Structural Engineering and Mechanics

  • 제75권2호
  • /
  • Pages.157-174
  • /
  • 2020
  • /
  • 1225-4568(pISSN)
  • /
  • 1598-6217(eISSN)
테크노프레스 (Techno-Press)
권호 표지
DOI QR코드

DOI QR Code

A simple analytical model for free vibration and buckling analysis of orthotropic rectangular plates

  • Sellam, Souad (LMPM, Department of Mechanical Engineering, University of Sidi Bel Abbes) ;
  • Draiche, Kada (Department of Civil Engineering, Ibn Khaldoun University) ;
  • Tlidji, Youcef (Department of Civil Engineering, Ibn Khaldoun University) ;
  • Addou, Farouk Yahia (Material and Hydrology Laboratory, University of Sidi Bel Abbes, Faculty of Technology, Civil Engineering Department) ;
  • Benachour, Abdelkader (Material and Hydrology Laboratory, University of Sidi Bel Abbes, Faculty of Technology, Civil Engineering Department)
  • 투고 : 2019.12.31
  • 심사 : 2020.02.12
  • 발행 : 2020.07.25
⟨ 이전 논문 다음 논문 ⟩

초록

In the present paper, a simple analytical model is developed based on a new refined parabolic shear deformation theory (RPSDT) for free vibration and buckling analysis of orthotropic rectangular plates with simply supported boundary conditions. The displacement field is simpler than those of other higher-order theories since it is modeled with only two unknowns and accounts for a parabolic distribution of the transverse shear stress through the plate thickness. The governing differential equations related to the present theory are obtained from the principle of virtual work, while the solution of the eigenvalue problem is achieved by assuming a Navier technique in the form of a double trigonometric series that satisfy the edge boundary conditions of the plate. Numerical results are presented and compared with previously published results for orthotropic rectangular plates in order to verify the precision of the proposed analytical model and to assess the impacts of several parameters such as the modulus ratio, the side-to-thickness ratio and the geometric ratio on natural frequencies and critical buckling loads. From these results, it can be concluded that the present computations are in excellent agreement with the other higher-order theories.

키워드

참고문헌

  1. Abbas A.I., Othman I.A.M. (2009), "Effect of rotation on thermoelastic waves with green-naghdi theory in a homogeneous isotropic hollow cylinder", J. Industrial Math.,., 1(2), 121-134.
  2. Abualnour, M., Chikh, A., Hebali, H., Kaci, A., Tounsi, A., Bousahla, A.A., Tounsi, A. (2019), "Thermomechanical analysis of antisymmetric laminated reinforced composite plates using a new four variable trigonometric refined plate theory", Comput. Concrete, 24(6), 489-498. https://doi.org/10.12989/cac.2019.24.6.489
  3. Adda Bedia, W., Houari, M.S.A., Bessaim, A., Bousahla, A.A., Tounsi, A., Saeed, T., Alhodaly, M.Sh. (2019), "A new hyperbolic two-unknown beam model for bending and buckling analysis of a nonlocal strain gradient nanobeams", J. Nano Res., 57, 175-191. https://doi.org/10.4028/www.scientific.net/jnanor.57.175
  4. Adhikari, B., and Singh, B. (2017), "An efficient higher order non-polynomial quasi 3-D theory for dynamic responses of laminated composite plates", Compos. Struct., 189, 386- 397.https://doi.org/10.1016/j.compstruct.2017.10.044.
  5. Akbas, S.D (2017a), "Nonlinear static analysis of functionally graded porous beams under thermal effect", Coupled Syst. Mech., 6(4), 399-415. https://doi.org/10.12989/csm.2017.6.4.399.
  6. Akbas, S.D (2017c), "Vibration and Static Analysis of Functionally Graded Porous Plates", J. Appl. Comput. Mech., 3(3), 199-207. https://doi.org/10.22055/JACM.2017.21540.1107.
  7. Akbas, S.D (2019), "Nonlinear static analysis of laminated composite beams under hygro-thermal effect", Struct. Eng. Mech., 72(4), 433-441. https://doi.org/10.12989/sem.2019.72.4.433.
  8. Akbas, S.D. (2016), "Forced vibration analysis of viscoelastic nanobeams embedded in an elastic medium", Smart Structures and Systems.,18(6), 1125-1143. https://doi.org/10.12989/sss.2016.18.6.1125.
  9. Akbas, S.D. (2017b), "Post-buckling responses of functionally graded beams with porosities", Steel Compos. Struct., 24(5), 579-589. https://doi.org/10.12989/scs.2017.24.5.579.
  10. Alimirzaei, S., Mohammadimehr, M., Tounsi, A. (2019), "Nonlinear analysis of viscoelastic micro-composite beam with geometrical imperfection using FEM: MSGT electro-magneto-elastic bending, buckling and vibration solutions", Structural Engineering and Mechanics, 71(5), 485-502. https://doi.org/10.12989/sem.2019.71.5.485
  11. Al-Osta, M.A. (2019), "Shear behaviour of RC beams retrofitted using UHPFRC panels epoxied to the sides", Comput. Concrete, 24(1), 37-49. https://doi.org/10.12989/cac.2019.24.1.037
  12. Asghar, S., Naeem, M.N., Hussain, M., Tounsi, A. (2020), "Prediction and assessment of nonlocal natural frequencies of DWCNTs: Vibration Analysis", Comput. Concrete, (Accepted),
  13. Balubaid, M., Tounsi, A., Dakhel, B., Mahmoud, S.R. (2019), "Free vibration investigation of FG nanoscale plate using nonlocal two variables integral refined plate theory", Comput. Concrete, 24(6), 579-586. https://doi.org/10.12989/cac.2019.24.6.579
  14. Barati, M.R., Shahverdi, H. (2020), "Finite element forced vibration analysis of refined shear deformable nanocompositegraphene platelet-reinforced beams", J Braz. Soc. Mech. Sci. Eng., 42, 33 (2020), https://doi.org/10.1007/s40430-019-2118-8.
  15. Batou, B., Nebab, M., Bennai, R., Ait Atmane, H., Tounsi, A., Bouremana, M. (2019), "Wave dispersion properties in imperfect sigmoid plates using various HSDTs", Steel Compos. Struct., 33(5), 699-716. https://doi.org/10.12989/scs.2019.33.5.699
  16. Benhenni, M., Hassaine Daouadji, T., Abbes, B., Li, Y.M. and Abbes, F. (2018), "Analytical and numerical results for free vibration of laminated composites plates", Int. J. Chem. Molecul. Eng., 12(6), 300-304. https://doi.org/10.12989/amr.2018.7.2.119.
  17. Berghouti, H., Adda Bedia, E.A., Benkhedda, A., Tounsi, A. (2019), "Vibration analysis of nonlocal porous nanobeams made of functionally graded material", Advances in Nano Research, 7(5), 351-364. https://doi.org/10.12989/anr.2019.7.5.351
  18. Boukhlif, Z., Bouremana, M., Bourada, F., Bousahla, A.A., Bourada, M., Tounsi, A., Al-Osta, M.A. (2019), "A simple quasi-3D HSDT for the dynamics analysis of FG thick plate on elastic foundation", Steel Compos. Struct., 31(5), 503-516. https://doi.org/10.12989/SCS.2019.31.5.503
  19. Boulefrakh, L., Hebali, H., Chikh, A., Bousahla, A.A., Tounsi, A., Mahmoud, S.R. (2019), "The effect of parameters of visco-Pasternak foundation on the bending and vibration properties of a thick FG plate", Geomech. Eng., 18(2), 161-178. https://doi.org/10.12989/GAE.2019.18.2.161
  20. Bourada, F., Bousahla, A.A., Bourada, M., Azzaz, A., Zinata, A., Tounsi, A. (2019), "Dynamic investigation of porous functionally graded beam using a sinusoidal shear deformation theory", Wind and Structures, 28(1), 19-30. https://doi.org/10.12989/was.2019.28.1.019
  21. Bousahla, A.A., Bourada, F., Mahmoud, S.R., Tounsi, A., Algarni, A., Adda Bedia, E.A., Tounsi, A. (2020), "Buckling and Dynamic behavior of the simply supported CNT-RC beams using an integral-first shear deformation theory", Comput.Concrete, (Accepted),
  22. Boussoula, A., Boucham, B., Bourada, M., Bourada, F., Tounsi, A., Bousahla, A.A., Tounsi, A. (2020), "A simple nth-order shear deformation theory for thermomechanical bending analysis of different configurations of FG sandwich plates", Smart Struct. Syst., 25.
  23. Boutaleb, S., Benrahou, K.H., Bakora, A., Algarni, A., Bousahla, A.A., Tounsi, A., Mahmoud, S.R., Tounsi, A. (2019), "Dynamic Analysis of nanosize FG rectangular plates based on simple nonlocal quasi 3D HSDT", Adv. Nano Res., 7(3), 189-206.
  24. Chaabane, L.A., Bourada, F., Sekkal, M., Zerouati, S., Zaoui, F.Z., Tounsi, A., Derras, A., Bousahla, A.A., Tounsi, A. (2019), "Analytical study of bending and free vibration responses of functionally graded beams resting on elastic foundation", Struct. Eng. Mech., 71(2), 185-196. https://doi.org/10.12989/SEM.2019.71.2.185
  25. Chandra Mouli, B, Ramji, K, Kar, V.R., Panda, S.K., Lalepalli Anil, K., Pandey, H.K. (2018), "Numerical study of temperature dependent eigenfrequency responses of tilted functionally graded shallow shell structures", Struct. Eng. Mech., 68(5), 527-536. https://doi.org/10.12989/sem.2018.68.5.527
  26. Chikh, A., Tounsi, A., Hebali, H. and Mahmoud, S.R. (2017), "Thermal buckling analysis of cross-ply laminated plates using a simplified HSDT", Smart Struc. Sys.,19(3), 289-297. https://doi.org/10.12989/sss.2017.19.3.289.
  27. Das, A., Hirwani, C.K., Panda, S.K., Topal, U., Dede, T. (2018a), "Prediction and analysis of optimal frequency of layered composite structure using higher-order FEM and soft computing techniques", Steel Compos. Struct., 29(6), 749-758. https://doi.org/10.12989/scs.2018.29.6.749
  28. Das, A., Mehar, K., Sharma, N., Mahapatra, T.R., Panda, S.K. (2018b), "Modal analysis of FG sandwich doubly curved shell structure, Struct. Eng. Mech., 68(6), 721-733. https://doi.org/10.12989/SEM.2018.68.6.721
  29. Dickinson, S.M., and Di Blasio, A. (1986), "On the use of orthogonal polynomials in the Reyleigh-Ritz method for the study of the flexural vibration and buckling of isotropic and orthotropic rectangular plates", J Sound Vib., 108(1), 51- 62.https://doi.org/10.1016/S0022-460X(86)80310-8.
  30. Draoui, A., Zidour, M., Tounsi, A., Adim, B. (2019), "Static and dynamic behavior of nanotubes-reinforced sandwich plates using (FSDT)", J. Nano Res., 57, 117-135. https://doi.org/10.4028/www.scientific.net/jnanor.57.117
  31. Ebrahimi, F., &Barati, M. R. (2017), "Vibration analysis of nonlocal strain gradient embedded single-layer graphene sheets under nonuniform in-plane loads", J. Vib. Control., 107754631773408. doi:10.1177/1077546317734083.
  32. Ebrahimi, F., &Barati, M. R. (2018), "Hygro-thermal vibration analysis of bilayer graphene sheet system via nonlocal strain gradient plate theory", J. Brazil Soc. Mech. Sci. Eng.,40(9), doi:10.1007/s40430-018-1350-y.
  33. Ebrahimi, F., Barati, M. R., &Civalek, O. (2019),
  34. Ebrahimi, F., Barati, M.R. (2019), "A Nonlocal Strain Gradient Mass Sensor Based on Vibrating Hygro-Thermally Affected GrapheneNanosheets", Iran J Sci Technol Trans. Mech. Eng., 43, 205-220. https://doi.org/10.1007/s40997-017-0131-z.
  35. Eltaher, M. A., &Wagih, A. (2020), "Micromechanical modeling of damage in elasto-plastic nanocomposites using unit cell representative volume element and cohesive zone model", Ceramics Intl., https://doi.org/10.1016/j.ceramint.2020.01.046.
  36. Eltaher, M. A., A.Wagih, Melaibari, A., Fathy, A., &Lubineau, G. (2019), "Effect of Al2O3 particles on mechanical and tribological properties of Al-Mg dual-matrix nanocomposites", Ceramics International., https://doi.org/10.1016/j.ceramint.2019.11.028.
  37. Eltaher, M. A., Mohamed, S.A. (2020), "Buckling and stability analysis of sandwich beams subjected to varying axial loads", Steel Compos. Struct., 34(2), 241-260. https://doi.org/https://doi.org/10.12989/scs.2020.34.2.241
  38. Faleh, N.M., Ahmed, R.A., Fenjan, R.M. (2018), "On vibrations of porous FG nanoshells", J. Eng. Sci., 133, 1-14. https://doi.org/10.1016/j.ijengsci.2018.08.007
  39. Fellah, M., Draiche, K., Houari, M.S.A., Tounsi, A., Saeed, T., Alhodaly, M.Sh. and Benguediab, M., (2019), "A novel refined shear deformation theory for the buckling analysis of thick isotropic plates", Struct. Eng. Mech., 69(3), 335-345. https://doi.org/10.12989/sem.2019.69.3.335.
  40. Ghugal, Y.M. and Pawar, M.D. (2011), "Buckling and vibration of plates by hyperbolic shear deformation theory", J. Aerosp. Eng. & Technol., 1(1), 1-12.
  41. Ghugal, Y.M. and Sayyad, A.S. (2011), "Free vibration analysis of thick orthotropic plates using trigonometric shear deformation theory", Latin American J. of solids and struct., 8, 229-243. https://doi.org/10.1590/S1679-78252011000300002.
  42. Gorman, D.J. (1993), "Accurate free vibration analysis of the completely free orthotropic rectangular plate by the method of superposition", J Sound Vib., 165(3), 409- 420.https://doi.org/10.1006/jsvi.1993.1267.
  43. Hamed, M.A., Salwa A Mohamed, S.A. and Mohamed A. Eltaher, M.A, (2020), "Buckling analysis of sandwich beam rested on elastic foundation and subjected to varying axial in-plane loads", Steel Compos. Struct., 34(1),75-89. https://doi.org/https://doi.org/10.12989/scs.2020.34.1.075.
  44. Hirwani, C.K., Panda, S.K. (2019), "Nonlinear thermal free vibration frequency analysis of delaminated shell panel using FEM", Composite Structures, 224, 111011.https://doi.org/10.1016/j.compstruct.2019.111011
  45. Hirwani, C.K., Patil, R.K., Panda, S.K., Mahapatra, S.S., Mandal, S.K., Srivastava, L., Buragohain, M.K. (2016), "Experimental and numerical analysis of free vibration of delaminated curved panel", Aerospace Sci. Technol., 54, 353-370.https://doi.org/10.1016/j.ast.2016.05.009 https://doi.org/10.1016/0020-7683(70)90076-4.
  46. Hussain, M., Naeem, M.N., Taj, M., Tounsi, A. (2020a), "Simulating vibrations of vibration of single-walled carbon nanotube using Rayleigh-Ritz's method", Adv. Nano Res., (Accepted),
  47. Hussain, M., Naeem, M.N., Tounsi, A. (2020b), "On mixing the Rayleigh-Ritz formulation with Hankel's function for vibration of fluid-filled FG cylindrical shell", Adv. Comput. Design, (Accepted),
  48. Hussain, M., Naeem, M.N., Tounsi, A., Taj, M. (2019), "Nonlocal effect on the vibration of armchair and zigzag SWCNTs with bending rigidity", Adv. Nano Res., 7(6), 431-442. https://doi.org/10.12989/anr.2019.7.6.431
  49. Joshan, Y.S., Grover, N., Singh, B.N. (2017), "A new non-polynomial four variable shear deformation theory in axiomatic formulation for hygro-thermo-mechanical analysis of laminated composite plates", Compos.Struct., 182, 685-693. https://doi.org/10.1016/j.compstruct.2017.09.029.
  50. Kaddari, M., Kaci, A., Bousahla, A.A.,Tounsi, A., Bourada, F., Tounsi, A., AddaBedia, E.A., Al-Osta, M.A. (2020), "A study on the structural behaviour of functionally graded porous plates on elastic foundation using a new quasi-3D model: Bending and Free vibration analysis", Comput. Concrete, 25(1), 37-57. https://doi.org/10.12989/cac.2020.25.1.037
  51. Kar, V.R. and Panda, S.K. (2015), "Free vibration responses of temperature dependent functionally graded curved panels under thermal environment", Lat. Am. j. solids struct.,12(11), 2006-2024. http://dx.doi.org/10.1590/1679-78251691
  52. Karami, B., Janghorban, M. and Tounsi, A. (2019a), "Galerkin's approach for buckling analysis of functionally graded anisotropic nanoplates/different boundary conditions", Eng. Comput., 35, 1297-1316. https://doi.org/10.1007/s00366-018-0664-9.
  53. Karami, B., Janghorban, M., Tounsi, A. (2019b), "Wave propagation of functionally graded anisotropic nanoplates resting on Winkler-Pasternak foundation", Struct. Eng. Mech., 7(1), 55-66.
  54. Karami, B., Janghorban, M., Tounsi, A. (2019d), "On exact wave propagation analysis of triclinic material using three dimensional bi-Helmholtz gradient plate model", Struct. Eng. Mech., 69(5), 487-497. https://doi.org/10.12989/SEM.2019.69.5.487
  55. Karami, B., Janghorban, M., Tounsi, A. (2020), "Novel study on functionally graded anisotropic doubly curved nanoshells", Eur. Phys. J. Plus, 135, 103.https://doi.org/10.1140/epjp/s13360-019-00079-y
  56. Karami, B., Shahsavari, D., Janghorban, M., Tounsi, A. (2019c), "Resonance behavior of functionally graded polymer composite nanoplates reinforced with grapheme nanoplatelets", J. Mech. Sci., 156, 94-105. https://doi.org/10.1016/j.ijmecsci.2019.03.036
  57. Karami, B., Janghorban, M., Tounsi, A. (2019e), "On pre-stressed functionally graded anisotropic nanoshell in magnetic field", J. Brazil Soc. Mech. Sci. Eng., 41, 495. https://doi.org/10.1007/s40430-019-1996-0
  58. Karkon, M. and Pajand, M.R., (2018), "Finite Element Analysis of Orthotropic Thin Plates Using Analytical Solution", Iran J SciTechnol Trans Civ Eng. https://doi.org/10.1007/s40996-018-0128-x.
  59. Katariya and Panda, S.K. (2019b), "Numerical frequency analysis of skew sandwich layered composite shell structures under thermal environment including shear deformation effects", Struct. Eng. Mech., 71(6), 657-668.https://doi.org/10.12989/sem.2019.71.6.657
  60. Katariya, P. and Panda, S. (2016), "Thermal buckling and vibration analysis of laminated composite curved shell panel", Aircraft Engineering and Aerospace Technology, 88(1), 97-107. https://doi.org/10.1108/AEAT-11-2013-0202
  61. Katariya, P., Das, A., Panda, S. (2018b), "Buckling analysis of SMA bonded sandwich structure-using FEM", IOP Conference Series: Materials Science and Engineering, 338(1), 012035. https://doi.org/10.1088/1757-899X/338/1/012035
  62. Katariya, P., Panda, S. and Mahapatra, T. (2018a), "Bending and vibration analysis of skew sandwich plate", Aircraft Engineering and Aerospace Technology, 90(6), 885-895. https://doi.org/10.1108/AEAT-05-2016-0087
  63. Katariya, P.V., Panda, S.K. (2019a), "Frequency and Deflection Responses of Shear Deformable Skew Sandwich Curved Shell Panel: A Finite Element Approach", Arab J SciEng, 44, 1631- 1648. https://doi.org/10.1007/s13369-018-3633-0
  64. Katariya, P.V., Panda, S.K., Hirwani, C.K., Mehar, K., Thakare, O. (2017b), "Enhancement of thermal buckling strength of laminated sandwich composite panel structure embedded with shape memory alloy fibre", Smart Struct. Syst., 20(5), 595-605.https://doi.org/10.12989/sss.2017.20.5.595
  65. Katariya, P.V., Panda, S.K., Mahapatra, T.R. (2017a), "Nonlinear thermal bucklingbehaviour of laminated composite panel structure including the stretching effect and higher-order finite element", Advances in Materials Research, 6(4), 349-361. https://doi.org/10.12989/amr.2017.6.4.349
  66. Khiloun, M., Bousahla, A.A., Kaci, A., Bessaim, A., Tounsi, A., Mahmoud, S.R. (2019), "Analytical modeling of bending and vibration of thick advanced composite plates using a four-variable quasi 3D HSDT", Eng. Comput., https://doi.org/10.1007/s00366-019-00732-1.
  67. Khosravi, F., Hosseini, S.A., Tounsi, A. (2020), "Torsional dynamic response of viscoelastic SWCNT subjected to linear and harmonic torques with general boundary conditions via Eringen's nonlocal differential model", Eur. Phys. J. Plus, 135, 183. https://doi.org/10.1140/epjp/s13360-020-00207-z
  68. Kim, S.E., Thai, H.T. and Lee, J. (2009), "Buckling analysis of plates using the two variable refined plate theory", Thin Walled Struct., 47(4), 455- 462.https://doi.org/10.1016/j.tws.2008.08.002.
  69. Kirchhoff, G.R. (1850), "Uber das gleichgewicht und die bewegungeinerelastischenscheibe", J. Pure App. Math., 40, 51- 88. https://doi.org/10.1515/crll.1850.40.51.
  70. Kolahchi, R., Zarei, M. S., Hajmohammad, M. H., NaddafOskouei, A. (2017), "Visco-nonlocal refined Zigzag theories for dynamic buckling of laminated nanoplates using differential cubature Bolotin methods", Thin-Walled Struct.,113, 162-169. https://doi.org/10.1016/j.tws.2017.01.016
  71. Kunche, M.C., Mishra, P.K., Nallala, H.B., Hirwani, C.K., Katariya, P.V., Panda, S., Panda, S.K. (2019), "Theoretical and experimental modal responses of adhesive bonded T-joints", Wind and Structures, 29(5), 361-369.https://doi.org/10.12989/was.2019.29.5.361
  72. Laura, P., Luisoni, L., Filipich, C. (1977), "A note on the determination of the fundamental frequency of vibration of thin, rectangular plates with edges possessing different rotational flexibility coefficients", J. Sound Vib., 55, 327- 333.https://doi.org/10.1016/S0022-460X(77)80016-3.
  73. Leissa, A.W. (1969), "Vibration of Plates", NASA-SP-160, US Government Printing Office, Washington DC.
  74. Leissa, A.W. (1973) "Free Vibrations of Rectangular Plate", J. of Sound and Vib., 31, 257-293. https://doi.org/10.1016/S002 2-460X(73)80371-2.
  75. Leissa, A.W. (1981), "Plate vibration research", 1976-1980: complicating effects. The Shock and Vib. Digest, 13(10), 19-36.
  76. Medani, M., Benahmed, A., Zidour, M., Heireche, H., Tounsi, A., Bousahla, A.A., Tounsi, A., Mahmoud, S.R. (2019), "Static and dynamic behavior of (FG-CNT) reinforced porous sandwich plate", Steel Compos. Struct., 32(5), 595-610. https://doi.org/10.12989/scs.2019.32.5.595
  77. Mehar, K., Panda, S. K. (2019), "Multiscale modeling approach for thermal buckling analysis of nanocomposite curved structure", Adv. Nano Res., 7(3), 181-190. https://doi.org/10.12989/anr.2019.7.3.181
  78. Mehar, K., Panda, S. K., Devarajan, Y., Choubey, G. (2019), "Numerical buckling analysis of graded CNT-reinforced composite sandwich shell structure under thermal loading", Composite Structures, 216, 406-414. https://doi.org/10.1016/j.compstruct.2019.03.002
  79. Mehar, K., Panda, S. K., Mahapatra, T. R. (2017), "Theoretical and experimental investigation of vibration characteristic of carbon nanotube reinforced polymer composite structure", J. Mech. Sci., 133, 319-329.https://doi.org/10.1016/j.ijmecsci.2017.08.057
  80. Mehar, K., Panda, S. K., Mahapatra, T. R. (2018), "Large deformation bending responses of nanotube-reinforced polymer composite panel structure: Numerical and experimental analyses", Proceedings of the Institution of Mechanical Engineers, Part G: Journal of Aerospace Engineering., 233(5), 1695-1704. 095441001876119. https://doi.org/10.1177/0954410018761192
  81. Mehar, K., Panda, S. K., Patle, B.K. (2018), "Stress, deflection, and frequency analysis of CNT reinforced graded sandwich plate under uniform and linear thermal environment: A finite element approach", Polymer Composites, 39(10), 3792-3809. https://doi.org/10.1002/pc.24409
  82. Meksi, R, Benyoucef, S., Mahmoudi, A., Tounsi, A., AddaBedia, E.A. and Mahmoud, SR. (2019), "An analytical solution for bending, buckling and vibration responses of FGM sandwich plates", J. Sandw. Struct. Mater.,21(2), 727-757. https://doi.org/10.1177/1099636217698443
  83. Mindlin, RD. (1951), "Influence of rotary inertia and shear on flexural motions of isotropic, elastic plates", ASME J ApplMech; 18(1), 31-38.https://doi.org/10.1007/978-1-4613-8865-4-29.
  84. Mirjavadi, S.S., Forsat, M., Barati, M. R., Abdella, G.M., MohaselAfshari, B., Hamouda, A. M. S., &Rabby, S. (2019a), "Dynamic response of metal foam FG porous cylindrical micro-shells due to moving loads with strain gradient size-dependency", European Phys. J. Plus., 134(5), https://doi.org/10.1140/epjp/i2019-12540-3.
  85. Mirjavadi, S.S., Forsat, M., Nikookar, M. et al. (2019b), "Nonlinear forced vibrations of sandwich smart nanobeams with two-phase piezo-magnetic face sheets", Eur. Phys. J. Plus., 134, 508 (2019), https://doi.org/10.1140/epjp/i2019-12806-8.
  86. Nguyen, T.N., Thai, C.H. and Xuan, H.N. (2016), "On the general framework of high order shear deformation theories for laminated composite plate structures: a novel unified approach", J. Mech. Sci., 110, 242-255. http://dx.doi.org/10.1016%2Fj.ijmecsci.2016.01.012. https://doi.org/10.1016/j.ijmecsci.2016.01.012
  87. Nor Hafizah, A.K., Lee, J.H., Aziz, Z.A. and Viswanatha, K.K. (2018), "Vibration of antisymmetric angle-ply laminated plates of higher-order theory with variable thickness", Math. Prob. Eng., 14. https://doi.org/10.1155/2018/7323628.
  88. Othman, I.A.M., Mahdy, A.S.M. (2018), "Numerical Studies for Solving a Free Convection Boundary-layer Flow Over a Vertical Plate", Mechanics and Mechanical Engineering., 22(1), 35-42.
  89. Othman, M. I. A., &Lotfy, K. (2009), "Two-Dimensional Problem of Generalized Magneto-Thermoelasticity with Temperature Dependent Elastic Moduli for Different Theories", Multidiscipline Modeling in Materials and Structures.,5(3), 235- 242. https://doi.org/10.1163/157361109789016961.
  90. Panda, S.K., Katariya, P.V. (2015), "Stability and free vibration behaviour of laminated composite panels under thermo-mechanical loading", Int. J. Appl. Comput. Math, 1, 475-490. https://doi.org/10.1007/s40819-015-0035-9
  91. Panda, S.K., Kolahchi, R. (2018), "Dynamic analysis in three layered conical shells utilising numerical methods", International Journal of Hydromechatronics,1(4), 427-446.https://doi.org/10.1504/IJHM.2018.097292
  92. Pandey, H.K., Hirwani, C.K., Sharma, N., Katariya, P.V., Panda, S.K. (2019), "Effect of nano glass cenosphere filler on hybrid composite eigenfrequency responses - An FEM approach and experimental verification", Adv. Nano Res., 7(6), 419-429. https://doi.org/10.12989/anr.2019.7.6.419
  93. Panjehpour, M., Eric Woo KeeLoh, Deepak TJ. (2018), "Structural Insulated Panels: State-of-the-Art", Trends Civil Eng. Architecture, 3(1) 336-340. https://doi.org/10.32474/TCEIA.2018.03.000151
  94. Papkov, S.O. and Banerjee, J.R. (2015), "A new method for free vibration and buckling analysis of rectangular orthotropic plates", J.Sound Vib., 339, 342-358. https://doi.org/10.1016/j.jsv.2014.11.007.
  95. Patle, B.K., Hirwani, C.K., Singh, R.P., Panda, S.K. (2018), "Eigenfrequency and deflection analysis of layered structure using uncertain elastic properties - a fuzzy finite element approach", J. Approximate Reasoning, 98, 163-176. https://doi.org/10.1016/j.ijar.2018.04.013
  96. Patni, M., Minera, S., Groh, R.M.J., Pirrera, A., Weaver, P.M., (2018), "Three-dimensional stress analysis for laminated composite and sandwich structures", Compos. Part B: Eng., 155, 299-328, https://doi.org/10.1016/j.compositesb.2018.08.127.
  97. Rajabi, J., Mohammadimehr, M. (2019), "Bending analysis of a micro sandwich skew plate using extended Kantorovich method based on Eshelby-Mori-Tanaka approach", Comput. Concrete, 23(5), 361-376. https://doi.org/10.12989/cac.2019.23.5.361
  98. Ramteke, P.M., Panda, S.K., Sharma, N. (2019), "Effect of grading pattern and porosity on the eigen characteristics of porous functionally graded structure", Steel Compos. Struct., 33(6), 865-875. https://doi.org/10.12989/scs.2019.33.6.865
  99. Ranjan, S., Khan, R., Dash, S., Sharma, N., Mahapatra, T.R., Panda, S.K. (2019), "Thermo-elastic free vibration analysis of functionally graded flat panel with temperature gradient along thickness", IOP Conference Series: Materials Science and Engineering, 577(1), 012123. https://doi.org/10.1088/1757-899X/577/1/012123
  100. Reddy, J.N. (1984), "A simple higher order theory for laminated composite plates", ASME J Appl Mech, 51(4), 745- 752.https://doi.org/10.1115/1.3167719.
  101. Sahoo, S.S., Hirwani, C.K., Panda, S.K., Sen, D. (2018), "Numerical analysis of vibration and transient behaviour of laminated composite curved shallow shell structure: An experimental validation", Scientia Iranica B, 25(4), 2218-2232. https://doi.org/ 10.24200/sci.2017.4346
  102. Sahoo, S.S., Panda, S.K., Mahapatra, T.R. (2016a), "Static, free vibration and transient response of laminated composite curved shallow panel - An experimental approach", Europ. J. Mechanics-A/Solids, 59, 95-113. https://doi.org/10.1016/j.euromechsol.2016.03.014
  103. Sahoo, S.S., Panda, S.K., Mahapatra, T.R. et al. (2019), "Numerical analysis of transient responses of delaminated layered structure using different mid-plane theories and experimental validation", Iran J. Sci. Technol. Trans. Mech. Eng., 43, 41-56. https://doi.org/10.1007/s40997-017-0111-3
  104. Sahoo, S.S., Panda, S.K., Sen, D. (2016b), "Effect of delamination on static and dynamic behavior of laminated composite plate", AIAA J., 54(8), 2530-2544. https://doi.org/10.2514/1.J054908
  105. Sahoo, S.S., Panda, S.K., Singh, V.K. (2017), "Experimental and numerical investigation of static and free vibration responses of woven glass/epoxy laminated composite plate", Proceedings of the Institution of Mechanical Engineers, Part L: Journal of Materials: Design and Applications, 231(5), 463-478. https://doi.org/10.1177/1464420715600191
  106. Salah, F., Boucham, B., Bourada, F., Benzair, A., Bousahla, A.A., Tounsi, A. (2019), "Investigation of thermal buckling properties of ceramic-metal FGM sandwich plates using 2D integral plate model", Steel Compos. Struct., 32(5), 595-610. https://doi.org/10.12989/scs.2019.32.5.595
  107. Sarangan, S., Singh, B.N. (2016), "Higher-order closed-form solution for the analysis of laminated composite and sandwich plates based on new shear deformation theories", Comp. Struct., 138, 391-403. https://doi.org/10.1016/j.compstruct.2015.11.049.
  108. Sayyad, A.S., Ghugal, Y.M. (2014) "Buckling and free vibration analysis of orthotropic plates by using exponential shear deformation theory", Lat. Am. J. Solid. Struct., 11(8), 1298-1314. http://dx.doi.org/10.1590/S1679-78252014000800001.
  109. Sayyad, A.S., Ghugal, Y.M. (2017), "A unified shear deformation theory for the bending of isotropic, functionally graded, laminated and sandwich beams and plates", Int. J App. Mech., 9(1), 1-36. https://doi.org/10.1142/S1758825117500077.
  110. Selmi, A. (2019), "Effectiveness of SWNT in reducing the crack effect on the dynamic behavior of aluminium alloy", Adv. Nano Res., 7(5), 365-377. https://doi.org/10.12989/anr.2019.7.5.365
  111. Semmah, A., Heireche, H., Bousahla, A.A., Tounsi, A. (2019), "Thermal buckling analysis of SWBNNT on Winkler foundation by non local FSDT", Adv. Nano Res., 7(2), 89-98. https://doi.org/10.12989/ANR.2019.7.2.089
  112. Singh, D.B., Singh, B.N. (2017), "New higher-order shear deformation theories for free vibration and buckling analysis of laminated and braided composite plates", J. Mech. Sci., 131-132, 265-277. https://doi.org/10.1016/j.ijmecsci.2017.06.053.
  113. Singh, V.K., Panda, S.K. (2016), "Numerical investigation on nonlinear vibration behavior of laminated cylindrical panel embedded with PZT layers", Procedia Eng., 144, 660-667. https://doi.org/10.1016/j.proeng.2016.05.062
  114. Sladek, J., Sladek, V., Zhang, C., Krivacek, J., Wen, P. (2006), "Analysis of orthotropic thick plates by meshless local Petrov- Galerkin (MLPG) method", J. Numer. Methods Eng., 67(13), 1830-1850. https://doi.org/10.1002/nme.1683.
  115. Srinivas, S., Rao, A.K., (1970), "Bending, vibration and buckling of simply-supported thick orthotropic rectangular plates and laminates", J. Solid. Struct. 6 (11), 1463-1481. https://doi.org/10.1016/0020-7683(70)90076-4
  116. Swain, P., Adhikari, B. and Dash, P. (2017), "A higher-order polynomial shear deformation theory for geometrically nonlinear free vibration response of laminated composite plate", Mech. Adv. Mater. Struct., 26(2), 129-138. https://doi.org/10.1080/15376494.2017.1365981.
  117. Thai, H.T. and Kim, S.E. (2011), "Levy-type solution for buckling analysis of orthotropic plates based on two variable refined plate theory", Compos. Struct., 93(7), 1738-1746. https://doi.org/10.1016/j.compstruct.2011.01.012.
  118. Thai, H.T. and Kim, S.E. (2012), "Levy-type solution for free vibration analysis of orthotropic plates based on two variable refined plate theory", Appl. Math. Model., 36(8), 3870-3882. https://doi.org/10.1016/j.apm.2011.11.003.
  119. Tounsi, A., Al-Dulaijan, S.U., Al-Osta, M.A., Chikh, A., Al-Zahrani, M.M., Sharif, A., Tounsi, 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(4),
  120. Wang, J., Huang, M. (1991) "Boundary element method for orthotropic thick plates", Acta Mech. Sinica, 7(3), 258- 266.https://doi.org/10.1007/BF02487594.
  121. Wang, Q., Shi, D., Shi, X. (2016), "A modified solution for the free vibration analysis of moderately thick orthotropic rectangular plates with general boundary conditions, internal line supports and resting on elastic foundation", Mecc., 51(8), 1985- 2017. https://doi.org/10.1007/s11012-015-0345-3.
  122. Warburton, G., Edney, S. (1984), "Vibrations of rectangular plates with elastically restrained edges", J. Sound Vib., 95(4), 537-552. https://doi.org/10.1016/0022-460X(84)90236-0.
  123. Xing, Y.F. and Liu, B. (2009), "New exact solutions for free vibrations of thin orthotropic rectangular plates", Compos. Struct., 89(4), 567-574. https://doi.org/10.1016/j.compstruct.2008.11.010.
  124. Zaoui, F.Z., 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, 159, 231-247. https://doi.org/10.1016/j.compositesb.2018.09.051
  125. Zarga, D., Tounsi, A., Bousahla, A.A., Bourada, F., Mahmoud, S.R. (2019), "Thermomechanical bending study for functionally graded sandwich plates using a simple quasi-3D shear deformation theory", Steel Compos. Struct., 32(3), 389-410. https://doi.org/10.12989/SCS.2019.32.3.389

피인용 문헌

  1. Physical stability response of a SLGS resting on viscoelastic medium using nonlocal integral first-order theory vol.37, pp.6, 2020, https://doi.org/10.12989/scs.2020.37.6.695
  2. Influences of porosity distributions and boundary conditions on mechanical bending response of functionally graded plates resting on Pasternak foundation vol.38, pp.1, 2020, https://doi.org/10.12989/scs.2021.38.1.001