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http://dx.doi.org/10.12989/eas.2019.17.5.447

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)
Publication Information
Earthquakes and Structures / v.17, no.5, 2019 , pp. 447-462 More about this Journal
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
free vibration; variables elastic foundations; Functionally graded plate; higher shear deformation theory;
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Times Cited By KSCI : 57  (Citation Analysis)
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86 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.   DOI
87 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.   DOI
88 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.   DOI
89 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.   DOI
90 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.   DOI
91 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.   DOI
92 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.   DOI
93 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.   DOI
94 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.   DOI
95 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.   DOI
96 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)
97 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.   DOI
98 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.   DOI
99 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.   DOI
100 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.
101 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.   DOI
102 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.
103 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.   DOI
104 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.   DOI
105 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.   DOI
106 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.
107 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.   DOI
108 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.   DOI
109 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.   DOI
110 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.   DOI
111 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.   DOI
112 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.   DOI
113 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.
114 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.   DOI
115 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.
116 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.   DOI
117 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.   DOI
118 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.   DOI
119 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.   DOI
120 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.   DOI
121 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.   DOI
122 Hirwani, C.K. and Panda, K. (2019a), "Nonlinear thermal free vibration frequency analysis of delaminated shell panel using FEM", Compos. Struct., 224, 111011.   DOI
123 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.   DOI
124 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,
125 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.   DOI
126 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.
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132 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.   DOI
133 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.   DOI
134 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.   DOI
135 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.   DOI
136 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.   DOI
137 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.   DOI
138 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.   DOI
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