A.N. Sherbourne, Influence of the prebuckling stress-field on the critical loads of inhomogeneous composite laminates. Composite Structures, 1993. 25: p. 363–369.
  5. Shiau, L.C. and G.C. Lee, Stress concentration around holes in composite laminates with variable fiber spacing. Composite Structures, 1993. 24(2): p. 107–115.
  6. Benatta, M.A., I. Mechab, A. Tounsi and E.A. Adda Bedia, Static analysis of functionally graded short beams including warping and shear deformation effects. Computational Materials Science, 2008. 44(2): p. 765–773,.
  7. Bedjilili Y., A. Tounsi, H.M. Berrabah, I. Mechab, E.A. Adda Bedia and S. Benaissa, Natural frequencies of composite beams with a variable fiber volume fraction including rotary inertia and shear deformation. Applied Mathematics and Mechanics, 2009. 30: p. 717–726.
  8. Kargarnovin, M.H. and M. Hashemi, Free vibration analysis of multilayered composite cylinder consisting fibers with variable volume fraction. Composite Structures, 2012. 94: p. 931–944.
  9. Kuo, S-Y., Aerothermoelastic analysis of composite laminates with variable fiber spacing. Computational Materials Science, 2014. 91: p 83–90.
  10. Kuo, S-Y., Flutter of thermally buckled angle-ply laminates with variable fiber spacing. Composites part  B, 2016. 95: p. 240–251.
  11. Ganesan, N., R. Sahana and P.V. Indira, Effect of hybrid fibers on tension stiffening of reinforced geopolymer concrete. Advances in Concrete Construction, 2017. 5(1): p. 75–86.
  12. Fu, Y., P. Zhang and F. Yang, Interlaminar stress distribution of composite laminated plates with functionally graded fiber volume fraction. Materials and Design, 2010. 31(6): p. 2904–2915.
  13. Murugan S., E.I.S. Flores and S. Adhikari, Optimal design of variable fiber spacing composites for morphing aircraft skins. Composite Structures, 2012. 94: p. 1626–1633.
  14. Al-Mosawi, A.I., Effect of variable fiber spacing on post-buckling of boron/epoxy fiber reinforced laminated composite plate. Applied Mechanics and Materials, 2013. 245: p. 126–131.
  15. M.S. Aravinda Kumar, S. Panda, D. Chakraborty, Design and analysis of a smart graded fiber-reinforced composite laminated plate. Composite Structures 124, 176–195,2015.
  16. Draiche K., A. Tounsi, Y. Khalfi, A trigonometric four variable plate theory for free vibration of rectangular composite plates with patch mass. Steel and Composite Structures, 2014. 17(1): p. 69–81.
  17. Thai, H.T., A nonlocal beam theory for bending, buckling, and vibration of nanobeams. International Journal of Engineering Science, 2012. 52: p. 56–64.
  18. Zenkour, A.M., A quasi-3D refined theory for functionally graded single-layered and sandwich plates with porosities. Composite Structures, 2018. 201: p. 38–48.
  19. Zenkour, A.M., Quasi-3D refined theory for functionally graded porous plates: Displacements and stresses. Physical Mesomechanics, 2020. 23(1): p. 39–53.
  20. Fahsi, B., R.B. Bouiadjra, A. Mahmoudi, S. Benyoucef, A. Tounsi, Assessing the effects of porosity on the bending, buckling, and vibrations of functionally graded beams resting on an elastic foundation by using a new refined quasi-3d theory. Mechanics of Composite Materials, 2019. 55(2): p. 219–230.
  21. Derbale A., M. Bouazza and N. Benseddiq, Analysis of the mechanical and thermal buckling of laminated beams by new refined shear deformation theory. Iranian Journal of Science and Technology, 2021. 45: p. 89–98.
  22. Bouazza, M. and A.M. Zenkour, Vibration of carbon nanotube-reinforced plates via refined nth-higher-order theory. Archive of Applied Mechanics, 2020. 90: p. 1755–1769.
  23. Ferreira, A.J.M., C.M.C. Roque and R.M.N Jorge, Free vibration analysis of symmetric laminated composite plates by FSDT and radial basis functions. Computer Methods in Applied Mechanics and Engineering, 2005. 194(39-41): p. 4265–4278.
  24. Xiang, S. and K.M. Wang, Free vibration analysis of symmetric laminated composite plates by trigonometric shear deformation theory and inverse multiquadric RBF. Thin-Walled Structures, 2009. 47(3): 304–310.
  25. Srinivas, S. and A.K. Rao, Bending, vibration and buckling of simply supported thick orthotropic rectangular plates and laminates. International Journal of Solids and Structures, 1970. 6: p. 1464–1481.
  26. Reddy, J.N., N.D. Phan, Stability and vibration of isotropic, orthotropic and laminated plates according to a higher-order shear deformation theory. Journal of Sound and Vibration, 1985. 98: p. 157–170.
  27. Hosseini Hashemi, Sh., S.R. Atashipour, M. Fadaee, An exact analytical approach for in-plane and out-of-plane free vibration analysis of thick laminated transversely isotropic plates. Archive of Applied Mechanics, 2012. 82: p. 677–698.
  28. Reddy, J.N., A simple higher-order theory for laminated composite plates. Journal of Applied Mechanics, 1984. 51: p. 745–752.
  29. Liu, S., A vibration analysis of composite laminated plates. Finite Elements in Analysis and Design, 1991. 9: p. 295–307.
  30. Noor, A.K., Free vibrations of multilayered composite plates. AIAA Journal, 1972. 11(7): p. 1038–1039.
  31. Phan N.D. and J.N. Reddy, Analysis of laminated composite plates using a higher order shear deformation theory. International Journal for Numerical Methods in Engineering, 1985. 21: p. 2201–2219.
  32. Rao, V.V.S. and P.K. Sinha, Dynamic response of multidirectional composites in hygrothermal environments. Composite Structures, 2004. 64: p. 329–338.
  33. Secgin, A. and A.S. Sarigul, Free vibration analysis of symmetrically laminated thin composite plates by using discrete singular convolution (DSC) approach: algorithm and verification. Journal of Sound and Vibration, 2008. 315: p. 197–211.
  34. Dai, K.Y., G.R. Liu, M.K. Lim, X.L. Chen, A mesh-free method for static and free vibration analysis of shear deformable laminated composite plates. Journal of Sound and Vibration, 2004. 269: p. 633–652.
  35. Chen X.L., G.R. Liu and S.P. Lim, An element free Galerkin method for the free vibration analysis of composite laminates of complicated shape. Composite Structures, 2003. 59: p. 279–289.
  36. Zenkour, A.M. and A.F. Radwan, Bending and buckling analysis of FGM plates resting on elastic foundations in hygrothermal environment. Archives of Civil and Mechanical Engineering, 2020. 20: p. 112.
  37. Zenkour, A.M., Quasi-3D refined theory for functionally graded porous plates: Displacements and stresses, Physical Mesomechanics, 2020. 23(1): p. 39–53.
  38. Bouazza M., A.M. Zenkour and N. Benseddiq, Effect of material composition on bendinganalysis of FG plates via a two-variable refined hyperbolic theory. Archives of Mechanics, 2018. 70(2): p. 107–129.
  39. Thai, H.T. and D.H. Choi. An efficient and simple refined theory for buckling analysis of functionally graded plates. Applied Mathematical Modelling, 2012. 36: p. 1008–1022.
  40. Zenkour, A.M., Bending analysis of functionally graded sandwich plates using a simple four-unknown shear and normal deformations theory. Journal of Sandwich Structures & Materials, 2013. 15(6): p. 629–656.
  41. Al Khateeb, S.A. and A.M. Zenkour, A refined four-unknown plate theory for advanced plates resting on elastic foundations in hygrothermal environment. Composite Structures, 2014. 111(1), p. 240–248.
  42. Zenkour, A.M., Thermal bending of layered composite plates resting on elastic foundations using four-unknown shear and normal deformations theory. Composite Structures, 2015. 122: p. 260–270.
  43. Thai, C.H., A.M. Zenkour, M. Abdel Wahab, H.N-X. Thai, A simple four-unknown shear and normal deformations theory for functionally graded isotropic and sandwich plates based on isogeometric analysis. Composite Structures, 2016. 139: p. 77–95.
  44. Zenkour, A.M. and R.A. Alghanmi, Stress analysis of a functionally graded plate integrated with piezoelectric faces via a four-unknown shear deformation theory. Results in Physics, 2019. 12: p. 268–277.
  45. Tran, T.T., V.K. Tran, Q-H. Pham and A.M. Zenkour, Extended four-unknown higher-order shear deformation nonlocal theory for bending, buckling and free vibration of functionally graded porous nanoshell resting on elastic foundation. Composite Structures, 2021. 264(15): p. 113737.
  46. Nejad M.Z., M. Jabbari and A. Hadi, A review of functionally graded thick cylindrical and conical shells. Journal of Computational Applied Mechanics, 2017. 48(2), p. 357–370.
  47. Gharibi M., M.Z. Nejad and A. Hadi, Elastic analysis of functionally graded rotating thick cylindrical pressure vessels with exponentially-varying properties using power series method of Frobenius. Journal of Computational Applied Mechanics, 2017. 48(1): 89–98.
  48. Xiang S., Y.X. Jin, Z.Y. Bi, S.X. Jiang, M.S. Yang, A n-order shear deformation theory for free vibration of functionally graded and composite sandwich plates. Composite Structures, 2011. 93: p. 2826–2832.
  49. Xiang S., S.X. Jiang, Z.Y. Bi, Y.X. Jin, M.S. Yang, A nth-order meshless generalization of Reddy’s third-order shear deformation theory for the free vibration on laminated composite plates. Composite Structures, 2011. 93: 299–307.
  50. Xiang S., G.W. Kang, B. Xing, A nth-order shear deformation theory for the free vibration analysis on the isotropic plates. Meccanica, 2012. 47: 1913–1921.
  51. Jones, R.M., Mechanics of Composite Materials. 1975: McGraw-Hill, New York.
  52. Reddy, J.N., Mechanics of laminated composite plates: theory and analysis. 1997: Boca Raton CRC Press.
Journal of Computational Applied Mechanics
Volume 52, Issue 2
June 2021
Pages 233-245
  • Receive Date: 16 March 2021
  • Revise Date: 31 March 2021
  • Accept Date: 31 March 2021