Free vibration of the porous functionally graded magneto-electro-elastic (FGMEE) microbeams in hygrothermal environment is investigated. Four kinds of distributions of porosities including uniform porosity, “O,”“X,” and “V” type porosities are assumed in this paper. For the functionally graded microbeam, the physical neutral surface is considered. The modified couple stress theory is adopted to capture the size effect. The equations of motion for the porous FGMEE microbeam are derived and solved by differential transformation method. In the numerical examples, the effect of electric and magnetic loadings, material length scale parameter, the temperature rise, the moisture concentration, material gradient index, and porosity volume fraction on the natural frequency are analyzed and discussed in detail. The results indicate that different porous distribution modes have different effects on natural frequency. Moisture concentration/temperature rise can reduce the natural frequency regardless of what the temperature and moisture modes is. These results will be useful for the design of the porous FGMEE structures.
AbbasIAZenkourAM (2013) LS model on electro–magneto–thermoelastic response of an infinite functionally graded cylinder. Composite Structures96: 89–96.
2.
AboudiJ (2001) Micromechanical analysis of fully coupled electro-magneto-thermo-elastic multiphase composites. Smart Materials and Structures10: 867–877.
3.
AlaimoABenedettiIMilazzoA (2014) A finite element formulation for large deflection of multilayered magneto-electro-elastic plates. Composite Structures107: 643–653.
4.
AnsariRGholamiRRouhiH (2015) Size-dependent nonlinear forced vibration analysis of magneto-electro-thermo-elastic Timoshenko nanobeams based upon the nonlocal elasticity theory. Composite Structures126: 216–226.
5.
ArefiMZenkourAM (2017) Thermo-electro-magneto-mechanical bending behavior of size-dependent sandwich piezomagnetic nanoplates. Mechanics Research Communications84: 27–42.
6.
ArikogluAOzkolI (2006) Solution of difference equations by using differential transform method. Applied Mathematics and Computation174(2): 1216–1228.
7.
AvellanedaMHarsheG (1994) Magnetoelectric effect in piezoelectric/magnetostrictive multilayer composites. Journal of Intelligent Material Systems and Structures5(4): 501–513.
8.
DaiTDaiHLLinZY (2019) Multi-field mechanical behavior of a rotating porous FGMEE circular disk with variable thickness under hygrothermal environment. Composite Structures210: 641–656.
9.
EbrahimiFBaratiMR (2016) A nonlocal higher-order refined magneto-electro-viscoelastic beam model for dynamic analysis of smart nanostructures. International Journal of Engineering Science107: 183–196.
10.
FarajpourAYazdiMRHRastgooA, et al. (2016) Nonlocal nonlinear plate model for large amplitude vibration of magneto-electro-elastic nanoplates. Composite Structures140: 323–336.
11.
FazzolariFACarreraE (2014) Thermal stability of FGM sandwich plates under various through-the-thickness temperature distributions. Journal of Thermal Stresses37: 1449–1481.
12.
GholamiRAnsariR (2017) A unified nonlocal nonlinear higher-order shear deformable plate model for postbuckling analysis of piezoelectric-piezomagnetic rectangular nanoplates with various edge supports. Composite Structures166: 202–218.
13.
JankowskiPZurKKFarajpourA (2022) Analytical and meshless DQM approaches to free vibration analysis of symmetric FGM porous nanobeams with piezoelectric effect. Engineering Analysis with Boundary Elements136: 266–289.
14.
KattimaniSCRayMC (2014) Smart damping of geometrically nonlinear vibrations of magneto-electro-elastic plates. Composite Structures114: 51–63.
15.
KeLLWangYS (2014) Free vibration of size-dependent magneto-electro-elastic nanobeams based on the nonlocal theory. Physica E63: 52–61.
16.
KiranMCKattimaniSC (2018) Assessment of porosity influence on vibration and static behaviour of functionally graded magneto-electro-elastic plate: A finite element study. European Journal of Mechanics - A/Solids71: 258–277.
17.
KiranMCKattimaniSCVinyasM (2018) Porosity influence on structural behaviour of skew functionally graded magneto-electro-elastic plate. Composite Structures191: 36–77.
18.
LiJY (2000) Magnetoelectroelastic multi-inclusion and inhomogeneity problems and their applications in composite materials. International Journal of Engineering Science38(18): 1993–2011.
19.
LiYDLeeKY (2010) Collinear unequal crack series in magnetoelectroelastic materials: Mode I case solved via new real fundamental solutions. Engineering Fracture Mechanics77(14): 2772–2790.
20.
LiYS (2014) Buckling analysis of magnetoelectroelastic plate resting on Pasternak elastic foundation. Mechanics Research Communications56(2): 104–114.
21.
LiYSCaiZYShiSY (2014) Buckling and free vibration of magnetoelectroelastic nanoplate based on nonlocal theory. Composite Structures111: 522–529.
22.
LiYSFengWJXuZH (2009) Fracture analysis of cracked 2D planar and axisymmetric problems of magneto-electro-elastic materials by the MLPG coupled with FEM. Computer Methods in Applied Mechanics and Engineering198(30–32): 2347–2359.
23.
LiYSMaPWangW (2016) Size-dependent bending, buckling and vibration of magnetoelectroelastic nanobeam. Journal of Intelligent Material Systems and Structures27(9): 1139–1149.
24.
LiYSRenJHFengWJ, et al. (2013) Dynamic fracture analysis of an annular interfacial crack between dissimilar magnetoelectroelastic layers. Archive of Applied Mechanics83(1): 151–170.
25.
LiYSZhangJJ (2014) Free vibration analysis of magnetoelectroelastic plate resting on Pasternak foundation. Smart Materials and Structures23: 025002.
26.
LiuJXLiuXLZhaoYB (2001) Green’s functions for anisotropic magnetoelectroelastic solids with an elliptical cavity or a crack. International Journal of Engineering Science39(12): 1405–1418.
27.
MilazzoAOrlandoC (2012) A beam finite element for magneto-electro-elastic multilayered composite structures. Composite Structures94(12): 3710–3721.
28.
NanCWBichurinMIDongSX, et al. (2008) Multiferroic magnetoelectric composites: Historical perspective, status, and future directions. Journal of Applied Physics103(3): 031101.
29.
PennaRFeoLLovisiG (2021) Hygro-thermal bending behavior of porous FG nano-beams via local/nonlocal strain and stress gradient theories of elasticity. Composite Structures263: 113627.
30.
PiovanMTOlmedoJFSampaioR (2015) Dynamics of magneto electro elastic curved beams: Quantification of parametric uncertainties. Composite Structures133: 621–629.
RuCQ (2000) Exact solution for finite electrode layers embedded at the interface of two piezoelectric half-planes. Journal of the Mechanics and Physics of Solids48(4): 693–708.
33.
ShiSHLiPJinF (2017) The establishment of coupled magneto-electro-thermo-elastic theory with the consideration of surface and non-local effects and its application in laminated nano-devices. Composite Structures179: 541–551.
34.
VinyasM (2020) On frequency response of porous functionally graded magneto-electro-elastic circular and annular plates with different electro-magnetic conditions using HSDT. Composite Structures240: 112044.
35.
VinyasMKattimaniSC (2017) Static studies of stepped functionally graded magneto-electro-elastic beam subjected to different thermal loads. Composite Structures163: 216–237.
36.
WangBLMaiYW (2003) Crack tip field in piezoelectric/piezomagnetic media. European Journal of Mechanics - A/Solids22(4): 591–602.
37.
WangQ (2002) On buckling of column structures with a pair of piezoelectric layers. Engineering Structures24(2): 199–205.
38.
WuPHuCQinQH (2018) Time-dependent behavior of layered magneto-electro-elastic cylindrical shell with viscoelastic interlayer. Composite Structures200: 874–885.
39.
XinLBHuZD (2015) Free vibration of layered magneto-electro-elastic beams by SS-DSC approach. Composite Structures125: 96–103.
40.
YangYLiXF (2019) Bending and free vibration of a circular magnetoelectroelastic plate with surface effects. International Journal of Mechanical Sciences 157–158: 858–871.
41.
ZhangLLiXW (2013) Buckling and vibration analysis of functionally graded magneto-electro-thermo-elastic circular cylindrical shells. Applied Mathematical Modelling37(4): 2279–2292.
42.
ZhongYFChenLYuWB, et al. (2013) Asymptotical construction of a Reissner-like model for multilayer functionally graded magneto-electro-elastic plates. Composite Structures96: 786–798.
43.
ZhouYYZhuJ (2016) Vibration and bending analysis of multiferroic rectangular plates using third-order shear deformation theory. Composite Structures153: 712–723.
