This article examines the application of nonlocal strain gradient elasticity theory to wave dispersion behavior of a size-dependent functionally graded nanoplate in thermal environments. The theory contains two scale parameters corresponding to nonlocal and strain gradient effects. A quasi-3D plate theory considering shear and normal deformations is employed to present the formulation. Mori–Tanaka micromechanical model is used to describe functionally graded material properties. Hamilton’s principle is employed to obtain the governing equations of nanoplate accounting for thickness stretching effect. These equations are solved analytically to find wave frequencies and phase velocities of functionally graded nanoplate. It is indicated that wave dispersion behavior of functionally graded nanoplates is significantly affected by temperature rise, nonlocality, length scale parameter, and material composition.
TounsiAHouariMSABenyoucefS. A refined trigonometric shear deformation theory for thermoelastic bending of functionally graded sandwich plates. Aerosp Sci Technol2013; 24: 209–220.
2.
ZidiMTounsiAHouariMSAet al.Bending analysis of FGM plates under hygro-thermo-mechanical loading using a four variable refined plate theory. Aerosp Sci Technol2014; 34: 24–34.
3.
HamidiAHouariMSAMahmoudSRet al.A sinusoidal plate theory with 5-unknowns and stretching effect for thermomechanical bending of functionally graded sandwich plates. Steel Compos Struct2015; 18: 235–253.
4.
EbrahimiF. Advances in functionally graded materials and structures, Croatia: INTECH Open Access Publisher, 2016.
5.
EbrahimiF. Analytical investigation on vibrations and dynamic response of functionally graded plate integrated with piezoelectric layers in thermal environment. Mech Adv Mater Struct2013; 20: 854–870.
6.
EbrahimiFNasirzadehP. A nonlocal Timoshenko beam theory for vibration analysis of thick nanobeams using differential transform method. J Theor Appl Mech2015; 53: 1041–1052.
7.
EbrahimiFBaratiMR. Buckling analysis of nonlocal third-order shear deformable functionally graded piezoelectric nanobeams embedded in elastic medium. J Braz Soc Mech Sci Eng2016, pp. 1–16.
8.
EbrahimiFBaratiMR. Buckling analysis of smart size-dependent higher order magnetoelectro-thermo-elastic functionally graded nanosize beams. J Mech2016, pp. 1–11.
9.
EbrahimiFBaratiMR. A nonlocal higher-order refined magneto-electro-viscoelastic beam model for dynamic analysis of smart nanostructures. Int J Eng Sci2016; 107: 183–196.
10.
EbrahimiFBaratiMR. A nonlocal higher-order shear deformation beam theory for vibration analysis of size-dependent functionally graded nanobeams. Arab J Sci Eng2016; 41: 1679–1690.
11.
EbrahimiFBaratiMR. Wave propagation analysis of quasi-3D FG nanobeams in thermal environment based on nonlocal strain gradient theory. Appl Phys A2016; 122: 843–843.
12.
EbrahimiFBaratiMR. On nonlocal characteristics of curved inhomogeneous Euler–Bernoulli nanobeams under different temperature distributions. Appl Phys A2016; 122: 880–880.
13.
EbrahimiFDamanM. Investigating surface effects on thermomechanical behavior of embedded circular curved nanosize beams. J Eng2016.
14.
TornabeneFFantuzziNViolaEet al.Stress and strain recovery for functionally graded free-form and doubly-curved sandwich shells using higher-order equivalent single layer theory. Compos Struct2015; 119: 67–89.
15.
YahiaSAAtmaneHAHouariMSAet al.Wave propagation in functionally graded plates with porosities using various higher-order shear deformation plate theories. Struct Eng Mech2015; 53: 1143–1165–1143–1165.
16.
MezianeMAAAbdelazizHHTounsiA. An efficient and simple refined theory for buckling and free vibration of exponentially graded sandwich plates under various boundary conditions. J Sandwich Struct Mater2014; 16: 293–318.
17.
BellifaHBenrahouKHHadjiLet al.Bending and free vibration analysis of functionally graded plates using a simple shear deformation theory and the concept the neutral surface position. J Braz Soc Mech Sci Eng2016; 38: 265–275.
18.
Al-BasyouniKSTounsiAMahmoudSR. Size dependent bending and vibration analysis of functionally graded micro beams based on modified couple stress theory and neutral surface position. Compos Struct2015; 125: 621–630.
19.
EbrahimiFGhadiriMSalariEet al.Application of the differential transformation method for nonlocal vibration analysis of functionally graded nanobeams. J Mech Sci Technol2015; 29: 1207–1215.
20.
EbrahimiFSalariE. Nonlocal thermo-mechanical vibration analysis of functionally graded nanobeams in thermal environment. Acta Astronaut2015; 113: 29–50.
21.
EringenAC. On differential equations of nonlocal elasticity and solutions of screw dislocation and surface waves. J Appl Phys1983; 54: 4703–4710.
22.
EringenACEdelenDGB. On nonlocal elasticity. Int J Eng Sci1972; 10: 233–248.
23.
YangYZhangLLimCW. Wave propagation in double-walled carbon nanotubes on a novel analytically nonlocal Timoshenko-beam model. J Sound Vib2011; 330: 1704–1717.
24.
AssadiAFarshiB. Size-dependent longitudinal and transverse wave propagation in embedded nanotubes with consideration of surface effects. Acta Mech2011; 222: 27–39.
25.
NarendarSGuptaSSGopalakrishnanS. Wave propagation in single-walled carbon nanotube under longitudinal magnetic field using nonlocal Euler–Bernoulli beam theory. Appl Math Modell2012; 36: 4529–4538.
26.
EltaherMAKhaterMEEmamSA. A review on nonlocal elastic models for bending, buckling, vibrations, and wave propagation of nanoscale beams. Appl Math Modell2016; 40: 4109–4128.
27.
LüCFLimCWChenWQ. Size-dependent elastic behavior of FGM ultra-thin films based on generalized refined theory. Int J Solids Struct2009; 46: 1176–1185.
28.
Rahaeifard M, Kahrobaiyan MH and Ahmadian MT. Sensitivity analysis of atomic force microscope cantilever made of functionally graded materials. In: ASME 2009 international design engineering technical conferences and computers and information in engineering conference, January 2009, pp.539–544. American Society of Mechanical Engineers, San Diego, California, USA.
29.
EltaherMAEmamSAMahmoudFF. Free vibration analysis of functionally graded size-dependent nanobeams. Appl Math Comput2012; 218: 7406–7420.
30.
EbrahimiFBaratiMR. Vibration analysis of nonlocal beams made of functionally graded material in thermal environment. Eur Phys J Plus2016; 131: 279–279.
31.
EbrahimiFBaratiMR. Dynamic modeling of a thermo–piezo-electrically actuated nanosize beam subjected to a magnetic field. Appl Phys A2016; 122: 1–18.
32.
EbrahimiFBaratiMR. Vibration analysis of smart piezoelectrically actuated nanobeams subjected to magneto-electrical field in thermal environment. J Vib Contr. Epub ahead of print 2016. DOI: 1077546316646239.
33.
EbrahimiFBaratiMR. An exact solution for buckling analysis of embedded piezoelectro-magnetically actuated nanoscale beams. Adv Nano Res2016; 4: 65–84.
34.
EbrahimiFBaratiMR. Electromechanical buckling behavior of smart piezoelectrically actuated higher-order size-dependent graded nanoscale beams in thermal environment. Int J Smart Nano Mater2016; 7: 69–90.
35.
EbrahimiFBaratiMR. Magnetic field effects on buckling behavior of smart size-dependent graded nanoscale beams. Eur Phys J Plus2016; 131: 1–14.
36.
EbrahimiFBaratiMR. Small scale effects on hygro-thermo-mechanical vibration of temperature dependent nonhomogeneous nanoscale beams. Mech Adv Mater Struct2016.
37.
EbrahimiFBaratiMR. A unified formulation for dynamic analysis of nonlocal heterogeneous nanobeams in hygro-thermal environment. Appl Phys A2016; 122: 792–792.
38.
TounsiAZemriAHouariMSAet al.A mechanical response of functionally graded nanoscale beam: an assessment of a refined nonlocal shear deformation theory beam theory. Struct Eng Mech2015; 54: 693–710–693–710.
39.
BounouaraFBenrahouKHBelkorissatIet al.A nonlocal zeroth-order shear deformation theory for free vibration of functionally graded nanoscale plates resting on elastic foundation. Steel Compos Struct2016; 20: 227–249.
40.
BelkorissatIHouariMSATounsiAet al.On vibration properties of functionally graded nano-plate using a new nonlocal refined four variable model. Steel Compos Struct2015; 18: 1063–1081.
41.
BaratiMRShahverdiH. An analytical solution for thermal vibration of compositionally graded nanoplates with arbitrary boundary conditions based on physical neutral surface position. Mech Adv Mater Struct2016, pp. 1–47.
42.
BouradaMKaciAHouariMSAet al.A new simple shear and normal deformations theory for functionally graded beams. Steel Compos Struct2015; 18: 409–423.
43.
HebaliHTounsiAHouariMSAet al.New quasi-3D hyperbolic shear deformation theory for the static and free vibration analysis of functionally graded plates. J Eng Mech2014; 140: 374–383.
44.
BelabedZHouariMSATounsiAet al.An efficient and simple higher order shear and normal deformation theory for functionally graded material (FGM) plates. Compos B: Eng2014; 60: 274–283.
45.
LamDCCYangFChongACMet al.Experiments and theory in strain gradient elasticity. J Mech Phys Solids2003; 51: 1477–1508.
46.
LimCWZhangGReddyJN. A higher-order nonlocal elasticity and strain gradient theory and its applications in wave propagation. J Mech Phys Solids2015; 78: 298–313.
47.
LiLLiXHuY. Free vibration analysis of nonlocal strain gradient beams made of functionally graded material. Int J Eng Sci2016; 102: 77–92.
48.
LiLHuYLingL. Flexural wave propagation in small-scaled functionally graded beams via a nonlocal strain gradient theory. Compos Struct2015; 133: 1079–1092.
49.
EbrahimiFBaratiMR. Flexural wave propagation analysis of embedded S-FGM nanobeams under longitudinal magnetic field based on nonlocal strain gradient theory. Arab J Sci Eng2016, pp. 1–12.
50.
EbrahimiFBaratiMRDabbaghA. A nonlocal strain gradient theory for wave propagation analysis in temperature-dependent inhomogeneous nanoplates. Int J Eng Sci2016; 107: 169–182.
51.
Natarajan S, Chakraborty S, Thangavel M, et al. Size-dependent free flexural vibration behavior of functionally graded nanoplates. Computational Materials Science 2012: 65; 74–80.
