Size-dependent free vibration analysis of a three-layered exponentially graded nano-/micro-plate with piezomagnetic face sheets resting on Pasternak’s foundation via MCST
Restricted accessResearch articleFirst published online January, 2020
Size-dependent free vibration analysis of a three-layered exponentially graded nano-/micro-plate with piezomagnetic face sheets resting on Pasternak’s foundation via MCST
The present work is devoted to the free vibration analysis of elastic three-layered nano-/micro-plate with exponentially graded core and piezomagnetic face-sheets using the modified couple stress theory. To capture size-dependency for a nano-/micro-sized rectangular plate, the couple stress theory is used as a non-classical continuum theory. The rectangular elastic three-layered nano-/micro-plate is resting on Pasternak’s foundation. The present model contains one material length scale parameter and can capture the size effect. Material properties of the core are supposed to vary along the thickness direction based on the exponential function. The governing equations of motion are derived from Hamilton’s principle based on the modified couple stress theory and first-order shear deformation theory. The analytical solution is presented to solve seven governing equations of motion using Navier’s solution. Eventually the natural frequency is scrutinized for different side length ratio, thickness ratio, inhomogeneity parameter, material length scale, and parameters of foundation numerically.
ReddyJN. Analysis of functionally graded plates. Int J Numer Meth Eng2000; 47: 663–684.
2.
PanE. Exact solution for simply-supported and multilayered magneto-electro-elastic plates. J Appl Mech2001; 68: 608–618.
3.
LibrescuLHauseT. Recent developments in the modeling and behavior of advanced sandwich constructions: a survey. Compos Struct2000; 48: 1–17.
4.
ZenkourAM. A comprehensive analysis of functionally graded sandwich plates: part 2 – buckling and free vibration. Int J Solids Struct2005; 42: 5243–5258.
5.
AagaahMRMahinfalahMJazarGN. Natural frequencies of laminated composite plates using third order shear deformation theory. Compos Struct2006; 72: 273–279.
6.
BhangaleRKGanesanN. Static analysis of simply supported functionally graded and layered magneto-electro-elastic plates. Int J Solids Struct2006; 43: 3230–3253.
7.
YangFChongACMLamDCC, et al.Couple stress based strain gradient theory for elasticity. Int J Solids Struct2002; 39: 2731–2743.
8.
YinLQianQWangL, et al.Vibration analysis of micro-scale plates based on modified couple stress theory. Acta Mech Solida Sin2010; 23: 386–393.
9.
TsiatasGC. A new Kirchhoff plate model based on a modified couple stress theory. Int J Solids Struct2009; 46: 2757–2764.
10.
ThaiHTChoiDH. Size-dependent functionally graded Kirchhoff and Mindlin plate models based on a modified couple stress theory. Compos Struct2013; 95: 142–153.
11.
ArefiM. Elastic solution of a curved beam made of functionally graded materials with different cross sections. Steel Compos Struct2015; 18: 659–672.
12.
WangYGLinWHLiuN. Large amplitude free vibration of size-dependent circular micro-plates based on the modified couple stress theory. Int J Mech Sci2013; 71: 51–57.
13.
NedriKMeicheENTounsiA. Free vibration analysis of laminated composite plates resting on elastic foundations by using a refined hyperbolic shear deformation theory. Mech Compos Mater2014; 49: 641–650.
14.
JungWYParkWTHanSC. Bending and vibration analysis of S-FGM micro-plates embedded in Pasternak elastic medium using the modified couple stress theory. Int J Mech Sci2014; 87: 150–162.
15.
MahiAAdda BediaElTounsiA. A new hyperbolic shear deformation theory for bending and free vibration analysis of isotropic, functionally graded, sandwich and laminated. Compos Plates Appl Math Model2015; 39: 2489–2508.
16.
SalehipourHNahviHShahidiAR. Exact closed-form free vibration analysis for functionally graded micro/nano plates based on modified couple stress and three-dimensional elasticity theories. Compos Struct2015; 124: 283–291.
17.
ZenkourAMArefiM. Nonlocal transient electrothermomechanical vibration and bending analysis of a functionally graded piezoelectric single-layered nanosheet rest on visco-Pasternak foundation. J Therm Stresses2017; 40: 167–184.
18.
VaeziMShirbaniMMHajnayebA. Free vibration analysis of magneto-electro-elastic micro-beams subjected to magneto-electric loads. Physica E2016; 75: 280–286.
19.
JomehzadehENooriHRSaidiAR. The size-dependent vibration analysis of micro-plates based on a modified couple stress theory. Physica E2011; 43: 877–883.
20.
ArefiMZenkourAM. Thermo-electro-mechanical bending behavior of sandwich nanoplate integrated with piezoelectric face-sheets based on trigonometric plate theory. Compos Struct2017; 162: 108–122.
21.
GuoJChenJPanE. Free vibration of three-dimensional anisotropic layered composite nanoplates based on modified couple-stress theory. Physica E2017; 87: 98–106.
22.
TahaniMAskariARMohandesY, et al.Size-dependent free vibration analysis of electrostatically pre-deformed rectangular micro-plates based on the modified couple stress theory. Int J Mech Sci2015; 94: 185–198.
23.
FarajpourAHairi YazdiMRRastgooA, et al.Nonlocal nonlinear plate model for large amplitude vibration of magneto-electro-elastic nanoplates. Compos Struct2016; 140: 323–336.
24.
BellifaHBenrahouKH, et al.Bending and free vibration analysis of functionally graded plates using a simple shear deformation theory and the concept the neutral surface position. Mech Sci Eng2016; 38: 265–275.
25.
HosseiniMJamalpoorABahremanM. Small-scale effects on the free vibrational behavior of embedded viscoelastic double-nanoplate-systems under thermal environment. Acta Astronaut2016; 129: 400–409.
26.
ŞimşekMAydınM. Size-dependent forced vibration of an imperfect functionally graded (FG) micro-plate with porosities subjected to a moving load using the modified couple stress theory. Compos Struct2017; 160: 408–421.
27.
ArefiMZenkourAM. Influence of micro-length-scale parameters and inhomogeneities on the bending, free vibration and wave propagation analyses of a FG Timoshenko’s sandwich piezoelectric micro-beam. J Sandw Struct Mater2017. DOI: 10.1177.1099636217714181.
28.
GuoJChenJPanE. Free vibration of three-dimensional anisotropic layered composite nanoplates based on modified couple-stress theory. Physica E2017; 87: 98–106.
29.
ArefiMZenkourAM. Employing the coupled stress components and surface elasticity for nonlocal solution of wave propagation of a functionally graded piezoelectric Love nanorod model. J Intel Mater Syst Struct2017. DOI: 1045389X17689930.
30.
ArefiMZenkourAM. Size-dependent vibration and bending analyses of the piezomagnetic three-layer nanobeams. Appl Phys A Mater2017; 123: 202–202.
31.
ArefiMZenkourAM. Transient analysis of a three-layer micro-beam subjected to electric potential. Int J Smart Nano Mater2017; 8: 20–40.
32.
ArefiMZenkourAM. Vibration and bending analysis of a sandwich micro-beam with two integrated piezo-magnetic face-sheets. Compos Struct2017; 159: 479–490.
33.
ArefiMZenkourAM. A simplified shear and normal deformations nonlocal theory for bending of functionally graded piezomagnetic sandwich nanobeams in magneto-thermo-electric environment. J Sandw Struct Mater2016; 18: 624–651.
34.
ArefiMZenkourAM. Employing sinusoidal shear deformation plate theory for transient analysis of three layers sandwich nanoplate integrated with piezo-magnetic face sheets. Smart Mater Struct2016; 25: 115040–115040.
35.
ThaiHTNguyenTKVoTP, et al.Analysis of functionally graded sandwich plates using a new first-order shear deformation theory. Eur J Mech A Solid2014; 45: 211–225.
36.
ReddyJN. Energy principles and variational methods in applied mechanics, New York: John Wiley & Sons, 2002.
37.
ArefiMZenkourAM. Effect of thermo-magneto-electro-mechanical fields on the bending behaviors of a three-layered nanoplate based on sinusoidal shear-deformation plate theory. J Sandw Struct Mater2017. DOI: 10.1177.1099636217697497.
38.
ArefiMZenkourAM. Nonlocal electro-thermo-mechanical analysis of a sandwich nanoplate containing a Kelvin–Voigt viscoelastic nanoplate and two piezoelectric layers. Acta Mech2017; 228: 475–493.
39.
ArefiMPourjamshidianMAraniAG. Application of nonlocal strain gradient theory and various shear deformation theories to nonlinear vibration analysis of sandwich nano-beam with FG-CNTRCs face-sheets in electro-thermal environment. Appl Phys A2017; 123: 323–323.
40.
ThaiHTKimSE. A size-dependent functionally graded Reddy plate model based on a modified couple stress theory. Compos B2013; 45: 1636–1645.
41.
BessaimAHouariMSA, et al.A new higher-order shear and normal deformation theory for the static and free vibration analysis of sandwich plates with functionally graded isotropic face sheets. J Sandwich Struct Mater2013; 15: 671–703.
42.
ArefiMZenkourAM. Wave propagation analysis of a functionally graded magneto-electro-elastic nanobeam rest on Visco-Pasternak foundation. Mech Res Commun2017; 79: 51–62.
43.
ArefiM. Analysis of wave in a functionally graded magneto-electro-elastic nano-rod using nonlocal elasticity model subjected to electric and magnetic potentials. Acta Mech2016; 227: 2529–2542.
44.
ArefiM. Surface effect and non-local elasticity in wave propagation of functionally graded piezoelectric nano-rod excited to applied voltage. Appl Math Mech (Engl Ed)2016; 37: 289–302.
45.
ArefiMZenkourAM. Free vibration, wave propagation and tension analyses of a sandwich micro/nano rod subjected to electric potential using strain gradient theory. Mater Res Express2016; 3: 115704–115704.
46.
ChenWJLiXP. A new modified couple stress theory for anisotropic elasticity and microscale laminated Kirchhoff plate model. Arch Appl Mech2014; 84: 323–341.
