Steel and Composite Structures

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Vibration behavior of trapezoidal sandwich plate with functionally graded-porous core and graphene platelet-reinforced layers

  • Liang, Di (College of Mechanical Engineering, Saitama Institute of Technology) ;
  • Wu, Qiong (College of Mechatronic Engineering, Nanjing Forestry University) ;
  • Lu, Xuemei (School of International Education, Nanning Normal University) ;
  • Tahouneh, Vahid (Young Researchers and Elite Club, Islamshahr Branch, Islamic Azad University)
  • Received : 2020.02.08
  • Accepted : 2020.06.10
  • Published : 2020.07.10
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Abstract

In this study, free vibration behavior of trapezoidal sandwich plates with porous core and two graphene platelets (GPLs) reinforced nanocomposite outer layers are presented. The distribution of pores and GPLs are supposed to be functionally graded (FG) along the thickness of core and nanocomposite layers, respectively. The effective Young's modulus of the GPL-reinforced (GPLR) nanocomposite layers is determined using the modified Halpin-Tsai micromechanics model, while the Poisson's ratio and density are computed by the rule of mixtures. The FSDT plate theory is utilized to establish governing partial differential equations and boundary conditions (B.C.s) for trapezoidal plate. The governing equations together with related B.C.s are discretized using a mapping- generalized differential quadrature (GDQ) method in the spatial domain. Then natural frequencies of the trapezoidal sandwich plates are obtained by GDQ method. Validity of current study is evaluated by comparing its numerical results with those available in the literature. A special attention is drawn to the role of GPLs weight fraction, GPLs patterns of two faces through the thickness, porosity coefficient and distribution of porosity on natural frequencies characteristics. New results show the importance of this permeates on vibrational characteristics of porous/GPLR nanocomposite plates. Finally, the influences of B.C.s and dimension as well as the plate geometry such as face to core thickness ratio on the vibration behaviors of the trapezoidal plates are discussed.

Keywords

References

  1. Affdl Halpin, J.C. and Kardos, J.L. (1976), "The Halpin-Tsai equations: A review", Polym. Eng. Sci., 16(5), 344-352. https://doi.org/10.1002/pen.760160512.
  2. Afrookhteh, S.S., Fathi, A., Naghdipour, M. and Alizadeh Sahraei, A. (2016), "An experimental investigation of the effects of weight fractions of reinforcement and timing of hardener addition on the strain sensitivity of carbon nanotube/polymer composites", U.P.B. Sci. Bull., Series B, 78(4), 121-130.
  3. Afrookhteh, S.S., Shakeri, M., Baniassadi, M. and Alizadeh Sahraei, A. (2018), "Microstructure reconstruction and characterization of the porous GDLs for PEMFC based on fibers orientation distribution", Fuel Cells, 18(2), https://doi.org/10.1002/fuce.201700239.
  4. Arefi, M. (2015), "Elastic solution of a curved beam made of functionally graded materials with different cross sections", Steel Compos. Struct., 18(3), 659-672. https://doi.org/10.12989/scs.2015.18.3.659.
  5. Barka, M., Benrahou, K.H., Bakora, A. and Tounsi, A. (2016), "Thermal post-buckling behavior of imperfect temperaturedependent sandwich FGM plates resting on Pasternak elastic foundation", Steel Compos. Struct., 22(1), 91-112. https://doi.org/10.12989/scs.2016.22.1.091.
  6. Bennai, R., Ait Atmane, H. and Tounsi, A. (2015), "A new higherorder shear and normal deformation theory for functionally graded sandwich beams", Steel Compos. Struct., 19(3), 521-546. https://doi.org/10.12989/scs.2015.19.3.521.
  7. Bert, C.W. and Malik, M. (1996), "Differential quadrature method in computational mechanics: a review", Appl. Mech. Rev., 49, 1-27. https://doi.org/10.1115/1.3101882.
  8. Bouchafa, A., Bouiadjra, M.B., Houari, M.S.A. and Tounsi, A. (2015), "Thermal stresses and deflections of functionally graded sandwich plates using a new refined hyperbolic shear deformation theory", Steel Compos. Struct., 18(6), 1493-1515. https://doi.org/10.12989/scs.2015.18.6.1493.
  9. Bouguenina, O., Belakhdar, K., Tounsi, A. and Bedia, E.A.A. (2015), "Numerical analysis of FGM plates with variable thickness subjected to thermal buckling", Steel Compos. Struct., 19(3), 679-695. https://doi.org/10.12989/scs.2015.19.3.679.
  10. Chen, C.S., Liu, F.H. and Chen, W.R. (2017), "vibration and stability of initially stressed sandwich plates with FGM face sheets in thermal environments", Steel Compos. Struct., 23(3), 251-261. https://doi.org/10.12989/scs.2017.23.3.251.
  11. Eyvazian, A., Hamouda, A.M., Tarlochan, F., Mohsenizadeh, S. and Ahmadi Dastjerdi, A. (2019), "Damping and vibration response of viscoelastic smart sandwich plate reinforced with non-uniform Graphene platelet with magnetorheological fluid core", Steel Compos. Struct., 33(6), 891-906. https://doi.org/10.12989/scs.2019.33.6.891.
  12. Fantuzzi, N., Tornabene, F., Bacciocchi, M. and Dimitri, R. (2017), "Free vibration analysis of arbitrarily shaped functionally graded carbon nanotube-reinforced plates", Compos. Part B, 115, 384-408. https://doi.org/10.1016/j.compositesb.2016.09.021.
  13. Finot, M. and Suresh, S. (1996), "Small and large deformation of thick and thin-film multilayers: effect of layer geometry, plasticity and compositional gradients", J. Mech. Phys. Solids, 44(5), 683-721. https://doi.org/10.1016/0022-5096(96)84548-0.
  14. Gupta, A.K. and Sharma, S. (2014), "Free transverse vibration of orthotropic thin trapezoidal plate of parabolically varying thickness subjected to linear temperature distribution", Shock and Vib., 2014, 1-6. http://dx.doi.org/10.1155/2014/392325.
  15. Gupta, A.K. and Sharma, P. (2016), "Vibration study of nonhomogeneous trapezoidal plates of variable thickness under thermal gradient", J.V.C. Control, 22(5), 1369-1379. https://doi.org/10.1177/1077546314535280.
  16. Gurses, M., Civalek, O ., Ersoy, H. and Kiracioglu, O. (2009), "Analysis of shear deformable laminated composite trapezoidal plates", Mater. Design, 30, 3030-3035. https://doi.org/10.1016/j.matdes.2008.12.016.
  17. Haldar, S. and Manna, M.C. (2003), "A high precision shear deformable element for free vibration of thick/thin composite trapezoidal plates", Steel Compos. Struct., 3(3), 213-229. https://doi.org/10.12989/scs.2003.3.3.213
  18. Halpin, J.C. and Tsai, S.W. (1969), "Effects of environmental factors on composite materials", AFML-TR-67-423.
  19. Houmat, A. (2001), "A sector Fourier p-element applied to free vibration analysis of sectorial plates", J. Sound Vib., 243(2), 269-282. https://doi.org/10.1006/jsvi.2000.3410
  20. Kamarian, S., Shakeri, M., Yas, M.H., Bodaghi, M. and Pourasghar, A. (2015), "Free vibration analysis of functionally graded nanocomposite sandwich beams resting on Pasternak foundation by considering the agglomeration effect of CNTs", J. Sandw. Struct. Mater., 1-31. https://doi.org/10.1177/1099636215590280.
  21. Kapidzic, Z. (2013), "Strength analysis and modeling of hybrid composite-aluminum aircraft structures", Linkoping Studies in Science and Technology, Licentiate Thesis No. 1590.
  22. Kettaf, F.Z., Houari, M.S.A., Benguediab, M. and Tounsi, A. (2013), "Thermal buckling of functionally graded sandwich plates using a new hyperbolic shear displacement model", Steel Compos. Struct., 15(4), 399-423. https://doi.org/10.12989/scs.2013.15.4.399.
  23. Kim, C.S. and Dickinson, S.M. (1989), "On the free, transverse vibration of annular and circular, thin, sectorial plates subjected to certain complicating effects", J. Sound Vib., 134(3), 407-421. https://doi.org/10.1016/0022-460X(89)90566-X.
  24. Kitipornchai, S., Chen, D. and Yang, J. (2017), "Free vibration and elastic buckling of functionally graded porous beams reinforced by graphene platelets", Mater. Design, 116, 656-665. https://doi.org/10.1016/j.matdes.2016.12.061.
  25. Koizumi, M. (1993), "The concept of FGM", Ceram. Trans. Funct. Grad. Mater., 34, 3-10.
  26. Liew, K.M. and Lam, K.Y. (1993), "On the use of 2-d orthogonal polynomials in the Rayleigh-Ritz method for flexural vibration of annular sector plates of arbitrary shape", Int. J. Mech. Sci., 35(2), 129-139. https://doi.org/10.1016/0020-7403(93)90071-2.
  27. Liew, K.M. and Liu, F.L. (2000), "Differential quadrature method for vibration analysis of shear deformable annular sector plates", J. Sound Vib., 230(2), 335-356. https://doi.org/10.1006/jsvi.1999.2623.
  28. Malekzadeh, P., Karami, G. (2005), "Polynomial and harmonic differential quadrature methods for free vibration of variable thickness skew plate", Eng. Struct., 27, 1563-1574. https://doi.org/10.1016/j.engstruct.2005.03.017
  29. Marin, M., Agarwal, R.P. and Mahmoud, S.R. (2013), "Nonsimple material problems addressed by the Lagrange's identity", Bound. Value Probl., 2013(1-14), 135. https://doi.org/10.1186/1687-2770-2013-135
  30. Marin, M. and Florea, O. (2014), "On temporal behaviour of solutions in thermoelasticity of porous micropolar bodies", An. St. Univ. Ovidius Constanta, 22(1), 169-188.
  31. Marin, M. (1994), "The Lagrange identity method in thermoelasticity of bodies with microstructure', Int. J. Eng. Sci., 32(8), 1229-1240. https://doi.org/10.1016/0020-7225(94)90034-5.
  32. Marin, M. and Nicaise, S. (2016), "Existence and stability results for thermoelastic dipolar bodies with double porosity", Continuum Mech. Thermodynam., 28(6), 1645-1657. https://doi.org/10.1007/s00161-016-0503-4
  33. Marin, M., Ellahi, R. and Chirila, A. (2017), "On solutions of Saint-Venant's problem for elastic dipolar bodies with voids", Carpathian J. Mathematics, 33(2), 219-232. https://doi.org/10.37193/CJM.2017.02.09
  34. Marin, M., Vlase, S., Ellahi, R. and Bhatti, M.M. (2019), "On the partition of energies for the backward in time problem of thermoelastic materials with a dipolar structure", Symmetry, Basel, 11(7), 1-16.
  35. Moradi-Dastjerdi, R. and Momeni-Khabisi, H. (2016), "Dynamic analysis of functionally graded nanocomposite plates reinforced by wavy carbon nanotube", Steel Compos. Struct., 22(2). https://doi.org/10.12989/scs.2016.22.2.277.
  36. Moradi-Dastjerdi, R., Foroutan, M., Pourasghar, A. (2013), "Dynamic analysis of functionally graded nanocomposite cylinders reinforced by carbon nanotube by a mesh-free method", Mater. Des., 44, 256-266. https://doi.org/10.1016/j.matdes.2012.07.069.
  37. Mukhopadhyay, M. (1979), "A semi-analytic solution for free vibration of annular sector plates", J. Sound Vib., 63(1), 87-95. https://doi.org/10.1016/0022-460X(79)90379-1
  38. Mukhopadhyay, M. (1982), "Free vibration of annular sector plates with edges possessing different degrees of rotational restraints", J. Sound Vib., 80(2), 275-279. https://doi.org/10.1016/0022-460X(82)90196-1.
  39. Park, W.T., Han, S.C., Jung, W.Y. and Lee, W.H. (2016), "Dynamic instability analysis for S-FGM plates embedded in Pasternak elastic medium using the modified couple stress theory", Steel Compos. Struct., 22(6), 1239-1259. https://doi.org/10.12989/scs.2016.22.6.1239.
  40. Pelletier Jacob, L. and Vel Senthil,S. (2006), "An exact solution for the steady state thermo elastic response of functionally graded orthotropic cylindrical shells", Int. J. Solid Struct., 43, 1131-1158. https://doi.org/10.1016/j.ijsolstr.2005.03.079.
  41. Rajabi, J. and Mohammadimehr, M. (2019), "Hydro-thermomechanical biaxial buckling analysis of sandwich micro-plate with isotropic/orthotropic cores and piezoelectric/polymeric nanocomposite face sheets based on FSDT on elastic foundations", Steel and Composite Structures, An Int'l Journal, 33(4), 509-523. https://doi.org/10.12989/scs.2019.33.4.509.
  42. Ramaiah, G.K. and Vijayakumar, K. (1974), "Natural frequencies of circumferentially truncated sector plates with simply supported straight edges", J. Sound Vib., 34(1), 53-61. https://doi.org/10.1016/S0022-460X(74)80354-8
  43. Rashad, M. and Yang, T.Y. (2018), "Numerical study of steel sandwich plates with RPF and VR cores materials under free air blast loads", Steel Compos. Struct., 27(6), 717-725. https://doi.org/10.12989/scs.2018.27.6.717.
  44. Reddy J.N. (2013), "An Introduction to Continuum Mechanics", Second Edition, Cambridge University Press, 2013.
  45. Sahla, M., Saidi, H., Draiche, K., Bousahla, A.A., Bourada, F. and Tounsi, A. (2019), "Free vibration analysis of angle-ply laminated composite and soft core sandwich plates", Steel Compos. Struct., 33(5), 663-679. https://doi.org/10.12989/scs.2019.33.5.663.
  46. Saidi, H., Houari, M.S.A., Tounsi, A. and Bedia, E.A. (2013), "Thermo-mechanical bending response with stretching effect of functionally graded sandwich plates using a novel shear deformation theory", Steel Compos. Struct., 15(2), 221-245. https://doi.org/10.12989/scs.2013.15.2.221.
  47. Salah, F., Boucham, B., Bourada, F. and Benzair, A. (2019), "Investigation of thermal buckling properties of ceramic-metal FGM sandwich plates using 2D integral plate model", Steel Compos. Struct., 33(6), 805-822. https://doi.org/10.12989/scs.2019.33.6.805.
  48. Seok, J.W. and Tiersten, H.F. (2004), "Free vibrations of annular sector cantilever plates part 1: out-of-plane motion", J. Sound Vib., 271(3-5), 757-772. https://doi.org/10.1016/S0022-460X(03)00414-0.
  49. Setoodeh, A.R. and Shojaee, M. (2016), "Application of TW-DQ method to nonlinear free vibration analysis of FG carbon nanotube-reinforced composite quadrilateral plates", Thin-Wall. Struct., 108, 1-11. http://dx.doi.org/10.1016/j.tws.2016.07.019.
  50. Sharma, K. and Marin, M. (2013), "Effect of distinct conductive an thermodynamic temperatures on the reflection of plane waves in micropolar elastic half-space", Scientific Bulletin, Series A Appl.Math. Phys., 75(2), 121-132.
  51. Sharma, A., Sharda, H.B. and Nath, Y. (2005a), "Stability and vibration of Mindlin sector plates: an analytical approach", AIAA J., 43(5), 1109-1116. https://doi.org/10.2514/1.4683.
  52. Sharma, A., Sharda, H.B. and Nath, Y. (2005b), "Stability and vibration of thick laminated composite sector plates", J. Sound Vib., 287(1-2), 1-23. https://doi.org/10.1016/j.jsv.2004.10.030.
  53. Shen, H.S. and Zhang, C.L. (2010), "Thermal buckling and postbuckling behavior of functionally graded carbon nanotubereinforced composite plates", Mater. Design., 31(7),3403-3411. https://doi.org/10.1016/j.matdes.2010.01.048.
  54. Shokrollahi, S. and Shafaghat, S. (2016), "A global Ritz formulation for the free vibration analysis of hybrid metalcomposite thick trapezoidal plates", Scientia Iranica T. B: Mech. Eng., 23(1), 249-259. https://doi.org/10.24200/sci.2016.3830
  55. Shu C., 2012, Differential Quadrature and its Application in Engineering, Springer Science & Business Media.
  56. Sobhani Aragh, B., Nasrollah Barati, A.H. and Hedayati, H. (2012), "Eshelby-Mori-Tanaka approach for vibrational behavior of continuously graded carbon nanotube-reinforced cylindrical panels", Compos. B Eng., 43(4), 1943-1954. https://doi.org/10.1016/j.compositesb.2012.01.004.
  57. Tahouneh, V. (2016), "Using an equivalent continuum model for 3D dynamic analysis of nanocomposite plates", Steel Compos. Struct., 20(3), 623-649. https://doi.org/10.12989/scs.2016.20.3.623.
  58. Tahouneh, V. (2017), "The effect of carbon nanotubes agglomeration on vibrational response of thick functionally graded sandwich plates", Steel Compos. Struct., 24(6), 711-726. https://doi.org/10.12989/scs.2017.24.6.711.
  59. Torabi, K. and Afshari, H. (2017), "Vibration analysis of a cantilevered trapezoidal moderately thick plate with variable thickness", Eng. Solid Mech., 30(8), 71-92. https://doi.org/10.5267/j.esm.2016.7.001.
  60. Tornabene, F. and Viola, E. (2008), "2-D solution for free vibrations of parabolic shells using generalized differential quadrature method", Eur. J. Mech. A/Solids, 27, 1001-1025. https://doi.org/10.1016/j.euromechsol.2007.12.007.
  61. Tornabene, F., Fantuzzi, N., Bacciocchi, M. and Viola, E. (2016), "Effect of agglomeration on the natural frequencies of functionally graded carbon nanotube-reinforced laminated composite doubly-curved shells", Compos. Part B, 89, 187-218. https://doi.org/10.1016/j.compositesb.2015.11.016.
  62. Tornabene, F., Fantuzzi, N. and Bacciocchi, M. (2017), "Linear static response of nanocomposite plates and shells reinforced by agglomerated carbon nanotubes", Compos. Part B., 115, 449-476. https://doi.org/10.1016/j.compositesb.2016.07.011.
  63. Tornabene, F., Fantuzzi, N., Ubertini, F. and Viola, E. (2015), "Strong formulation finite element method based on differential quadrature: A survey", Appl. Mech. Rev., 67(2), 1-55. https://doi.org/10.1115/1.4028859.
  64. Tornabene, F., Fantuzzi, N. and Bacciocchi, M. (2019), "Refined shear deformation theories for laminated composite arches and beams with variable thickness: Natural frequency analysis", Eng. Anal. Bound. Elem., 100, 24-47. https://doi.org/10.1016/j.enganabound.2017.07.029.
  65. Tornabene, F., Fantuzzi, N. and Bacciocchi, M. (2017), "Foam core composite sandwich plates and shells with variable stiffness: Effect of the curvilinear fiber path on the modal response", J. Sandw. Struct. Mater., 21(1), 320-365. https://doi.org/10.1177/1099636217693623.
  66. Wu, C.P. and Liu, Y.C. (2016), "A state space meshless method for the 3D analysis of FGM axisymmetric circular plates", Steel Compos. Struct., 22(1), 161-182. https://doi.org/10.12989/scs.2016.22.1.161.
  67. Zamani, M., Fallah, A. and Aghdam, M.M. (2012), "Free vibration analysis of moderately thick trapezoidal symmetrically laminated plates with various combinations of boundary conditions", Eur. J. Mech. A/Solids, 36(2012), 204-212. https://doi.org/10.1016/j.euromechsol.2012.03.004.
  68. Zhao, Z., Feng, C., Dong, Y., Wang, Y. and Yang, J. (2019), "Geometrically nonlinear bending of functionally graded nanocomposite trapezoidal plates reinforced with graphene platelets (GPLs)", Int. J. Mech. Mater. Des., 15(4). https://doi.org/10.1007/s10999-019-09442-4.
  69. Zhao, Z., Feng, C., Wang, Y. and Yang, J. (2017), "Bending and vibration analysis of functionally graded trapezoidal nanocomposite plates reinforced with graphene nanoplatelets (GPLs)", Compos. Struct., 180, https://doi.org/10.1016/j.compstruct.2017.08.044.
  70. Zhu, X.H. and Meng, Z.Y. (1995), "Operational principle fabrication and displacement characteristics of a functionally gradient piezoelectricceramic actuator", Sensor. Actuat., 48(3), 169-176. https://doi.org/10.1016/0924-4247(95)00996-5.

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