Earthquakes and Structures

Techno-Press (테크노프레스)
권호 표지
DOI QR코드

DOI QR Code

Effect of nonlinear elastic foundations on dynamic behavior of FG plates using four-unknown plate theory

  • Nebab, Mokhtar (Faculty Civil Engineering and Architecture, Civil Engineering Department, University Hassiba Benbouali of Chlef) ;
  • Atmane, Hassen Ait (Faculty Civil Engineering and Architecture, Civil Engineering Department, University Hassiba Benbouali of Chlef) ;
  • Bennai, Riadh (Faculty Civil Engineering and Architecture, Civil Engineering Department, University Hassiba Benbouali of Chlef) ;
  • Tahar, Benabdallah (Deanship of Quality and Academic Accreditation, King Abdualziz University)
  • Received : 2019.07.04
  • Accepted : 2019.09.11
  • Published : 2019.11.25
⟨ Previous Next ⟩

Abstract

This present paper concerned with the analytic modelling for vibration of the functionally graded (FG) plates resting on non-variable and variable two parameter elastic foundation, based on two-dimensional elasticity using higher shear deformation theory. Our present theory has four unknown, which mean that have less than other higher order and lower theory, and we denote do not require the factor of correction like the first shear deformation theory. The indeterminate integral are introduced in the fields of displacement, it is allowed to reduce the number from five unknown to only four variables. The elastic foundations are assumed a classical model of Winkler-Pasternak with uniform distribution stiffness of the Winkler coefficient (kw), or it is with variables distribution coefficient (kw). The variable's stiffness of elastic foundation is supposed linear, parabolic and trigonometry along the length of functionally plate. The properties of the FG plates vary according to the thickness, following a simple distribution of the power law in terms of volume fractions of the constituents of the material. The equations of motions for natural frequency of the functionally graded plates resting on variables elastic foundation are derived using Hamilton principal. The government equations are resolved, with respect boundary condition for simply supported FG plate, employing Navier series solution. The extensive validation with other works found in the literature and our results are present in this work to demonstrate the efficient and accuracy of this analytic model to predict free vibration of FG plates, with and without the effect of variables elastic foundations.

Keywords

References

  1. Abdelaziz, H.H., Ait Amar Meziane, M., Bousahla, A.A., Tounsi, A., Mahmoud, S.R. and Alwabli, A.S. (2017), "An efficient hyperbolic shear deformation theory for bending, buckling and free vibration of FGM sandwich plates with various boundary conditions", Steel Compos. Struct., 25(6), 693-704. https://doi.org/10.12989/scs.2017.25.6.693.
  2. Abualnour, M., Houari, M.S.A., Tounsi, A., Bedia, E.A.A. and Mahmoud, S.R. (2018), "A novel quasi-3D trigonometric plate theory for free vibration analysis of advanced composite plates", Compos. Struct., 184, 688-697. https://doi.org/10.1016/j.compstruct.2017.10.047.
  3. Addou, F.Y., Meradjah, M., M.A.A, Bousahla, Benachour, A., Bourada, F., Tounsi, A. and Mahmoud, S.R. (2019), "Influences of porosity on dynamic response of FG plates resting on Winkler/Pasternak/Kerr foundation using quasi 3D HSDT", Comput. Concrete, 24(4), 347-367. https://doi.org/10.12989/cac.2019.24.4.347.
  4. Ahmed, A. (2014), "Post buckling analysis of sandwich beams with functionally graded faces using a consistent higher order theory", Int. J. Civil Struct. Environ., 4(2), 59-64.
  5. Ait Atmane, H, Tounsi, A. and Bernard, F. (2017), "Effect of thickness stretching and porosity on mechanical response of a functionally graded beams resting on elastic foundations", Int. J. Mech. Mater. Des., 13(1), 71-84. https://doi.org/10.1007/s10999-015-931.
  6. Ait Atmane, H., Tounsi, A. and Bernard, F. (2015), "Effect of thickness stretching and porosity on mechanical response of a functionally graded beams resting on elastic foundations", Int. J. Mech. Mater. Des., 13(1), 71-84. https://doi.org/10.1007/s10999-015-9318-x.
  7. Ait Atmane, H., Tounsi, A., Mechab, I. and Adda Bedia, E.A. (2010), "Free vibration analysis of functionally graded plates resting on Winkler-Pasternak elastic foundations using a new shear deformation theory", Int. J. Mech. Mater. Des., 6(2), 113-121. https://doi.org/10.1007/s10999-010-9110-x.
  8. Akavci, S.S. (2014), "An efficient shear deformation theory for free vibration of functionally graded thick rectangular plates on elastic foundation", Compos. Structures., 108, 667-676. https://doi.org/10.1016/j.compstruct.2013.10.019.
  9. Al-Basyouni, K.S., Tounsi, A. and Mahmoud, S.R. (2015), "Size dependent bending and vibration analysis of functionally graded micro beams based on modified couple stress theory and neutral surface position", Compos. Struct., 125, 621-630. https://doi.org/10.1016/j.compstruct.2014.12.070.
  10. Aldousari, S.M. (2017), "Bending analysis of different material distributions of functionally graded beam", Appl. Phys. A, 123, 296. https://doi.org/10.1007/s00339-017-0854-0.
  11. Al Khateeb, S.A. and Zenkour, A.M. (2014), "A refined four-unknown plate theory for advanced plates resting on elastic foundations in hygrothermal environment", Compos. Struct., 111 240-248. https://doi.org/10.1016/j.compstruct.2013.12.033.
  12. Ansari, R., Torabi, J. and Shojaei, M.F. (2017), "Buckling and vibration analysis of embedded functionally graded carbon nanotube-reinforced composite annular sector plates under thermal loading", Compos. Part B: Eng., 109 197-213. https://doi.org/10.1016/j.compositesb.2016.10.050.
  13. Atmane, H.A., Tounsi, A., Bernard, F. and Mahmoud, S. (2015), "A computational shear displacement model for vibrational analysis of functionally graded beams with porosities", Steel Compos. Struct., 19(2), 369-384. https://doi.org/10.12989/scs.2015.19.2.369.
  14. Attia, A., Tounsi, A., Adda Bedia, E.A. and Mahmoud, S.R. (2015), "Free vibration analysis of functionally graded plates with temperature-dependent properties using various four variable refined plate theories", Steel Compos. Struct., 18(1), 187-212. https://doi.org/10.12989/scs.2015.18.1.187.
  15. Attia, A., Bousahla, A.A., Tounsi, A., Mahmoud, S. and Alwabli, A.S. (2018), "A refined four variable plate theory for thermoelastic analysis of FGM plates resting on variable elastic foundations", Struct. Eng. Mech., 65(4), 453-464. https://doi.org/10.12989/sem.2018.65.4.453.
  16. Ayache, B., Fahsi, B., Fourn, H., Ait Atmane, H. and Tounsi, A. (2018), "Analysis of wave propagation and free vibration of porous (FGM) beam with a novel four variable refined theory", Earthq. Struct., 15(4), 369-382. https://doi.org/10.12989/eas.2018.15.4.369.
  17. Ayat, H., Kellouche, Y., Ghrici, M. and Boukhatem, B. (2018), "Compressive strength prediction of limestone filler concrete using artificial neural networks", Adv. Comput. Des., 3(3), 289-302. https://doi.org/10.12989/acd.2018.3.3.289.
  18. Bakhadda, B., Bachir Bouiadjra, M., Bourada, F., Bousahla, A.A., Tounsi, A. and Mahmoud, S.R. (2018), "Dynamic and bending analysis of carbon nanotube-reinforced composite plates with elastic foundation", Wind Struct., 27(5), 311-324. https://doi.org/10.12989/was.2018.27.5.311.
  19. Behera, S. and Kumari, P. (2018), "Free vibration of Levy-type rectangular laminated plates using efficient zig-zag theory", Adv. Comput. Des., 3(3), 213-232. https://doi.org/10.12989/acd.2018.3.3.213.
  20. Beldjelili, Y., Tounsi, A. and Mahmoud, S.R. (2016), "Hygro-thermo-mechanical bending of S-FGM plates resting on variable elastic foundations using a four-variable trigonometric plate theory", Smart Struct. Syst., 18(4), 755-786. https://doi.org/10.12989/sss.2016.18.4.755.
  21. Bellifa, H., Benrahou, K.H., Hadji, L., Houari, M.S.A. and 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. Brazil. Soc. Mech. Sci. Eng., 38(1), 265-275. https://doi.org/10.1007/s40430-015-0354-0.
  22. Bellifa, H., Bakora, A., Tounsi, A., Bousahla, A.A. and Mahmoud, S.R. (2017a), "An efficient and simple four variable refined plate theory for buckling analysis of functionally graded plates", Steel Compos. Struct., 25(3), 257-270. https://doi.org/10.12989/scs.2017.25.3.257.
  23. Bellifa, H., Benrahou, K.H., Bousahla, A.A., Tounsi, A. and Mahmoud, S.R. (2017b), "A nonlocal zeroth-order shear deformation theory for nonlinear postbuckling of nanobeams", Struct. Eng. Mech., 62(6), 695-702. https://doi.org/10.12989/sem.2017.62.6.695.
  24. Benachour, A., Tahar, H.D., Atmane, H.A., Tounsi, A. and Ahmed, M.S. (2011), "A four variable refined plate theory for free vibrations of functionally graded plates with arbitrary gradient", Compos. Part B: Eng., 42(6), 1386-1394. https://doi.org/10.1016/j.compositesb.2011.05.032.
  25. Benadouda, M., Atmane, H.A., Tounsi, A., Bernard, F. and Mohmoud, S. (2017), "An efficient shear deformation theory for wave propagation in functionally graded material beams with porosities", Earthq. Struct., 13(3), 255-265. https://doi.org/10.12989/eas.2017.13.3.255.
  26. Benahmed, A., Houari, M.S.A., Benyoucef, S., Belakhdar, K. and Tounsi, A. (2017), "A novel quasi-3D hyperbolic shear deformation theory for functionally graded thick rectangular plates on elastic foundation", Geomech. Eng., 12(1), 9-34. https://doi.org/10.12989/gae.2017.12.1.009.
  27. Benchohra, M., Driz, H., Bakora, A., Tounsi, A., Adda Bedia, E.A. and Mahmoud, S.R. (2018), "A new quasi-3D sinusoidal shear deformation theory for functionally graded plates", Struct. Eng. Mech., 65(1), 19-31. https://doi.org/10.12989/sem.2018.65.1.019.
  28. Bendaho, B., Belabed, Z., Bourada, M., Benatta, M.A., Bourada, F. and Tounsi, A. (2019), "Assessment of new 2D and quasi-3D Nonlocal theories for free vibration analysis of size-dependent functionally graded (FG) nanoplates", Adv. Nano Res., 7(4), 279-294. https://doi.org/10.12989/anr.2019.7.4.277.
  29. Benmansour, D.L., Kaci, A., Bousahla, A.A., Heireche, H., Tounsi, A., Alwabli, A.S., Alhebshi, A.M., Al-ghmady, K. and Mahmoud, S.R. (2019), "The nano scale bending and dynamic properties of isolated protein microtubules based on modified strain gradient theory", Adv. Nano Res. (accepted)
  30. Bennai, R., Atmane, H.A. and Tounsi, A. (2015), "A new higher-order shear and normal deformation theory for functionally graded sandwich beams", Steel Compos. Struct., 19(3), 521-546. https://doi.org/10.12989/scs.2015.18.3.793.
  31. Berghouti, H., Adda Bedia, E.A. Benkhedda, A. and Tounsi, A. (2019), "Vibration analysis of nonlocal porous nanobeams made of functionally graded material", Adv. Nano Res., 7(5), 3511-364. https://doi.org/10.12989/anr.2019.7.5.351.
  32. Bisen, H.B., Hirwani, C.K., Satankar, R.K., Panda, S.K., Mehar, K. and Patel, B. (2018), "Numerical study of frequency and deflection responses of natural fiber (luffa) reinforced polymer composite and experimental validation", J. Nat. Fiber., 1-15. https://doi.org/10.1080/15440478.2018.1503129.
  33. Bouadi, A., Bousahla, A.A., Houari, M.S.A., Heireche, H. and Tounsi, A. (2018), "A new nonlocal HSDT for analysis of stability of single layer graphene sheet", Adv. Nano Res., 6(2), 147-162. https://doi.org/10.12989/anr.2018.6.2.147.
  34. Bouhadra, A., Tounsi, A., Bousahla, A.A., Benyoucef, S. and Mahmoud, S.R. (2018), "Improved HSDT accounting for effect of thickness stretching in advanced composite plates", Struct. Eng. Mech., 66(1), 61-73. https://doi.org/10.12989/sem.2018.66.1.061.
  35. Boukhari, A., Atmane, H.A., Tounsi, A., Adda, B. and Mahmoud, S. (2016), "An efficient shear deformation theory for wave propagation of functionally graded material plates", Struct. Eng. Mech., 57(5), 837-859. https://doi.org/10.12989/sem.2016.57.5.837.
  36. Boukhlif, Z., Bouremana, M., Bourada, F., Bousahla, A.A., Bourada, M., Tounsi, A. and 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.
  37. Boulefrakh, L., Hebali, H., Chikh, A., Bousahla, A.A., Tounsi, A. and 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.
  38. Bounouara, F., Benrahou, K.H., Belkorissat, I. and Tounsi, A. (2016), "A nonlocal zeroth-order shear deformation theory for free vibration of functionally graded nanoscale plates resting on elastic foundation", Steel Compos. Struct., 20(2), 227-249. https://doi.org/10.12989/scs.2016.20.2.227.
  39. Bourada, F., Bousahla, A.A., Bourada, M., Azzaz, A., Zinata, A. and Tounsi, A. (2019), "Dynamic investigation of porous functionally graded beam using a sinusoidal shear deformation theory", Wind Struct., 28(1), 19-30. https://doi.org/10.12989/was.2019.28.1.019.
  40. Bourada, F., Amara, K., Bousahla, A.A., Tounsi, A. and Mahmoud, S.R. (2018), "A novel refined plate theory for stability analysis of hybrid and symmetric S-FGM plates", Struct. Eng. Mech., 68(6), 661-675. https://doi.org/10.12989/sem.2018.68.6.661.
  41. Bousahla, A.A., Benyoucef, S., Tounsi, A. and Mahmoud, S. (2016), "On thermal stability of plates with functionally graded coefficient of thermal expansion", Struct. Eng. Mech., 60(2), 313-335. https://doi.org/10.12989/sem.2016.60.2.313.
  42. Boussoula, A., Boucham, B., Bourada, M., Bourada, F., Tounsi, A., Bousahla, A.A. and Tounsi, A. (2019), "A simple nth-order shear deformation theory for thermomechanical bending analysis of different configurations of FG sandwich plates", Smart Struct. Syst. (accepted)
  43. Boutaleb, S., Benrahou, K.H., Bakora, A., Algarni, A., Bousahla, A.A., Tounsi, A., Mahmoud, S.R. and Tounsi, A. (2019), "Dynamic Analysis of nanosize FG rectangular plates based on simple nonlocal quasi 3D HSDT", Adv. Nano Res., 7(3), 189-206. https://doi.org/10.12989/anr.2019.7.3.191.
  44. Brischetto, S., Tornabene, F., Fantuzzi, N. and Viola, E. (2016), "3D exact and 2D generalized differential quadrature models for free vibration analysis of functionally graded plates and cylinders", Meccanica, 51(9), 2059-2098. https://doi.org/10.1007/s11012-016-0361-y.
  45. Chaabane, L.A., Bourada, F., Sekkal, M., Zerouati, S., Zaoui, F.Z., Tounsi, A., Derras, A., Bousahla, A.A. and 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.
  46. Chakraverty, S. and Pradhan, K.K. (2017), "Flexural vibration of functionally graded thin skew plates resting on elastic foundations", Int. J. Dyn. Control, 6(1), 97-121. https://doi.org/10.1007/s40435-017-0308-8.
  47. Chandra Mouli, B., Ramji, K., Kar, V.R., Panda, S.K., Lalepalli Anil, K. and 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.
  48. Cherif, R.H., Meradjah, M., Zidour, M., Tounsi, A., Belmahi, H. and Bensattalah, T. (2018), "Vibration analysis of nano beam using differential transform method including thermal effect", J. Nano Res., 54, 1-14. https://doi.org/10.4028/www.scientific.net/JNanoR.54.1.
  49. Chikh, A., Tounsi, A., Hebali, H. and Mahmoud, S.R. (2017), "Thermal buckling analysis of cross-ply laminated plates using a simplified HSDT", Smart Struct. Syst., 19(3), 289-297. https://doi.org/10.12989/sss.2017.19.3.289.
  50. Daouadji, T.H., Henni, A.H., Tounsi, A. and El Abbes, A.B. (2012), "A new hyperbolic shear deformation theory for bending analysis of functionally graded plates", Model. Simul. Eng., 2012, Article No. 29. https://doi.org/10.1155/2012/159806.
  51. Dash, S., Sharma, N., Mahapatra, T.R., Panda, S.K. and Sahu, P. (2018a), "Free vibration analysis of functionally graded sandwich flat panel", IOP Conf. Ser.: Mater. Sci. Eng., 377, 012140. https://doi.org/10.1088/1757-899X/377/1/012140
  52. Dash, S., Mehar, K., Sharma, N., Mahapatra, T.R. and 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.
  53. Draiche, K., Tounsi, A. and Mahmoud, S.R. (2016), "A refined theory with stretching effect for the flexure analysis of laminated composite plates", Geomech. Eng., 11(5), 671-690. https://doi.org/10.12989/gae.2016.11.5.671.
  54. Draiche, K., Bousahla, A.A., Tounsi, A., Alwabli, A.S., Tounsi, A. and Mahmoud, S.R. (2019), "Static analysis of laminated reinforced composite plates using a simple first-order shear deformation theory", Comput. Concrete, 24(4), 369-378. https://doi.org/10.12989/cac.2019.24.4.369.
  55. Draoui, A., Zidour, M., Tounsi, A. and 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.
  56. Duc, N.D., Lee, J., Nguyen-Thoi, T. and Thang, P.T. (2017), "Static response and free vibration of functionally graded carbon nanotube-reinforced composite rectangular plates resting on Winkler-Pasternak elastic foundations", Aerosp. Sci. Technol., 68, 391-402. https://doi.org/10.1016/j.ast.2017.05.032.
  57. El-Haina, F., Bakora, A., Bousahla, A.A., Tounsi, A. and Mahmoud, S. (2017), "A simple analytical approach for thermal buckling of thick functionally graded sandwich plates", Struct. Eng. Mech., 63(5), 585-595. https://doi.org/10.12989/sem.2017.63.5.585.
  58. Fahsi, A., Tounsi, A., Hebali, H., Chikh, A., Adda Bedia, E.A. and Mahmoud, S.R. (2017), "A four variable refined nth-order shear deformation theory for mechanical and thermal buckling analysis of functionally graded plates", Geomech. Eng., 13(3), 385-410. https://doi.org/10.12989/gae.2017.13.3.385.
  59. Faleh, N.M., Ahmed, R.A. and Fenjan, R.M. (2018), "On vibrations of porous FG nanoshells", Int. J. Eng. Sci., 133, 1-14. https://doi.org/10.1016/j.ijengsci.2018.08.007.
  60. Farid, M., Zahedinejad, P. and Malekzadeh, P. (2010), "Three-dimensional temperature dependent free vibration analysis of functionally graded material curved panels resting on two-parameter elastic foundation using a hybrid semi-analytic, differential quadrature method", Mater. Des., 31(1), 2-13. https://doi.org/10.1016/j.matdes.2009.07.025.
  61. Fourn, H., Atmane, H.A., Bourada, M., Bousahla, A.A., Tounsi, A. and Mahmoud, S. (2018), "A novel four variable refined plate theory for wave propagation in functionally graded material plates", Steel Compos. Struct., 27(1), 109-122. https://doi.org/10.12989/scs.2018.27.1.109.
  62. Haciyev, V.C., Sofiyev, A.H. and Kuruoglu, N. (2018), "Free bending vibration analysis of thin bidirectionally exponentially graded orthotropic rectangular plates resting on two-parameter elastic foundations", Compos. Struct., 184 372-377. https://doi.org/10.1016/j.compstruct.2017.10.014.
  63. Hasani Baferani, A., Saidi, A.R. and Ehteshami, H. (2011), "Accurate solution for free vibration analysis of functionally graded thick rectangular plates resting on elastic foundation", Compos. Struct., 93(7), 1842-1853. https://doi.org/10.1016/j.compstruct.2011.01.020.
  64. Hebali, H., Tounsi, A., Houari, M.S.A., Bessaim, A. and Bedia, E.A.A. (2014), "New Quasi-3D hyperbolic shear deformation theory for the static and free vibration analysis of functionally graded plates", J. Eng. Mech., 140(2), 374-383. https://doi.org/10.1061/(ASCE)EM.1943-7889.0000665.
  65. Hellal, H., Bourada, M., Hebali, H., Bourada, F., Tounsi, A., Bousahla, A.A. and Mahmoud, S.R. (2019), "Dynamic and stability analysis of functionally graded material sandwich plates in hygro-thermal environment using a simple higher shear deformation theory", J. Sandw. Struct. Mater., https://doi.org/10.1177/1099636219845841.
  66. Hirwani, C.K., Patil, R.K., Panda, S.K., Mahapatra, S.S., Mandal, S.K., Srivastava, L. and Buragohain, M.K. (2016), "Experimental and numerical analysis of free vibration of delaminated curved panel", Aerosp. Sci. Technol., 54, 353-370. https://doi.org/10.1016/j.ast.2016.05.009.
  67. Hirwani, C.K., Panda, S.K. and Mahapatra, S.S. (2017a), "Nonlinear transient finite-element analysis of delaminated composite shallow shell panels", AIAA J., 55(5), 1-15. https://doi.org/10.2514/1.J055624.
  68. Hirwani, C.K., Mahapatra, T.R., Panda, S.K., Sahoo, S.S., Singh, V.K. and Patle, B.K. (2017b), "Nonlinear free vibration analysis of laminated carbon/epoxy curved panels", Defence Sci. J., 67(2), 207-218. https://doi.org/10.14429/dsj.67.10072
  69. Hirwani, C.K., Panda, S.K., T.R. and Mahapatra, S.S. (2017c), "Numerical study and experimental validation of dynamic characteristics of delaminated composite flat and curved shallow shell structure", J. Aerosp. Eng., 30(5), 04017045. https://doi.org/10.1061/(ASCE)AS.1943-5525.0000756.
  70. Hirwani, C.K., Panda, S.K., T.R. and Mahapatra, S.S. (2018a), "Nonlinear finite element analysis of transient behavior of delaminated composite plate", J. Vib. Acoust., 140(2), 021001. https://doi.org/10.1115/1.4037848.
  71. Hirwani, C.K., Panda, S.K., Mahapatra, S.S., Mandal, S.K. and De, A.K. (2018b), "Dynamic behaviour of delaminated composite plate under blast loading", Gas Turbine India Conference, V002T05A032-V002T05A032,
  72. Hirwani, C.K. and Panda, K. (2018), "Numerical nonlinear frequency analysis of pre-damaged curved layered composite structure using higher-order finite element method", Int. J. Nonlin. Mech., 102, 14-24. https://doi.org/10.1016/j.ijnonlinmec.2018.03.005.
  73. Hirwani, C.K. and Panda, K. (2019a), "Nonlinear thermal free vibration frequency analysis of delaminated shell panel using FEM", Compos. Struct., 224, 111011. https://doi.org/10.1016/j.compstruct.2019.111011
  74. Hirwani, C.K. and Panda, K. (2019b), "Nonlinear transient analysis of delaminated curved composite structure under blast/pulse load", Eng. Comput., 1-14. https://doi.org/10.1007/s00366-019-00757-6.
  75. Hosseini-Hashemi, S., Fadaee, M. and Rokni Damavandi Taher, H. (2011), "Exact solutions for free flexural vibration of Levy-type rectangular thick plates via third-order shear deformation plate theory", Appl. Math. Model.. 35(2), 708-727. https://doi.org/10.1016/j.apm.2010.07.028.
  76. Jha, D.K., Kant, T. and Singh, R.K. (2013), "Free vibration response of functionally graded thick plates with shear and normal deformations effects", Compos. Struct., 96 799-823. https://doi.org/10.1016/j.compstruct.2012.09.034.
  77. Karami, B., Janghorban, M. and Tounsi, A. (2019a), "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.
  78. Karami, B., Janghorban, M. and Tounsi, A. (2019b), "Wave propagation of functionally graded anisotropic nanoplates resting on Winkler-Pasternak foundation", Struct. Eng. Mech., 70(1), 55-66. https://doi.org/10.12989/sem.2019.70.1.055.
  79. Karami, B., Shahsavari, D., Janghorban, M. and Tounsi, A. (2019c), "Resonance behavior of functionally graded polymer composite nanoplates reinforced with grapheme nanoplatelets", Int. J. Mech. Sci., 156, 94-105. https://doi.org/10.1016/j.ijmecsci.2019.03.036.
  80. Karami, B., Janghorban, M. and Tounsi, A. (2018a), "Galerkin's approach for buckling analysis of functionally graded anisotropic nanoplates/different boundary conditions", Eng. Comput., 35(4), 1297-1316. https://doi.org/10.1007/s00366-018-0664-9.
  81. Karami, B., Janghorban, M., Shahsavari, D. and Tounsi, A. (2018b), "A size-dependent quasi-3D model for wave dispersion analysis of FG nanoplates", Steel Compos. Struct/, 28(1), 99-110. https://doi.org/10.12989/scs.2018.28.1.099.
  82. Karami, B., Janghorban, M. and Tounsi, A. (2018c), "Variational approach for wave dispersion in anisotropic doubly-curved nanoshells based on a new nonlocal strain gradient higher order shell theory", Thin Wall. Struct., 129, 251-264. https://doi.org/10.1016/j.tws.2018.02.025.
  83. Karami, B., Janghorban, M. and Tounsi, A. (2018d), "Nonlocal strain gradient 3D elasticity theory for anisotropic spherical nanoparticles", Steel Compos. Struct., 27(2), 201-216. https://doi.org/10.12989/scs.2018.27.2.201.
  84. Karami, B., Janghorban, M. and Tounsi, A. (2017), "Effects of triaxial magnetic field on the anisotropic nanoplates", Steel Compos. Struct., 25(3), 361-374. https://doi.org/10.12989/scs.2017.25.3.361.
  85. Khiloun, M., Bousahla, A.A., Kaci, A., Bessaim, A., Tounsi, A. and Mahmoud, S.R. (2019), "Analytical modeling of bending and vibration of thick advanced composite plates using a four-variable quasi 3D HSDT", Eng. Comput., 1-15. https://doi.org/10.1007/s00366-019-00732-1.
  86. Koizumi, M. (1997), "FGM activities in Japan", Compos. Part B: Eng., 28(1), 1-4. https://doi.org/10.1016/S1359-8368(96)00016-9.
  87. Kolahchi, R., Bidgoli, A.M.M. and Heydari, M.M. (2015), "Size dependent bending analysis of FGM nano-sinusoidal plates resting on orthotropic elastic medium", Struct. Eng. Mech., 55(5), 1001-1014. : http://dx.doi.org/10.12989/sem.2015.55.5.1001.
  88. Lee, W.H., Han, S.C. and Park, W.T. (2015), "A refined higher order shear and normal deformation theory for E-, P-, and SFGM plates on Pasternak elastic foundation", Compos. Struct., 122 330-342. https://doi.org/10.1016/j.compstruct.2014.11.047.
  89. Leissa, A.W. (1973), "The free vibration of rectangular plates", J. Sound Vib., 31(3), 257-293. https://doi.org/10.1016/S0022-460X(73)80371-2.
  90. Liu, F.L. and Liew, K.M. (1999), "Analysis of vibrating thick rectangular plates with mixed boundary constraints using differential quadrature element method", J. Sound Vib., 225(5), 915-934. https://doi.org/10.1006/jsvi.1999.2262.
  91. Lu, C.F., Lim, C.W. and Chen, W.Q. (2009), "Exact solutions for free vibrations of functionally graded thick plates on elastic foundations", Mech. Adv. Mater. Struct., 16(8), 576-584. https://doi.org/10.1080/15376490903138888.
  92. Mahi, A., Adda Bedia, E.A. and 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(9), 2489-2508. https://doi.org/10.1016/j.apm.2014.10.045.
  93. Malekzadeh, P. (2009), "Three-dimensional free vibration analysis of thick functionally graded plates on elastic foundations", Compos. Struct., 89(3), 367-373. https://doi.org/10.1016/j.compstruct.2008.08.007.
  94. Mahmoudi, A., Benyoucef, S., Tounsi, A., Benachour, A., Adda Bedia, E.A. and Mahmoud, S.R. (2019), "A refined quasi-3D shear deformation theory for thermo-mechanical behavior of functionally graded sandwich plates on elastic foundations", J. Sandw. Struct. Mater., 21(6), 1906-1929. https://doi.org/10.1177/1099636217727577.
  95. Mantari, J.L., Granados, E.V. and Guedes Soares, C. (2014), "Vibrational analysis of advanced composite plates resting on elastic foundation", Compos. Part B: Eng., 66 407-419. https://doi.org/10.1016/j.compositesb.2014.05.026.
  96. Matsunaga, H. (2008), "Free vibration and stability of functionally graded plates according to a 2-D higher-order deformation theory", Compos. Struct., 82(4), 499-512. https://doi.org/10.1016/j.compstruct.2007.01.030.
  97. Medani, M., Benahmed, A., Zidour, M., Heireche, H., Tounsi, A., Bousahla, A.A., Tounsi, A. and 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.
  98. Meftah, A., Bakora, A., Zaoui, F.Z., Tounsi, A. and Bedia, E.A.A. (2017), "A non-polynomial four variable refined plate theory for free vibration of functionally graded thick rectangular plates on elastic foundation", Steel Compos. Struct., 23(3), 317-330. https://doi.org/10.12989/scs.2017.23.3.317.
  99. Mehar, K., Panda, S.K., Dehengia, A. and Kar, V.R. (2016), "Vibration analysis of functionally graded carbon nanotube reinforced composite plate in thermal environment", J. Sandw. Struct. Mater., 18(2), 151-173. https://doi.org/10.1177/1099636215613324.
  100. Mehar, K. and Panda, S.K. (2016), "Geometrical nonlinear free vibration analysis of FG-CNT reinforced composite flat panel under uniform thermal field", Compos. Struct., 143, 336-346. https://doi.org/10.1016/j.compstruct.2016.02.038.
  101. Mehar, K., Panda, S.K., Bui, T.Q. and Mahapatra, T.R. (2017a), "Nonlinear thermoelastic frequency analysis of functionally graded CNT-reinforced single/doubly curved shallow shell panels by FEM", J. Therm. Stress., 40(7), 899-916. https://doi.org/10.1080/01495739.2017.1318689.
  102. Mehar, K., Panda, S.K. and Mahapatra, T.R. (2017b), "Theoretical and experimental investigation of vibration characteristic of carbon nanotube reinforced polymer composite structure", Int. J. Mech. Sci., 133, 319-329. https://doi.org/10.1016/j.ijmecsci.2017.08.057.
  103. Meksi, R, Benyoucef, S., Mahmoudi, A., Tounsi, A., Adda Bedia, 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.
  104. Menasria, A., Bouhadra, A., Tounsi, A., Bousahla, A.A. and Mahmoud, S. (2017), "A new and simple HSDT for thermal stability analysis of FG sandwich plates", Steel Compos. Struct., 25(2), 157-175. https://doi.org/10.12989/scs.2017.25.2.157.
  105. Meziane, M.A.A., Abdelaziz, H.H. and Tounsi, A. (2014), "An efficient and simple refined theory for buckling and free vibration of exponentially graded sandwich plates under various boundary conditions", J. Sandw. Struct. Mater., 16(3), 293-318. https://doi.org/10.1177/1099636214526852.
  106. Nagino, H., Mikami, T. and Mizusawa, T. (2008), "Three-dimensional free vibration analysis of isotropic rectangular plates using the B-spline Ritz method", J. Sound Vib., 317(1-2), 329-353. https://doi.org/10.1016/j.jsv.2008.03.021.
  107. Nebab, M., Ait Atmane, H.., Bennai, R., Tounsi, A. and Bedia, E. (2019), "Vibration response and wave propagation in FG plates resting on elastic foundations using HSDT", Struct. Eng. Mech., 69(5), 511-525. https://doi.org/10.12989/sem.2019.69.5.511.
  108. Nebab, M., Ait Atmane, H. and Bennai, R. (2018), "Analyse en flexion des plaques FGM sur fondation elastique", Acad. J. Civil Eng., 36(1), 516-519. https://doi.org/10.26168/ajce.36.1.109.
  109. Neves, A.M.A., Ferreira, A.J.M., Carrera, E., Cinefra, M., Roque, C.M.C., Jorge, R.M.N. and Soares, C.M.M. (2013), "Static, free vibration and buckling analysis of isotropic and sandwich functionally graded plates using a quasi-3D higher-order shear deformation theory and a meshless technique", Compos. Part B: Eng., 44(1), 657-674. https://doi.org/10.1016/j.compositesb.2012.01.089.
  110. Pasternak, P. (1954), "On a new method of an elastic foundation by means of two foundation constants", Gosudarstvennoe Izdatelstvo Literaturi po Stroitelstuve i Arkhitekture.
  111. Pradhan, S.C. and Murmu, T. (2009), "Thermo-mechanical vibration of FGM sandwich beam under variable elastic foundations using differential quadrature method", J. Sound and Vib., 321(1-2), 342-362. https://doi.org/10.1016/j.jsv.2008.09.018.
  112. Rashed, Y.F., Aliabadi, M.H. and Brebbia, C.A. (1998), "The boundary element method for thick plates on a Winkler foundation", Int. J. Numer. Meth. Eng., 41(8), 1435-1462. https://doi.org/10.1002/(SICI)1097-0207(19980430)41:8<1435::AID-NME345>3.0.CO;2-O.
  113. Reddy, J.N. (2000), "Analysis of functionally graded plates", Int. J. Numer. Meth. Eng., 47(13), 663-684. https://doi.org/10.1002/(SICI)1097-0207(20000110/30)47:1/3<663::AID-NME787>3.0.CO;2-8.
  114. Semmah, A., Heireche, H., Bousahla, A.A. and 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.
  115. Shahsavari, D., Shahsavari, M., Li, L. and Karami, B. (2018), "A novel quasi-3D hyperbolic theory for free vibration of FG plates with porosities resting on Winkler/Pasternak/Kerr foundation", Aerosp. Sci. Technol., 72, 134-149. https://doi.org/10.1016/j.ast.2017.11.004.
  116. Sharma, N., Mahapatra, T.R., Panda, S.K. and Hirwani, C.K. (2018a), "Acoustic radiation and frequency response of higher-order shear deformable multilayered composite doubly curved shell panel-An experimental validation", Appl. Acoust., 133, 38-51. https://doi.org/10.1016/j.apacoust.2017.12.013.
  117. Sharma, N., Mahapatra, T.R., Panda, S.K. and Mehar, K. (2018b), "Evaluation of vibroacoustic responses of laminated composite sandwich structure using higher-order finite-boundary element model", Steel Compos. Struct., 28(5), 629-639. https://doi.org/10.12989/scs.2018.28.5.629.
  118. Shufrin, I. and Eisenberger, M. (2005), "Stability and vibration of shear deformable plates-first order and higher order analyses", Int. J. Solid. Struct., 42(3-4), 1225-1251. https://doi.org/10.1016/j.ijsolstr.2004.06.067.
  119. Sobhy, M. (2013), "Buckling and free vibration of exponentially graded sandwich plates resting on elastic foundations under various boundary conditions", Compos/ Struct., 99 76-87. https://doi.org/10.1016/j.compstruct.2012.11.018.
  120. Sobhy, M. (2015), "Thermoelastic Response of FGM Plates with Temperature-Dependent Properties Resting on Variable Elastic Foundations", Int/ J/ Appl/ Mech., 7(6), 1550082. https://doi.org/10.1142/S1758825115500829.
  121. Sobhy, M. and Alotebi, M.S. (2018), "Transient hygrothermal analysis of FG sandwich plates lying on a visco-Pasternak foundation via a simple and accurate plate theory", Arab. J. Sci. Eng., 43(10), 5423-5437. https://doi.org/10.1007/s13369-018-3142-1.
  122. Songsuwan, W., Pimsarn, M. and Wattanasakulpong, N. (2018), "Dynamic responses of functionally graded sandwich beams resting on elastic foundation under harmonic moving loads", Int. J. Struct. Stab. Dyn., 18(9), 1850112. https://doi.org/10.1142/S0219455418501122.
  123. Taibi, F.Z., Benyoucef, S., Tounsi, A., Bachir Bouiadjra, R., Adda Bedia, E.A. and Mahmoud, S.R. (2015), "A simple shear deformation theory for thermo-mechanical behaviour of functionally graded sandwich plates on elastic foundations", J. Sandw. Struct. Mater., 17(2), 99-129. https://doi.org/10.1177/1099636214554904.
  124. Thai, H.T. and Choi, D.H. (2011), "A refined plate theory for functionally graded plates resting on elastic foundation", Compos. Sci. Technol., 71(16), 1850-1858. https://doi.org/10.1016/j.compscitech.2011.08.016.
  125. Tlidji, Y., Zidour, M., Draiche, K., Safa, A., Bourada, M., Tounsi, A., Bousahla, A.A. and Mahmoud, S.R. (2019), "Vibration analysis of different material distributions of functionally graded microbeam", Struct. Eng. Mech., 69(6), 637-649. https://doi.org/10.12989/sem.2019.69.6.637.
  126. Torabi, J., Ansari, R. and Hasrati, E. (2018), "Mechanical buckling analyses of sandwich annular plates with functionally graded carbon nanotube-reinforced composite face sheets resting on elastic foundation based on the higher-order shear deformation plate theory", J. Sandw. Struct. Mater., https://doi.org/10.1177/1099636218789617.
  127. Tran, L.V. and Kim, S.E. (2018), "Static and free vibration analyses of multilayered plates by a higher-order shear and normal deformation theory and isogeometric analysis", Thin Wall. Struct., 130, 622-640. https://doi.org/10.1016/j.tws.2018.06.013.
  128. Winkler, E. (1867), Die Lehre von der Elasticitaet und Festigkeit, Prag Dominicus.
  129. Yahia, S.A., Atmane, H.A., Houari, M.S.A. and Tounsi, A. (2015), "Wave propagation in functionally graded plates with porosities using various higher-order shear deformation plate theories", Struct. Eng. Mech., 53(6), 1143-1165. http://dx.doi.org/10.12989/sem.2015.53.6.1143.
  130. Ying, J., Lu, C.F. and Chen, W.Q. (2008), "Two-dimensional elasticity solutions for functionally graded beams resting on elastic foundations", Compos. Struct., 84(3), 209-219. https://doi.org/10.1016/j.compstruct.2007.07.004.
  131. Youcef, D.O., Kaci, A., Benzair, A., Bousahla, A.A. and Tounsi, A. (2018), "Dynamic analysis of nanoscale beams including surface stress effects", Smart Struct. Syst., 21(1), 65-74. https://doi.org/10.12989/sss.2018.21.1.065.
  132. Yousfi, M., Atmane, H.A., Meradjah, M., Tounsi, A. and Bennai, R. (2018), "Free vibration of FGM plates with porosity by a shear deformation theory with four variables", Struct. Eng. Mech., 66(3), 353-368. https://doi.org/10.12989/sem.2018.66.3.353.
  133. Younsi, A., Tounsi, A., Zaoui, F.Z., Bousahla, A.A. and Mahmoud, S. (2018), "Novel quasi-3D and 2D shear deformation theories for bending and free vibration analysis of FGM plates", Geomech. Eng., 14(6), 519-532. https://doi.org/10.12989/GAE.2018.14.6.519
  134. Zaoui, F.Z., Ouinas, D. and 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.
  135. Zarga, D., Tounsi, A., Bousahla, A.A., Bourada, F. and 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.
  136. Zenkour, A.M. (2009), "The refined sinusoidal theory for FGM plates on elastic foundations", Int. J. Mech. Sci., 51(11-12), 869-880. https://doi.org/10.1016/j.ijmecsci.2009.09.026.
  137. Zhang, L.W., Lei, Z.X. and Liew, K.M. (2016), "Free vibration analysis of FG-CNT reinforced composite straight-sided quadrilateral plates resting on elastic foundations using the IMLS-Ritz method", J. Vib. Control, 23(6), 1026-1043. https://doi.org/10.1177/1077546315587804.
  138. Zine, A., Tounsi, A., Draiche, K., Sekkal, M. and Mahmoud, S.R. (2018), "A novel higher-order shear deformation theory for bending and free vibration analysis of isotropic and multilayered plates and shells", Steel Compos. Struct., 26(2), 125-137. https://doi.org/10.12989/scs.2018.26.2.125.
  139. Zhou, D., Cheung, Y.K., Au, F.T.K. and Lo, S.H. (2002), "Three-dimensional vibration analysis of thick rectangular plates using Chebyshev polynomial and Ritz method", Int. J. Solid. Struct., 39(26), 6339-6353. https://doi.org/10.1016/S0020-7683(02)00460-2.

Cited by

  1. Physical stability response of a SLGS resting on viscoelastic medium using nonlocal integral first-order theory vol.37, pp.6, 2019, 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, 2019, https://doi.org/10.12989/scs.2021.38.1.001
  3. Confinement effectiveness of Timoshenko and Euler Bernoulli theories on buckling of microfilaments vol.11, pp.1, 2021, https://doi.org/10.12989/acc.2021.11.1.081
  4. The nano scale buckling properties of isolated protein microtubules based on modified strain gradient theory and a new single variable trigonometric beam theory vol.10, pp.1, 2019, https://doi.org/10.12989/anr.2021.10.1.015
  5. Buckling analysis of functionally graded plates using HSDT in conjunction with the stress function method vol.27, pp.1, 2019, https://doi.org/10.12989/cac.2021.27.1.073
  6. Investigation on the dynamic response of porous FGM beams resting on variable foundation using a new higher order shear deformation theory vol.39, pp.1, 2019, https://doi.org/10.12989/scs.2021.39.1.095
  7. Thermoelastic response of functionally graded sandwich plates using a simple integral HSDT vol.91, pp.7, 2019, https://doi.org/10.1007/s00419-021-01973-7