The current investigation aims to account for the influence of porosity modeling while studying the dynamic response of functionally graded material (FGM) plates within the framework of a new, higher-order shear deformation theory for the first time. In the newly developed porosity modeling, the reciprocal effect of mass density and Young’s modulus is considered. Furthermore, silicon carbide in the ceramic phase and nickel in the metallic phase are selected as the constituent materials of the functionally graded plate. Based upon the new higher-order theory, the kinetic and kinematic relations are derived. This theory does not need any shear correction factor. The dynamic form of the principle of virtual work is employed to achieve governing equations of structure. Afterward, Galerkin’s method is implemented to solve obtained governing equations of porous, functionally graded plates. In order to verify the accuracy of the method, the obtained results were compared with the results reported in the literature, and good agreement was found. At last, the influences of some parameters such as porosity coefficient, length to thickness ratio, and aspect ratio of the porous, FGM plate on the dimensionless frequency are studied and the results are illustrated in detail.
UchidaYYamadaJKathuriaY, et al.Excimer laser processing of functionally graded materials. Functionally Graded Materials 19961997; ■■■: 337–342.
2.
DoganV. Nonlinear vibration of FGM plates under random excitation. Compos Struct2013; 95: 366–374.
3.
AkbariMKianiYAghdamM, et al.Free vibration of FGM Lévy conical panels. Compos Struct2014; 116: 732–746.
4.
KadkhodayanMGolmakaniM. Non-linear bending analysis of shear deformable functionally graded rotating disk. Int J Non Lin Mech2014; 58: 41–56.
5.
XuYQianYSongG. Stochastic finite element method for free vibration characteristics of random FGM beams. Appl Math Model2016; 40: 10238–10253.
6.
ElishakoffIEisenbergerMDelmasA. Buckling and vibration of functionally graded material columns sharing Duncan's mode shape, and new cases. Structures2016; 5: 170–174.
7.
LiLLiXHuY. Nonlinear bending of a two-dimensionally functionally graded beam. Compos Struct2018; 184: 1049–1061.
8.
ZouatniaNHadjiL. Effect of the micromechanical models on the bending of FGM beam using a new hyperbolic shear deformation theory. Earthq Struct2019; 16: 177–183.
9.
GolmakaniMMalikanMPourSG, et al.Bending analysis of functionally graded nanoplates based on a higher-order shear deformation theory using dynamic relaxation method. Continuum Mech Therm2021; ■■■: 1–20.
10.
KumarVSinghSSaranV, et al.Vibration characteristics of porous FGM plate with variable thickness resting on Pasternak's foundation. Eur J Mech Solid2021; 85: 104124.
11.
BabaeeAJelovicaJ. Nonlinear transient thermoelastic response of FGM plate under sudden cryogenic cooling. Ocean Eng2021; 226: 108875.
12.
SitliYMhadaKBourihaneO, et al.Buckling and post-buckling analysis of a functionally graded material (FGM) plate by the asymptotic numerical method. Structures2021; 31: 1031–1040.
13.
EbrahimiFSeyfiANouraeiM, et al.Influence of magnetic field on the wave propagation response of functionally graded (FG) beam lying on elastic foundation in thermal environment. Waves Random Complex Media2021; ■■■: 1–19.
14.
LiuPChenGF. Porous materials: processing and applications. ■■■: Elsevier Science, 2014.
15.
NguyenNVNguyenHXLeeS, et al.Geometrically nonlinear polygonal finite element analysis of functionally graded porous plates. Adv Eng Software2018; 126: 110–126.
16.
ZhaoJChoeKXieF, et al.Three-dimensional exact solution for vibration analysis of thick functionally graded porous (FGP) rectangular plates with arbitrary boundary conditions. Compos B Eng2018; 155: 369–381.
17.
EbrahimiFSeyfiADabbaghA. Dispersion of waves in FG porous nanoscale plates based on NSGT in thermal environment. Adv Nano Res2019; 7: 325–335.
18.
EbrahimiFSeyfiADabbaghA. A novel porosity-dependent homogenization procedure for wave dispersion in nonlocal strain gradient inhomogeneous nanobeams. Eur Phys J Plus2019; 134: 1–11.
19.
KimJŻurKKReddyJ. Bending, free vibration, and buckling of modified couples stress-based functionally graded porous micro-plates. Compos Struct2019; 209: 879–888.
20.
ZhuBXuQLiM, et al.Nonlinear free and forced vibrations of porous functionally graded pipes conveying fluid and resting on nonlinear elastic foundation. Compos Struct2020; 252: 112672.
21.
KumarRLalASinghB, et al.Non-linear analysis of porous elastically supported FGM plate under various loading. Compos Struct2020; 233: 111721.
22.
Phung-VanPThaiCHFerreiraA, et al.Isogeometric nonlinear transient analysis of porous FGM plates subjected to hygro-thermo-mechanical loads. Thin-Walled Struct2020; 148: 106497.
23.
SinghSHarshaS. Thermo-mechanical analysis of porous sandwich S-FGM plate for different boundary conditions using Galerkin Vlasov's method: a semi-analytical approach. Thin-Walled Struct2020; 150: 106668.
24.
AdhikariBDashPSinghB. Buckling analysis of porous FGM sandwich plates under various types nonuniform edge compression based on higher order shear deformation theory. Compos Struct2020; 251: 112597.
25.
RastehkenariSFGhadiriM. Nonlinear random vibrations of functionally graded porous nanobeams using equivalent linearization method. Appl Math Model2021; 89: 1847–1859.
26.
GenaoFYKimJŻurKK. Nonlinear finite element analysis of temperature-dependent functionally graded porous micro-plates under thermal and mechanical loads. Compos Struct2021; 256: 112931.
27.
TaoCDaiT. Analyses of thermal buckling and secondary instability of post-buckled S-FGM plates with porosities based on a meshfree method. Appl Math Model2021; 89: 268–284.
28.
ShELKattimaniSVinyasM. Nonlinear free vibration and transient responses of porous functionally graded magneto-electro-elastic plates. Arch Civ Mech Eng2022; 22: 1–26.
29.
HSNKKattimaniSNguyen-ThoiT. Influence of porosity distribution on nonlinear free vibration and transient responses of porous functionally graded skew plates. Def Technol2021; 17: 1918–1935.
30.
Madrahalli ChidanandamurthyKWangWFangC, et al.Static, buckling, and free vibration characteristics of porous skew partially functionally graded magneto-electro-elastic plate. Mech Base Des Struct Mach2021: 1–36.
31.
KumarHNKattimaniS. Effect of different geometrical non-uniformities on nonlinear vibration of porous functionally graded skew plates: a finite element study. Def Technol, 2021.
32.
EsayasLSKattimaniS. Effect of porosity on active damping of geometrically nonlinear vibrations of a functionally graded magneto-electro-elastic plate. Def Technol, 2021.
33.
EsmaeilzadehMGolmakaniMLuoY, et al.Transient behavior of imperfect bi-directional functionally graded sandwich plates under moving loads. Eng Comput2021; ■■■: 1–11.
34.
EsmaeilzadehMGolmakaniMSadeghianM. A nonlocal strain gradient model for nonlinear dynamic behavior of bi-directional functionally graded porous nanoplates on elastic foundations. Mech Base Des Struct Mach2020; ■■■: 1–20.
35.
AlijaniFBakhtiari-NejadFAmabiliM. Nonlinear vibrations of FGM rectangular plates in thermal environments. Nonlinear Dynam2011; 66: 251–270.
36.
Al RjoubYSHamadAG. Free vibration of functionally Euler-Bernoulli and Timoshenko graded porous beams using the transfer matrix method. KSCE J Civ Eng2017; 21: 792–806.
37.
BertCW. Prediction of elastic moduli of solids with oriented porosity. J Mater Sci1985; 20: 2220–2224.
38.
ChenXLuYZhuB, et al.Nonlinear resonant behaviors of bi-directional functionally graded material microbeams: one-/two-parameter bifurcation analyses. Compos Struct2019; 223: 110896.
39.
ArisHAhmadiH. Nonlinear vibration analysis of FGM truncated conical shells subjected to harmonic excitation in thermal environment. Mech Res Commun2020; 104: 103499.
40.
SeyfiAAghdamM. Vibrational behavior of temperature-dependent imperfect functionally graded plate lying on an elastic substrate. Mech Base Des Struct Mach2021; ■■■: 1–22.
41.
ZaouiFZOuinasDTounsiA. New 2D and quasi-3D shear deformation theories for free vibration of functionally graded plates on elastic foundations. Compos B Eng2019; 159: 231–247.
42.
BouazzaMZenkourAM. Hygro-thermo-mechanical buckling of laminated beam using hyperbolic refined shear deformation theory. Compos Struct2020; 252: 112689.
43.
Nguyen-XuanHTranLVThaiCH, et al.Isogeometric analysis of functionally graded plates using a refined plate theory. Compos B Eng2014; 64: 222–234.
44.
ReddyJ. Analysis of functionally graded plates. Int J Numer Methods Eng2000; 47: 663–684.
45.
KhraishiTAZbibHMde la RubiaTD. The treatment of traction-free boundary condition in three-dimensional dislocation dynamics using generalized image stress analysis. Mater Sci Eng: A2001; 309: 283–287.
46.
BaratiMRShahverdiH. An analytical solution for thermal vibration of compositionally graded nanoplates with arbitrary boundary conditions based on physical neutral surface position. Mech Adv Mater Struct2017; 24: 840–853.
47.
MatsunagaH. Free vibration and stability of functionally graded plates according to a 2-D higher-order deformation theory. Compos Struct2008; 82: 499–512.
48.
DemirhanPATaskinV. Bending and free vibration analysis of Levy-type porous functionally graded plate using state space approach. Compos B Eng2019; 160: 661–676.
