In this paper, in order to satisfied the design and manufacturing requirements of functional materials, an investigation is carried out to study the free vibration and thermal buckling characteristics of porous P- and S-type functionally graded materials (FGM) circular plates in non-uniform thermal fields in the context of first-order shear deformation theory. FGM is formed by gradient changes in metals and ceramics, the thermomechanical properties were characterized by a gradient along the thickness direction of the circular plate by a power-law function containing porosity correction. The differential equations of motion control are derived using the Hamiltonian variational principle, and the dimensionless equations of motion and boundary conditions are solved analytically by the DTM transformation procedure. The problem has been degraded and compared with the results of the existing literature to confirm its validity. In conclusion, the influence of each parameter on the dimensionless natural frequency of the porous FGM circular plate and the influence of relevant parameters on the critical temperature rise are calculated and evaluated. The porosity weakens the overall stiffness and equivalent mass of the structure, and the foundation enhances the stiffness. The DTM calculation iteration speed is fast, and the results are highly consistent. The results can be used to provide model guidance and data support for future studies of porous FGM circular plates as well as follow-up studies.
ZhangHXiangXHuangB, et al. Static homotopy response analysis of structure with random variables of arbitrary distributions by minimizing stochastic residual error. Comput Struct2023; 288: 11.
2.
LuZBrennanMJYangT, et al. An investigation of a two-stage nonlinear vibration isolation system. J Sound Vib2013; 332(6): 1456–1464.
3.
CuiWZhaoLGeY, et al. A generalized van der Pol nonlinear model of vortex-induced vibrations of bridge decks with multistability. Nonlinear Dyn2024; 112(1): 259–272.
4.
ShiXYangYZhuX, et al. Stochastic dynamics analysis of the rocket shell coupling system with circular plate fasteners based on spectro-geometric method. Compos Struct2024; 329: 117727.
5.
ZhangC. The active rotary inertia driver system for flutter vibration control of bridges and various promising applications. Sci China Technol Sci2023; 66(2): 390–405.
6.
YeeKOngOZSGhayeshMH, et al. Various homogenisation schemes for vibration characteristics of axially FG core multilayered microbeams with metal foam face layers based on third order shear deformation theory. Appl Math Model2024; 125: 189–217.
7.
ShenHSWangZX. Assessment of Voigt and Mori–Tanaka models for vibration analysis of functionally graded plates. Compos Struct2012; 94(7): 2197–2208.
8.
GaoKGaoWWuD, et al. Nonlinear dynamic buckling of the imperfect orthotropic E-FGM circular cylindrical shells subjected to the longitudinal constant velocity. Int J Mech Sci2018; 138-139: 199–209.
9.
MellalFBennaiRAvcarM, et al. On the vibration and buckling behaviors of porous FG beams resting on variable elastic foundation utilizing higher-order shear deformation theory. Acta Mech2023; 234: 3955–3977.
10.
ReddyJNPraneethNNamP. Dual mesh control domain analysis of functionally graded circular plates accounting for moderate rotations. Compos Struct2021; 257: 113153.
11.
LiewKMAlibeiglooA. Predicting bucking and vibration behaviors of functionally graded carbon nanotube reinforced composite cylindrical panels with three-dimensional flexibilities. Compos Struct2021; 256(1): 113039.
12.
ŻurKKArefiMKimJ, et al. Free vibration and buckling analyses of magneto-electro-elastic FGM nanoplates based on nonlocal modified higher-order sinusoidal shear deformation theory. Compos B Eng2020; 182: 107601.
13.
ShenHSWangZX. Nonlinear analysis of shear deformable FGM beams resting on elastic foundations in thermal environments. Int J Mech Sci2014; 81(4): 195–206.
14.
RahmaniMMohammadiYKakavandF. Vibration analysis of different types of porous FG circular sandwich plates. Int J Adv Manuf Technol2019; 12(3): 63–75.
15.
Behravan RadAShariyatM. Three-dimensional magneto-elastic analysis of asymmetric variable thickness porous FGM circular plates with non-uniform tractions and Kerr elastic foundations. Compos Struct2015; 125: 558–574.
16.
LongVTTungHV. Postbuckling responses of porous FGM spherical caps and circular plates including edge constraints and nonlinear three-parameter elastic foundations. Mech Based Des Struc2023; 51(8): 4214–4236.
17.
TahirSITounsiAChikhA, et al. An integral four-variable hyperbolic HSDT for the wave propagation investigation of a ceramic-metal FGM plate with various porosity distributions resting on a viscoelastic foundation. Wave Random Complex2021; 34(3): 1616–1639.
18.
NguyenLBThaiCHZenkourAM, et al. An isogeometric Bézier finite element method for vibration analysis of functionally graded piezoelectric material porous plates. Int J Mech Sci2019; 157–158: 165–183.
19.
CongPHChienTMKhoaND, et al. Nonlinear thermomechanical buckling and post-buckling response of porous FGM plates using Reddy's HSDT. Aerosp Sci Technol2018; 77: 419–428.
20.
KimJŻurKKReddyJN. Bending, free vibration, and buckling of modified couples stress-based functionally graded porous micro-plates. Compos Struct2019; 209: 879–888.
21.
ThanhCLTranLVBuiTQ, et al. Isogeometric analysis for size-dependent nonlinear thermal stability of porous FG microplates. Compos Struct2019; 221: 110838.
22.
YinZGaoHLinG. Bending and free vibration analysis of functionally graded plates made of porous materials according to a novel the semi-analytical method. Eng Anal Bound Elem2021; 133: 185–199.
23.
KumarVSinghSJSaranVH, et al. Vibration characteristics of porous FGM plate with variable thickness resting on Pasternak's foundation. Eur J Mech A-Solid2021; 85: 104124.
24.
PrshikMRVikashKNitinS, et al. Geometrical nonlinear numerical frequency prediction of porous functionally graded shell panel under thermal environment. Int J Nonlin Mech2022; 143: 104041.
25.
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.
26.
FuTChenZYuH, et al. An analytical study of sound transmission through corrugated core FGM sandwich plates filled with porous material. Compos B Eng2018; 151: 161–172.
27.
KayaMO. Free vibration analysis of a rotating Timoshenko beam by differential transform method. Aircr Eng Aerosp Technol2006; 78(3): 194–203.
28.
WattanasakulpongNUngbhakornV. Linear and nonlinear vibration analysis of elastically restrained ends FGM beams with porosities. Aerosp Sci Technol2014; 32(1): 111–120.
29.
SinghSJHarshaSP. Thermo-mechanical analysis of porous sandwich S-FGM plate for different boundary conditions using Galerkin Vlasov's method: A semi-analytical approach. Thin Wall Struct2020; 150: 106668.
30.
DucNDTuanNDTranP, et al. Nonlinear stability of eccentrically stiffened S-FGM elliptical cylindrical shells in thermal environment. Thin Wall Struct2016; 108: 280–290.
31.
DucNDThangPTDaoNT, et al. Nonlinear buckling of higher deformable S-FGM thick circular cylindrical shells with metal–ceramic–metal layers surrounded on elastic foundations in thermal environment. Compos Struct2015; 121: 134–141.
32.
SinghSJHarshaSP. Nonlinear dynamic analysis of sandwich S-FGM plate resting on Pasternak foundation under thermal environment. Eur J Mech A-Solid2019; 76: 155–179.
33.
ZhangDGZhouYH. A theoretical analysis of FGM thin plates based on physical neutral surface. Comput Mater Sci2008; 44(2): 716–720.
34.
ShariyatMAlipourMMAlipourM. Differential transform vibration and modal stress analyses of circular plates made of two-directional functionally graded materials resting on elastic foundations. Arch Appl Mech2011; 81(9): 1289–1306.
35.
LalRSainiR. Vibration analysis of FGM circular plates under non-linear temperature variation using generalized differential quadrature rule. Appl Acoust2020; 158: 107027.
36.
AriaAIRabczukTFriswellMI. A finite element model for the thermo-elastic analysis of functionally graded porous nanobeams. Eur J Mech A-Solid2019; 77: 103767.
37.
WangWXueGTengZ. Analysis of free vibration characteristics of porous FGM circular plates in a temperature field. J Vib Eng Technol2022; 10(4): 1369–1380.
38.
TengZWangWGuC. Free vibration and buckling characteristics of porous functionally graded materials (FGMs) micro-beams based on the modified couple stress theory. Z Angew Math Me2022; 102.
39.
PradhanKKChakravertyS. Free vibration of functionally graded thin elliptic plates with various edge supports. Struct Eng Mech2015; 53(2): 337–354.
40.
ShabanMAlipourMMAlipourM. Semi-analytical solution for free vibration of thick functionally graded plates rested on elastic foundation with elastically restrained edge. Acta Mech Solida Sin2011; 24(4): 340–354.
41.
LiQChenY. Thermal vibration analysis of functionally graded circular plates based on Levinson's third-order shear deformation theory. Mech Based Des Struc2023; 51(9): 5088–5105.
