Four-variable quasi-3D model for nonlinear thermal vibration of FG plates lying on Winkler-Pasternak-Kerr foundation

Document Type : Research Article

Authors

1 - Department of Civil Engineering Material and Hydrology Laboratory, Faculty of Technology, University of Sidi Bel Abbes, Khenchela, Algeria. - Department of Civil Engineering, Faculty of Science &Technology, Abbes Laghrour University, Khenchela, Algeria.

2 - Department of Civil Engineering Material and Hydrology Laboratory, Faculty of Technology, University of Sidi Bel Abbes, Khenchela, Algeria. - Department des Sciences et de la Technologie, Universite de Tissemsilt, Hamouda, Algerie

3 Department of Civil Engineering Material and Hydrology Laboratory, Faculty of Technology, University of Sidi Bel Abbes, Khenchela, Algeria

4 - Department of Civil Engineering Material and Hydrology Laboratory, Faculty of Technology, University of Sidi Bel Abbes, Khenchela, Algeria. - Yonsei Frontier Lab, Yonsei University, Seoul, Korea. - Department of Civil and Environmental Engineering, King Fahd University of Petroleum & Minerals, Dhahran, Eastern Province, Saudi Arabia. - Interdisciplinary Research Center for Construction and Building Materials, KFUPM, Dhahran, Saudi Arabia.

5 Department of Mathematics, Govt. College University Faisalabad, Faisalabad, Pakistan

Abstract

This paper presents the nonlinear thermodynamic results of Functionally Graded (FG) plates lying on Winkler/Pasternak and Kerr foundation through an analytical formulation. The field displacement is defined by only four unknowns, including an indeterminate integral and a new shape function representing the transverse shear stresses. Material properties of the FG plates are temperature-dependent and graded according to a simple power-law distribution. Also, the thermodynamic equations of motion are deduced based on Hamilton’s principle. The exactitude of the present theory results is verified with those obtained by various researchers. The effects of temperature-dependence material properties, power-law index, nonlinear temperature rising, elastic foundation parameters, aspect, and slenderness ratio are discussed. The results show that the increase in elastic foundation parameters would enhance the thermodynamic response of the FG plates. Nevertheless, the degree of improvement would be related to the nonlinear temperature change. Moreover, the plate’s configuration effect is more significant when the nonlinear temperature difference is high.

Keywords

Main Subjects


References:
1.Sayyad, A.S. and Ghugal, Y.M. “Modeling andanalysis of functionally graded sandwich beams: Areview”, Mechanics of Advanced Materials and Structures, 26(21), pp. 1776-1795 (2019).https://doi.org/10.1080/15376494.2018.1447178
2.Thai, H.T., Nguyen, T.K., Vo, T.P., et al. “Analysis offunctionally graded sandwich plates using a new first-order shear deformation theory”, European Journal ofMechanics-A/Solids, 45, pp. 211-225 (2014).https://doi.org/10.1016/j.euromechsol.2013.12.008
3.Huang, X.L. and Shen, H.S. “Nonlinear vibration anddynamic response of functionally graded plates inthermal environments”, International Journal ofSolids and Structures, 41(9-10), pp. 2403-2427(2004). https://doi.org/10.1016/j.ijsolstr.2003.11.012
4.Lei, Z.X., Zhang, L.W., and Liew, K.M. “Bucklinganalysis of CNT reinforced functionally gradedlaminated composite plates”, CompositeStructures, 152, pp. 62-73 (2016).https://doi.org/10.1016/j.compstruct.2016.05.047
5.Sayyad, A.S., and Ghugal, Y.M. “A unified sheardeformation theory for the bending of isotropic,functionally graded, laminated and sandwich beamsand plates”, International Journal of AppliedMechanics, 9(01), 1750007 (2017).https://doi.org/10.1142/S1758825117500077
6.Parida, S. and Mohanty, S.C. “Free vibration analysisof rotating functionally graded material plate undernonlinear thermal environment using higher ordershear deformation theory”, Proceedings of theInstitution of Mechanical Engineers, Part C: Journalof Mechanical Engineering Science, 233(6), pp. 2056-2073 (2018).https://doi.org/10.1177/0954406218777535
7.Van Do, V.N. and Lee, C.H. “Quasi-3D isogeometricbuckling analysis method for advanced compositeplates in thermal environments”, Aerospace Scienceand Technology, 92, pp. 34-54 (2019).https://doi.org/10.1016/j.ast.2019.05.056
8.Li, S.R. and Ma, H.K. “Analysis of free vibration offunctionally graded material micro-plates withthermoelastic damping”, Archive of AppliedMechanics, 90(6), pp. 1285-1304 (2020).https://doi.org/10.1007/s00419-020-01664-9
9.Mehditabar, A., Rahimi, G.H., and Vahdat, S.E.“Integrity assessment of functionally graded pipeproduced by centrifugal casting subjected to internalpressure: experimental investigation”, Archive ofApplied Mechanics, 90(8), pp. 1723-1736 (2020).https://doi.org/10.1007/s00419-020-01692-5
10.Guerroudj, H.Z., Yeghnem, R., Kaci, A., et al.“Eigenfrequencies of advanced composite plates usingan efficient hybrid quasi-3D shear deformationtheory”, Smart Structures and Systems, 22(1), pp. 121-132 (2018). https://doi.org/10.12989/sss.2018.22.1.121
11.Mahmoudi, A., Benyoucef, S., Tounsi, A., et al. “Onthe effect of the micromechanical models on the freevibration of rectangular FGM plate resting on elasticfoundation”, Earthquakes and Structures, 14(2), p.117 (2018).https://doi.org/10.12989/eas.2018.14.2.117
12.Zenkour, A.M. and Radwan, A.F. “Hygrothermo-mechanical buckling of FGM plates resting on elasticfoundations using a quasi-3D model”, InternationalJournal for Computational Methods in EngineeringScience and Mechanics, 20(2), pp. 85-98 (2019).https://doi.org/10.1080/15502287.2019.1568618
13.Woodward, B. and Kashtalyan, M. “Three-dimensional elasticity analysis of sandwich panelswith functionally graded transversely isotropiccore”, Archive of Applied Mechanics, 89, pp. 2463-2484 (2019). https://doi.org/10.1007/s00419-019-01589-y
14.Hieu, P.T., and Van Tung, H. “Thermal andthermomechanical buckling of shear deformable FG-CNTRC cylindrical shells and toroidal shell segmentswith tangentially restrained edges”, Archive of Applied Mechanics, 90(7), pp. 1529-1546 (2020).https://doi.org/10.1007/s00419-020-01682-7
15.Ye, R., Zhao, N., Yang, D., et al. “Bending and freevibration analysis of sandwich plates with functionally graded soft core, using the new refined higher-orderanalysis model”, Journal of Sandwich Structures &Materials, 23(2), pp. 680-710 (2021).https://doi.org/10.1177/1099636220909763
16.Shariyat, M. “A generalized global–local high-ordertheory for bending and vibration analyses of sandwichplates subjected to thermo-mechanicalloads”, International Journal of MechanicalSciences, 52(3), pp. 495-514 (2010).https://doi.org/10.1016/j.ijmecsci.2009.11.010
17.Malekzadeh, P. and Monajjemzadeh, S.M. “Dynamicresponse of functionally graded plates in thermalenvironment under moving load”, Composites Part B:Engineering, 45(1), pp. 1521-1533 (2013).https://doi.org/10.1016/j.compositesb.2012.09.022
18.Attia, A., Tounsi, A., Bedia, E.A., et al. “Free vibrationanalysis of functionally graded plates withtemperature-dependent properties using various fourvariable refined plate theories”, Steel Compos.Struct, 18(1), pp. 187-212 (2015).http://dx.doi.org/10.12989/scs.2015.18.1.187
19.Zaoui, F.Z., Ouinas, D., Tounsi, A., et al.“Fundamental frequency analysis of functionallygraded plates with temperature-dependent propertiesbased on improved exponential-trigonometric two-dimensional higher shear deformationtheory”, Archive of Applied Mechanics, 91(3), pp.859-881 (2021). https://doi.org/10.1007/s00419-020-01793-1
20.Arshid, E., Arshid, H., Amir, S., et al. “Free vibrationand buckling analyses of FG porous sandwich curvedmicrobeams in thermal environment under magneticfield based on modified couple stresstheory”, Archives of Civil and MechanicalEngineering, 21, pp. 1-23 (2021).https://doi.org/10.1007/s43452-020-00150-x
21.Li, C., Shen, H.S., and Yang, J. “Nonlinear vibrationbehavior of FG sandwich beams with auxetic porouscopper core in thermal environments”, InternationalJournal of Structural Stability and Dynamics, 23(13),2350144 (2023).https://doi.org/10.1142/S0219455423501444
22.Singha, T.D., Bandyopadhyay, T., and Karmakar, A.“A numerical solution for thermal free vibrationanalysis of rotating pre-twisted FG-GRC cylindricalshell panel”, Mechanics of Advanced Materials andStructures, 30(15), pp. 3013-3031 (2023).https://doi.org/10.1080/15376494.2022.2067924
23.Abouelregal, A.E., Mohammad-Sedighi, H.,Faghidian, S.A., et al. “Temperature-dependentphysical characteristics of the rotating nonlocalnanobeams subject to a varying heat source and adynamic load”, Facta Universitatis, Series:Mechanical Engineering, 19(4), pp. 633-656 (2021).https://doi.org/10.22190/FUME201222024A
24.Nasr, M.E., Abouelregal, A.E., Soleiman, A., et al.“Thermoelastic Vibrations of Nonlocal NanobeamsResting on a Pasternak Foundation via DPLModel”, Journal of Applied and ComputationalMechanics, 7(1), pp. 34-44 (2021).https://doi.org/10.22055/jacm.2020.34228.2362
25.Malekzadeh, P., Shahpari, S.A. and Ziaee, H.R.“Three-dimensional free vibration of thickfunctionally graded annular plates in thermalenvironment”, Journal of Sound andVibration, 329(4), pp. 425-442 (2010).https://doi.org/10.1016/j.jsv.2009.09.025
26.Malekzadeh, P., and Safaeian Hamzehkolaei, N. “A3D discrete layer-differential quadrature free vibrationof multi-layered FG annular plates in thermalenvironment”, Mechanics of Advanced Materials andStructures, 20(4), pp. 316-330 (2013).https://doi.org/10.1080/15376494.2011.627637
27.Tu, T.M., Quoc, T.H., and Van Long, N. “Vibrationanalysis of functionally graded plates using the eight-unknown higher order shear deformation theory inthermal environments”, Aerospace Science andTechnology, 84, pp. 698-711 (2019).https://doi.org/10.1016/j.ast.2018.11.010
28.Zaoui, F.Z., Tounsi, A., and Ouinas, D. “Free vibrationof functionally graded plates resting on elasticfoundations based on quasi-3D hybrid-type higher order shear deformation theory”, Smart Structures and Systems, 20(4), pp. 509-524 (2017). https://doi.org/10.12989/sss.2017.20.4.509
29.Zhou, L. “A novel similitude method for predictingnatural frequency of FG porous plates under thermalenvironment”, Mechanics of Advanced Materials andStructures, 29(27), pp. 6786-6802 (2022).https://doi.org/10.1080/15376494.2021.1985197
30.Mamen, B., Bouhadra, A., Bourada, F., et al.“Combined effect of thickness stretching andtemperature-dependent material properties ondynamic behavior of imperfect FG beams using threevariable quasi-3D model”, Journal of VibrationEngineering & Technologies, 11(5), pp. 1-23 (2022). https://doi.org/10.1007/s42417-022-00704-8
31.Touloukian, Y.S. “Thermophysical properties of hightemperature solid materials”, Volume 4. Oxides andtheir solutions and mixtures. Part I. Simple oxygencompounds and their mixtures. Defense TechnicalInformation Center, (1966). DTIC AD0649951
32.Salari, E., Ashoori, A.R., Vanini, S.S., et al. “Nonlineardynamic buckling and vibration of thermally post-buckled temperature-dependent FG porousnanobeams based on the nonlocal theory”, PhysicaScripta, 97(8),085216(2022).https://doi.org/10.1088/1402-4896/ac8187
33.Javaheri, R. and Eslami, M.R. “Thermal buckling offunctionally graded plates based on higher ordertheory”, Journal of Thermal Stresses, 25(7), pp. 603-625 (2002).https://doi.org/10.1080/01495730290074333
34.Shahrjerdi, A., Mustapha, F., Bayat, M., et al. “Freevibration analysis of solar functionally graded plateswith temperature-dependent material properties usingsecond order shear deformation theory”, Journal ofMechanical Science and Technology, 25(9), pp. 2195-2209 (2011).https://doi.org/10.1007/s12206-011-0610-x
35.Ebrahimi, F., and Barati, M.R. “Temperaturedistribution effects on buckling behavior of smartheterogeneous nanosize plates based on nonlocal four-variable refined plate theory”, International Journalof Smart and Nano Materials, 7(3), pp. 119-143(2016).https://doi.org/10.1080/19475411.2016.1223203
36.Bouhadra, A., Menasria, A., and Rachedi, M.A.“Boundary conditions effect for buckling analysis ofporous functionally graded nanobeams”, Advances inNano Research, 10(4), p. 313 (2021).https://doi.org/10.12989/anr.2021.10.4.313
37.Esmaeilzadeh, M. and Kadkhodayan, M. “Dynamicanalysis of stiffened bi-directional functionally gradedplates with porosities under a moving load by dynamicrelaxation method with kinetic damping”, AerospaceScience and Technology, 93, 105333 (2019).https://doi.org/10.1016/j.ast.2019.105333
38.Li, S.R., Su, H.D. and Cheng, C.J. “Free vibration offunctionally graded material beams with surface-bonded piezoelectric layers in thermalenvironment”, Applied Mathematics andMechanics, 30(8), pp. 969-982 (2009). https://doi.org/10.1007/s10483-009-0803-7
39.Li, M., Soares, C.G., and Yan, R. “Free vibrationanalysis of FGM plates on Winkler/Pasternak/Kerr foundation by using a simple quasi-3D HSDT”, Composite Structures, 264, 113643 (2021). https://doi.org/10.1016/j.compstruct.2021.113643
40.Reddy, J.N. and Chin, C.D. “Thermomechanicalanalysis of functionally graded cylinders andplates”. Journal of Thermal Stresses, 21(6), pp. 593-626 (1998).https://doi.org/10.1080/01495739808956165
Volume 32, Issue 2
Transactions on Mechanical Engineering
January and February 2025 Article ID:6746
  • Receive Date: 28 April 2022
  • Revise Date: 31 January 2023
  • Accept Date: 10 March 2024