JOURNAL BROWSE
Search
Advanced SearchSearch Tips
A nonlocal zeroth-order shear deformation theory for free vibration of functionally graded nanoscale plates resting on elastic foundation
facebook(new window)  Pirnt(new window) E-mail(new window) Excel Download
 Title & Authors
A nonlocal zeroth-order shear deformation theory for free vibration of functionally graded nanoscale plates resting on elastic foundation
Bounouara, Fatima; Benrahou, Kouider Halim; Belkorissat, Ismahene; Tounsi, Abdelouahed;
 Abstract
The objective of this work is to present a zeroth-order shear deformation theory for free vibration analysis of functionally graded (FG) nanoscale plates resting on elastic foundation. The model takes into consideration the influences of small scale and the parabolic variation of the transverse shear strains across the thickness of the nanoscale plate and thus, it avoids the employ use of shear correction factors. Also, in this present theory, the effect of transverse shear deformation is included in the axial displacements by using the shear forces instead of rotational displacements as in available high order plate theories. The material properties are supposed to be graded only in the thickness direction and the effective properties for the FG nanoscale plate are calculated by considering Mori-Tanaka homogenization scheme. The equations of motion are obtained using the nonlocal differential constitutive expressions of Eringen in conjunction with the zeroth-order shear deformation theory via Hamilton`s principle. Numerical results for vibration of FG nanoscale plates resting on elastic foundations are presented and compared with the existing solutions. The influences of small scale, shear deformation, gradient index, Winkler modulus parameter and Pasternak shear modulus parameter on the vibration responses of the FG nanoscale plates are investigated.
 Keywords
nonlocal elasticity theory;nanoscale-plates;free vibration;plate theory;functionally graded materials;
 Language
English
 Cited by
1.
A novel higher order shear deformation theory based on the neutral surface concept of FGM plate under transverse load,;;;

Advances in materials Research, 2016. vol.5. 2, pp.107-120 crossref(new window)
2.
Thermal post-buckling behavior of imperfect temperature-dependent sandwich FGM plates resting on Pasternak elastic foundation,;;;;

Steel and Composite Structures, 2016. vol.22. 1, pp.91-112 crossref(new window)
3.
Thermal effects on nonlocal vibrational characteristics of nanobeams with non-ideal boundary conditions,;;

Smart Structures and Systems, 2016. vol.18. 6, pp.1087-1109 crossref(new window)
4.
A new simple three-unknown sinusoidal shear deformation theory for functionally graded plates,;;;;

Steel and Composite Structures, 2016. vol.22. 2, pp.257-276 crossref(new window)
5.
Bending analysis of FGM plates using a sinusoidal shear deformation theory,;;;

Wind and Structures, 2016. vol.23. 6, pp.543-558 crossref(new window)
6.
Forced vibration analysis of viscoelastic nanobeams embedded in an elastic medium,;

Smart Structures and Systems, 2016. vol.18. 6, pp.1125-1143 crossref(new window)
7.
A refined theory with stretching effect for the flexure analysis of laminated composite plates,;;;

Geomechanics and Engineering, 2016. vol.11. 5, pp.671-690 crossref(new window)
8.
A novel four variable refined plate theory for bending, buckling, and vibration of functionally graded plates,;;;;

Steel and Composite Structures, 2016. vol.22. 3, pp.473-495 crossref(new window)
9.
A novel four variable refined plate theory for laminated composite plates,;;;

Steel and Composite Structures, 2016. vol.22. 4, pp.713-732 crossref(new window)
10.
A new refined nonlocal beam theory accounting for effect of thickness stretching in nanoscale beams,;;;;

Advances in nano research, 2016. vol.4. 4, pp.251-264 crossref(new window)
11.
A new 3-unknowns non-polynomial plate theory for buckling and vibration of functionally graded sandwich plate,;;;

Structural Engineering and Mechanics, 2016. vol.60. 4, pp.547-565 crossref(new window)
12.
Interfacial stresses in RC beam bonded with a functionally graded material plate,;;;

Structural Engineering and Mechanics, 2016. vol.60. 4, pp.693-705 crossref(new window)
13.
An analytical approach for buckling of functionally graded plates,;;

Advances in materials Research, 2016. vol.5. 3, pp.141-169 crossref(new window)
14.
A new five unknown quasi-3D type HSDT for thermomechanical bending analysis of FGM sandwich plates,;;;;

Steel and Composite Structures, 2016. vol.22. 5, pp.975-999 crossref(new window)
15.
Thermo-mechanical postbuckling of symmetric S-FGM plates resting on Pasternak elastic foundations using hyperbolic shear deformation theory,;;;;;;

Structural Engineering and Mechanics, 2016. vol.57. 4, pp.617-639 crossref(new window)
16.
An efficient shear deformation theory for wave propagation of functionally graded material plates,;;;;;

Structural Engineering and Mechanics, 2016. vol.57. 5, pp.837-859 crossref(new window)
17.
Size-dependent mechanical behavior of functionally graded trigonometric shear deformable nanobeams including neutral surface position concept,;;;;

Steel and Composite Structures, 2016. vol.20. 5, pp.963-981 crossref(new window)
18.
Free vibration analysis of chiral double-walled carbon nanotube using non-local elasticity theory,;;;;;

Advances in nano research, 2016. vol.4. 1, pp.31-44 crossref(new window)
19.
Thermal stability analysis of solar functionally graded plates on elastic foundation using an efficient hyperbolic shear deformation theory,;;;;

Geomechanics and Engineering, 2016. vol.10. 3, pp.357-386 crossref(new window)
20.
An efficient and simple shear deformation theory for free vibration of functionally graded rectangular plates on Winkler-Pasternak elastic foundations,;;;;;;

Wind and Structures, 2016. vol.22. 3, pp.329-348 crossref(new window)
21.
Thermal stability of functionally graded sandwich plates using a simple shear deformation theory,;;;;

Structural Engineering and Mechanics, 2016. vol.58. 3, pp.397-422 crossref(new window)
22.
An analytical method for free vibration analysis of functionally graded sandwich beams,;;;;

Wind and Structures, 2016. vol.23. 1, pp.59-73 crossref(new window)
23.
Nonlocal vibration analysis of FG nano beams with different boundary conditions,;;;

Advances in nano research, 2016. vol.4. 2, pp.85-111 crossref(new window)
24.
A simple hyperbolic shear deformation theory for vibration analysis of thick functionally graded rectangular plates resting on elastic foundations,;;;

Geomechanics and Engineering, 2016. vol.11. 2, pp.289-307 crossref(new window)
25.
Buckling analysis of isotropic and orthotropic plates using a novel four variable refined plate theory,;;;

Steel and Composite Structures, 2016. vol.21. 6, pp.1287-1306 crossref(new window)
26.
Buckling of symmetrically laminated plates using nth-order shear deformation theory with curvature effects,;;;;

Steel and Composite Structures, 2016. vol.21. 6, pp.1347-1368 crossref(new window)
27.
On thermal stability of plates with functionally graded coefficient of thermal expansion,;;;;

Structural Engineering and Mechanics, 2016. vol.60. 2, pp.313-335 crossref(new window)
28.
Hygro-thermo-mechanical bending of S-FGM plates resting on variable elastic foundations using a four-variable trigonometric plate theory,;;;

Smart Structures and Systems, 2016. vol.18. 4, pp.755-786 crossref(new window)
29.
Thermal buckling behaviour of shear deformable functionally graded single/doubly curved shell panel with TD and TID properties,;;;

Advances in materials Research, 2016. vol.5. 4, pp.205-221 crossref(new window)
1.
Small-scale effects on hygro-thermo-mechanical vibration of temperature-dependent nonhomogeneous nanoscale beams, Mechanics of Advanced Materials and Structures, 2017, 24, 11, 924  crossref(new windwow)
2.
Thermal post-buckling behavior of imperfect temperature-dependent sandwich FGM plates resting on Pasternak elastic foundation, Steel and Composite Structures, 2016, 22, 1, 91  crossref(new windwow)
3.
Size-dependent thermoelastic analysis of a functionally graded nanoshell, Modern Physics Letters B, 2018, 32, 03, 1850033  crossref(new windwow)
4.
Forced vibration analysis of functionally graded porous deep beams, Composite Structures, 2018, 186, 293  crossref(new windwow)
5.
Hygro-thermo-mechanical bending of S-FGM plates resting on variable elastic foundations using a four-variable trigonometric plate theory, Smart Structures and Systems, 2016, 18, 4, 755  crossref(new windwow)
6.
Thermal effects on nonlocal vibrational characteristics of nanobeams with non-ideal boundary conditions, Smart Structures and Systems, 2016, 18, 6, 1087  crossref(new windwow)
7.
Thermo-mechanical vibration of rotating axially functionally graded nonlocal Timoshenko beam, Applied Physics A, 2017, 123, 1  crossref(new windwow)
8.
Post-buckling analysis of functionally graded nanobeams incorporating nonlocal stress and microstructure-dependent strain gradient effects, International Journal of Mechanical Sciences, 2017, 120, 159  crossref(new windwow)
9.
Buckling analysis of tapered nanobeams using nonlocal strain gradient theory and a generalized differential quadrature method, Materials Research Express, 2017, 4, 6, 065003  crossref(new windwow)
10.
A refined theory with stretching effect for the flexure analysis of laminated composite plates, Geomechanics and Engineering, 2016, 11, 5, 671  crossref(new windwow)
11.
Wave propagation analysis of size-dependent rotating inhomogeneous nanobeams based on nonlocal elasticity theory, Journal of Vibration and Control, 2017, 107754631771153  crossref(new windwow)
12.
A simple hyperbolic shear deformation theory for vibration analysis of thick functionally graded rectangular plates resting on elastic foundations, Geomechanics and Engineering, 2016, 11, 2, 289  crossref(new windwow)
13.
Nonlocal transient electrothermomechanical vibration and bending analysis of a functionally graded piezoelectric single-layered nanosheet rest on visco-Pasternak foundation, Journal of Thermal Stresses, 2017, 40, 2, 167  crossref(new windwow)
14.
Nonlocal vibration analysis of FG nano beams with different boundary conditions, Advances in nano research, 2016, 4, 2, 85  crossref(new windwow)
15.
Nonlinear electroelastic vibration analysis of NEMS consisting of double-viscoelastic nanoplates, Applied Physics A, 2016, 122, 10  crossref(new windwow)
16.
Isogeometric buckling analysis of composite variable-stiffness panels, Composite Structures, 2017, 165, 192  crossref(new windwow)
17.
Nonlocal Timoshenko Beam for Vibrations of Magnetically Affected Inclined Single-Walled Carbon Nanotubes as Nanofluidic Conveyors, Acta Physica Polonica A, 2017, 131, 6, 1439  crossref(new windwow)
18.
Free vibration of symmetric and sigmoid functionally graded nanobeams, Applied Physics A, 2016, 122, 9  crossref(new windwow)
19.
Employing sinusoidal shear deformation plate theory for transient analysis of three layers sandwich nanoplate integrated with piezo-magnetic face-sheets, Smart Materials and Structures, 2016, 25, 11, 115040  crossref(new windwow)
20.
Numerical investigation of nonlinear thermomechanical deflection of functionally graded CNT reinforced doubly curved composite shell panel under different mechanical loads, Composite Structures, 2017, 161, 287  crossref(new windwow)
21.
A nonlocal strain gradient refined beam model for buckling analysis of size-dependent shear-deformable curved FG nanobeams, Composite Structures, 2017, 159, 174  crossref(new windwow)
22.
Thermo-mechanical postbuckling of symmetric S-FGM plates resting on Pasternak elastic foundations using hyperbolic shear deformation theory, Structural Engineering and Mechanics, 2016, 57, 4, 617  crossref(new windwow)
23.
Size-dependent electro-magneto-elastic bending analyses of the shear-deformable axisymmetric functionally graded circular nanoplates, The European Physical Journal Plus, 2017, 132, 10  crossref(new windwow)
24.
Vibration analysis of viscoelastic inhomogeneous nanobeams incorporating surface and thermal effects, Applied Physics A, 2017, 123, 1  crossref(new windwow)
25.
A new simple three-unknown sinusoidal shear deformation theory for functionally graded plates, Steel and Composite Structures, 2016, 22, 2, 257  crossref(new windwow)
26.
A new refined nonlocal beam theory accounting for effect of thickness stretching in nanoscale beams, Advances in nano research, 2016, 4, 4, 251  crossref(new windwow)
27.
Large-Amplitude Vibration of Functionally Graded Doubly-Curved Panels Under Heat Conduction, AIAA Journal, 2017, 55, 12, 4376  crossref(new windwow)
28.
Buckling of symmetrically laminated plates using nth-order shear deformation theory with curvature effects, Steel and Composite Structures, 2016, 21, 6, 1347  crossref(new windwow)
29.
Free vibration analysis of chiral double-walled carbon nanotube using non-local elasticity theory, Advances in nano research, 2016, 4, 1, 31  crossref(new windwow)
30.
Free vibration investigation of nano mass sensor using differential transformation method, Applied Physics A, 2017, 123, 3  crossref(new windwow)
31.
A general higher-order nonlocal couple stress based beam model for vibration analysis of porous nanocrystalline nanobeams, Superlattices and Microstructures, 2017, 112, 64  crossref(new windwow)
32.
An efficient shear deformation theory for wave propagation of functionally graded material plates, Structural Engineering and Mechanics, 2016, 57, 5, 837  crossref(new windwow)
33.
A novel four variable refined plate theory for bending, buckling, and vibration of functionally graded plates, Steel and Composite Structures, 2016, 22, 3, 473  crossref(new windwow)
34.
Buckling analysis of functionally graded rectangular nano-plate based on nonlocal exponential shear deformation theory, International Journal of Mechanical Sciences, 2016, 113, 94  crossref(new windwow)
35.
On flexural wave propagation responses of smart FG magneto-electro-elastic nanoplates via nonlocal strain gradient theory, Composite Structures, 2017, 162, 281  crossref(new windwow)
36.
Thermal stability analysis of solar functionally graded plates on elastic foundation using an efficient hyperbolic shear deformation theory, Geomechanics and Engineering, 2016, 10, 3, 357  crossref(new windwow)
37.
Thermal stress and deformation analysis of a size-dependent curved nanobeam based on sinusoidal shear deformation theory, Alexandria Engineering Journal, 2017  crossref(new windwow)
38.
Nonlinear analysis of size-dependent and material-dependent nonlocal CNTs, Composite Structures, 2016, 153, 902  crossref(new windwow)
39.
Free vibration of anisotropic single-walled carbon nanotube based on couple stress theory for different chirality, Journal of Low Frequency Noise, Vibration and Active Control, 2017, 36, 3, 277  crossref(new windwow)
40.
A novel four variable refined plate theory for laminated composite plates, Steel and Composite Structures, 2016, 22, 4, 713  crossref(new windwow)
41.
A two-variable simplified nth-higher-order theory for free vibration behavior of laminated plates, Composite Structures, 2017, 182, 533  crossref(new windwow)
42.
Nonlocal strain gradient theory calibration using molecular dynamics simulation based on small scale vibration of nanotubes, Physica B: Condensed Matter, 2017, 514, 61  crossref(new windwow)
43.
Interfacial stresses in RC beam bonded with a functionally graded material plate, Structural Engineering and Mechanics, 2016, 60, 4, 693  crossref(new windwow)
44.
Coupled twist–bending static and dynamic behavior of a curved single-walled carbon nanotube based on nonlocal theory, Microsystem Technologies, 2017, 23, 7, 2393  crossref(new windwow)
45.
On guided wave propagation in fully clamped porous functionally graded nanoplates, Acta Astronautica, 2018, 143, 380  crossref(new windwow)
46.
Analytical modeling of dynamic behavior of piezo-thermo-electrically affected sigmoid and power-law graded nanoscale beams, Applied Physics A, 2016, 122, 9  crossref(new windwow)
47.
Investigating post-buckling of geometrically imperfect metal foam nanobeams with symmetric and asymmetric porosity distributions, Composite Structures, 2017, 182, 91  crossref(new windwow)
48.
On nonlocal characteristics of curved inhomogeneous Euler–Bernoulli nanobeams under different temperature distributions, Applied Physics A, 2016, 122, 10  crossref(new windwow)
49.
Thermal buckling behaviour of shear deformable functionally graded single/doubly curved shell panel with TD and TID properties, Advances in materials Research, 2016, 5, 4, 205  crossref(new windwow)
50.
Thermal stability of functionally graded sandwich plates using a simple shear deformation theory, Structural Engineering and Mechanics, 2016, 58, 3, 397  crossref(new windwow)
51.
A novel quasi-3D trigonometric plate theory for free vibration analysis of advanced composite plates, Composite Structures, 2018, 184, 688  crossref(new windwow)
52.
Shear buckling of single layer graphene sheets in hygrothermal environment resting on elastic foundation based on different nonlocal strain gradient theories, European Journal of Mechanics - A/Solids, 2018, 67, 200  crossref(new windwow)
53.
A study on nonlinear vibration behavior of CNT-based representative volume element, Aerospace Science and Technology, 2016, 55, 272  crossref(new windwow)
54.
Influence of various temperature distributions on critical speed and vibrational characteristics of rotating cylindrical microshells with modified lengthscale parameter, The European Physical Journal Plus, 2017, 132, 6  crossref(new windwow)
55.
Dynamic buckling of polymer–carbon nanotube–fiber multiphase nanocomposite viscoelastic laminated conical shells in hygrothermal environments, Journal of Sandwich Structures & Materials, 2017, 109963621774328  crossref(new windwow)
56.
Critical Buckling Load of Chiral Double-Walled Carbon Nanotubes Embedded in an Elastic Medium, Mechanics of Composite Materials, 2018, 53, 6, 827  crossref(new windwow)
57.
Buckling analysis of isotropic and orthotropic plates using a novel four variable refined plate theory, Steel and Composite Structures, 2016, 21, 6, 1287  crossref(new windwow)
58.
Influence of size effect on flapwise vibration behavior of rotary microbeam and its analysis through spectral meshless radial point interpolation, Applied Physics A, 2017, 123, 5  crossref(new windwow)
59.
Nonlinear bending of a two-dimensionally functionally graded beam, Composite Structures, 2018, 184, 1049  crossref(new windwow)
60.
Hygrothermal effects on vibration characteristics of viscoelastic FG nanobeams based on nonlocal strain gradient theory, Composite Structures, 2017, 159, 433  crossref(new windwow)
61.
An analytical method for free vibration analysis of functionally graded sandwich beams, Wind and Structures, 2016, 23, 1, 59  crossref(new windwow)
62.
Size-dependent nonlinear vibration of beam-type porous materials with an initial geometrical curvature, Composite Structures, 2018, 184, 1177  crossref(new windwow)
63.
Bending analysis of different material distributions of functionally graded beam, Applied Physics A, 2017, 123, 4  crossref(new windwow)
64.
Interfacial stress analysis of functionally graded beams strengthened with a bonded hygrothermal aged composite plate, Composite Interfaces, 2017, 24, 2, 149  crossref(new windwow)
65.
A new 3-unknowns non-polynomial plate theory for buckling and vibration of functionally graded sandwich plate, Structural Engineering and Mechanics, 2016, 60, 4, 547  crossref(new windwow)
66.
Wave propagation analysis of quasi-3D FG nanobeams in thermal environment based on nonlocal strain gradient theory, Applied Physics A, 2016, 122, 9  crossref(new windwow)
67.
Bending analysis of FGM plates using a sinusoidal shear deformation theory, Wind and Structures, 2016, 23, 6, 543  crossref(new windwow)
68.
Thermal buckling of embedded sandwich piezoelectric nanoplates with functionally graded core by a nonlocal second-order shear deformation theory, Proceedings of the Institution of Mechanical Engineers, Part C: Journal of Mechanical Engineering Science, 2018, 095440621875645  crossref(new windwow)
69.
Dynamic modeling of smart shear-deformable heterogeneous piezoelectric nanobeams resting on Winkler–Pasternak foundation, Applied Physics A, 2016, 122, 11  crossref(new windwow)
70.
Size-dependent thermally affected wave propagation analysis in nonlocal strain gradient functionally graded nanoplates via a quasi-3D plate theory, Proceedings of the Institution of Mechanical Engineers, Part C: Journal of Mechanical Engineering Science, 2018, 232, 1, 162  crossref(new windwow)
71.
Size-dependent vibration analysis of viscoelastic nanocrystalline silicon nanobeams with porosities based on a higher order refined beam theory, Composite Structures, 2017, 166, 256  crossref(new windwow)
72.
Vibration analysis of bonded double-FGM viscoelastic nanoplate systems based on a modified strain gradient theory incorporating surface effects, Applied Physics A, 2017, 123, 3  crossref(new windwow)
73.
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, Applied Physics A, 2017, 123, 5  crossref(new windwow)
74.
Electro-magnetic effects on nonlocal dynamic behavior of embedded piezoelectric nanoscale beams, Journal of Intelligent Material Systems and Structures, 2017, 28, 15, 2007  crossref(new windwow)
75.
Wave dispersion characteristics of axially loaded magneto-electro-elastic nanobeams, Applied Physics A, 2016, 122, 11  crossref(new windwow)
76.
On thermal stability of plates with functionally graded coefficient of thermal expansion, Structural Engineering and Mechanics, 2016, 60, 2, 313  crossref(new windwow)
77.
Buckling and free vibration of shallow curved micro/nano-beam based on strain gradient theory under thermal loading with temperature-dependent properties, Applied Physics A, 2017, 123, 1  crossref(new windwow)
78.
A novel higher order shear deformation theory based on the neutral surface concept of FGM plate under transverse load, Advances in materials Research, 2016, 5, 2, 107  crossref(new windwow)
79.
Thermal buckling optimisation of composite plates using firefly algorithm, Journal of Experimental & Theoretical Artificial Intelligence, 2017, 29, 4, 787  crossref(new windwow)
80.
Vibration of two-dimensional imperfect functionally graded (2D-FG) porous nano-/micro-beams, Computer Methods in Applied Mechanics and Engineering, 2017, 322, 615  crossref(new windwow)
81.
Non-linear thermal post-buckling analysis of FGM Timoshenko beam under non-uniform temperature rise across thickness, Engineering Science and Technology, an International Journal, 2016, 19, 3, 1608  crossref(new windwow)
82.
Electromechanical buckling behavior of smart piezoelectrically actuated higher-order size-dependent graded nanoscale beams in thermal environment, International Journal of Smart and Nano Materials, 2016, 7, 2, 69  crossref(new windwow)
83.
Thermo-mechanical analysis of FG nanobeam with attached tip mass: an exact solution, Applied Physics A, 2016, 122, 12  crossref(new windwow)
84.
Dynamic modeling of porous heterogeneous micro/nanobeams, The European Physical Journal Plus, 2017, 132, 12  crossref(new windwow)
85.
Analysis of postbuckling of graded porous GPL-reinforced beams with geometrical imperfection, Mechanics of Advanced Materials and Structures, 2018, 1  crossref(new windwow)
86.
An efficient and simple shear deformation theory for free vibration of functionally graded rectangular plates on Winkler-Pasternak elastic foundations, Wind and Structures, 2016, 22, 3, 329  crossref(new windwow)
87.
A general bi-Helmholtz nonlocal strain-gradient elasticity for wave propagation in nanoporous graded double-nanobeam systems on elastic substrate, Composite Structures, 2017, 168, 885  crossref(new windwow)
88.
Effect of Longitudinal Magnetic Field on Vibration Characteristics of Single-Walled Carbon Nanotubes in a Viscoelastic Medium, Brazilian Journal of Physics, 2017, 47, 6, 640  crossref(new windwow)
89.
Nonlocal nonlinear finite element analysis of composite plates using TSDT, Composite Structures, 2018, 185, 38  crossref(new windwow)
90.
Effects of physical boundary conditions on the transverse vibration of single-layer graphene sheets, Applied Physics A, 2016, 122, 9  crossref(new windwow)
91.
Dynamic response of a single-walled carbon nanotube under a moving harmonic load by considering modified nonlocal elasticity theory, The European Physical Journal Plus, 2018, 133, 2  crossref(new windwow)
92.
Forced vibration analysis of viscoelastic nanobeams embedded in an elastic medium, Smart Structures and Systems, 2016, 18, 6, 1125  crossref(new windwow)
93.
Bending, buckling and vibration analyses of MSGT microcomposite circular-annular sandwich plate under hydro-thermo-magneto-mechanical loadings using DQM, International Journal of Smart and Nano Materials, 2017, 1  crossref(new windwow)
94.
Buckling analysis of nonuniform nonlocal strain gradient beams using generalized differential quadrature method, Alexandria Engineering Journal, 2017  crossref(new windwow)
95.
Nonlocal electro-thermo-mechanical analysis of a sandwich nanoplate containing a Kelvin–Voigt viscoelastic nanoplate and two piezoelectric layers, Acta Mechanica, 2017, 228, 2, 475  crossref(new windwow)
 References
1.
Adda Bedia, W., Benzair, A., Semmah, A., Tounsi, A. and Mahmoud, S.R. (2015), "On the thermal buckling characteristics of armchair single-walled carbon nanotube embedded in an elastic medium based on nonlocal continuum elasticity", Brazil. J. Phys., 45(2), 225-233. crossref(new window)

2.
Aghababaei, R. and Reddy, J.N. (2009), "Nonlocal third-order shear deformation plate theory with application to bending and vibration of plates", J. Sound Vib., 326(1-2), 277-289. crossref(new window)

3.
Aissani, K., Bachir Bouiadjra, M., Ahouel, M. and Tounsi, A. (2015), "A new nonlocal hyperbolic shear deformation theory for nanobeams embedded in an elastic medium", Struct. Eng. Mech., Int. J., 55(4), 743-762. crossref(new window)

4.
Ait Amar Meziane, M., Abdelaziz, H.H. and Tounsi, A. (2014), "An efficient and simple refined theory for buckling and free vibration of exponentially graded sandwich plates under various boundary conditions", J. Sandw. Struct. Mater., 16(3), 293-318. crossref(new window)

5.
Ait Atmane, H., Tounsi, A., Bernard, F. and Mahmoud, S.R. (2015), "A computational shear displacement model for vibrational analysis of functionally graded beams with porosities", Steel Compos. Struct., Int. J., 19(2), 369-384.

6.
Ait Yahia, S., Ait Atmane, H., Houari, M.S.A. and Tounsi, A. (2015), "Wave propagation in functionally graded plates with porosities using various higher-order shear deformation plate theories", Struct. Eng. Mech., Int. J., 53(6), 1143-1165. crossref(new window)

7.
Al-Basyouni, K.S., Tounsi, A. and Mahmoud, S.R. (2015), "Size dependent bending and vibration analysis of functionally graded micro beams based on modified couple stress theory and neutral surface position", Compos. Struct., 125, 621-630. crossref(new window)

8.
Amara, K., Tounsi, A., Mechab, I. and Adda-Bedia, E.A. (2010), "Nonlocal elasticity effect on column buckling of multiwalled carbon nanotubes under temperature field", Appl. Math. Model., 34(12), 3933-3942. crossref(new window)

9.
Ansari, R., Ashrafi, M.A., Pourashraf, T. and Sahmani, S. (2015), "Vibration and buckling characteristics of functionally graded nanoplates subjected to thermal loading based on surface elasticity theory", Acta Astronautica, 109, 42-51. crossref(new window)

10.
Belabed, Z., Houari, M.S.A., Tounsi, A., Mahmoud, S.R. and Anwar Beg, O. (2014), "An efficient and simple higher order shear and normal deformation theory for functionally graded material (FGM) plates", Composites: Part B, 60, 274-283. crossref(new window)

11.
Belkorissat, I., Houari, M.S.A., Tounsi, A., Adda Bedia, E.A. and Mahmoud, S.R. (2015), "On vibration properties of functionally graded nano-plate using a new nonlocal refined four variable model", Steel Compos. Struct., Int. J., 18(4), 1063-1081. crossref(new window)

12.
Benachour, A., Daouadji, H.T., Ait Atmane, H., Tounsi, A. and Meftah, S.A. (2011), "A four variable refined plate theory for free vibrations of functionally graded plates with arbitrary gradient", Composites Part B, 42(6), 1386-1394. crossref(new window)

13.
Benguediab, S., Tounsi, A., Zidour, M. and Semmah, A. (2014), "Chirality and scale rffects on mechanical buckling properties of zigzag double-walled carbon nanotubes", Composites Part B, 57, 21-24. crossref(new window)

14.
Bennai, R., Ait Atmane, H. and Tounsi, A. (2015), "A new higher-order shear and normal deformation theory for functionally graded sandwich beams", Steel Compos. Struct., Int. J., 19(3), 521-546. crossref(new window)

15.
Benzair, A., Tounsi, A., Besseghier, A., Heireche, H., Moulay, N. and Boumia, L. (2008), "The thermal effect on vibration of single-walled carbon nanotubes using nonlocal Timoshenko beam theory", J. Phys. D: Appl. Phys., 41(22), 225404. crossref(new window)

16.
Berrabah, H.M., Tounsi, A., Semmah, A. and Adda Bedia, E.A. (2013), "Comparison of various refined nonlocal beam theories for bending, vibration and buckling analysis of nanobeams", Struct. Eng. Mech., Int. J., 48(3), 351-365. crossref(new window)

17.
Besseghier, A., Heireche, H., Bousahla, A.A., Tounsi, A. and Benzair, A. (2015), "Nonlinear vibration properties of a zigzag single-walled carbon nanotube embedded in a polymer matrix", Adv. Nano Res., Int. J., 3(1), 29-37. crossref(new window)

18.
Bouchafa, A., Bachir Bouiadjra, M., Houari, M.S.A. and Tounsi, A. (2015), "Thermal stresses and deflections of functionally graded sandwich plates using a new refined hyperbolic shear deformation theory", Steel Compos. Struct., Int. J., 18(6), 1493-1515. crossref(new window)

19.
Bouderba, B., Houari, M.S.A. and Tounsi, A. (2013), "Thermomechanical bending response of FGM thick plates resting on Winkler-Pasternak elastic foundations", Steel Compos. Struct., Int. J., 14(1), 85-104. crossref(new window)

20.
Bourada, M., Tounsi, A., Houari, M.S.A. and Adda Bedia, E.A. (2012), "A new four-variable refined plate theory for thermal buckling analysis of functionally graded sandwich plates", J. Sandw. Struct. Mater., 14(1), 5-33. crossref(new window)

21.
Bourada, M., Kaci, A., Houari, M.S.A. and Tounsi, A. (2015), "A new simple shear and normal deformations theory for functionally graded beams", Steel Compos. Struct., Int. J., 18(2), 409-423. crossref(new window)

22.
Bousahla, A.A., Houari, M.S.A., Tounsi, A. and Adda Bedia, E.A. (2014), "A novel higher order shear and normal deformation theory based on neutral surface position for bending analysis of advanced composite plates", Int. J. Computat. Method., 11(6), 1350082. crossref(new window)

23.
Bunch, J., van der Zande, A.M. and Verbridge, S.S. (2007), "Electromechanical resonators from grapheme sheets", Science, 315(5811), 490-493. crossref(new window)

24.
Cheng, Z.-Q. and Batra, R.C. (2000), "Three-dimensional thermoelastic deformations of a functionally graded elliptic plate", Composites: Part B, 31(2), 97-106.

25.
Chakraverty, S. and Pradhan, K.K. (2014), "Free vibration of exponential functionally graded rectangular plates in thermal environment with general boundary conditions", Aerosp. Sci. Technol., 36, 132-156. crossref(new window)

26.
Draiche, K., Tounsi, A. and Khalfi, Y. (2014), "A trigonometric four variable plate theory for free vibration of rectangular composite plates with patch mass", Steel Compos. Struct., Int. J., 17(1), 69-81. crossref(new window)

27.
El Meiche, N., Tounsi, A., Ziane, N., Mechab, I. and Adda Bedia, E.A. (2011), "A new hyperbolic shear deformation theory for buckling and vibration of functionally graded sandwich plate", Int. J. Mech. Sci., 53(4), 237-247. crossref(new window)

28.
Eringen, A.C. (1972), "Nonlocal polar elastic continua", Int. J. Eng. Sci., 10(1), 1-16. crossref(new window)

29.
Eringen, A.C. (1983), "On differential equations of nonlocal elasticity and solutions of screw dislocation and surface waves", J. Appl. Phys., 54(9), 4703-4710. crossref(new window)

30.
Fekrar, A., Houari, M.S.A., Tounsi, A. and Mahmoud, S.R. (2014), "A new five-unknown refined theory based on neutral surface position for bending analysis of exponential graded plates", Meccanica, 49(4), 795-810. crossref(new window)

31.
Fu, Y., Du, H. and Zhang, S. (2003), "Functionally graded TiN/TiNi shape memory alloy films", Mater. Lett., 57(20), 2995-2999. crossref(new window)

32.
Hamidi, A., Houari, M.S.A., Mahmoud, S.R. and Tounsi, A. (2015), "A sinusoidal plate theory with 5-unknowns and stretching effect for thermomechanical bending of functionally graded sandwich plates", Steel Compos. Struct., Int. J., 18(1), 235-253. crossref(new window)

33.
Hashemi, S.H. and Samaei, A.T. (2011), "Buckling analysis of micro/nanoscale plates via nonlocal elasticity theory", Physica E: Low-dimension. Syst. Nanostruct., 43(7), 1400-1404. crossref(new window)

34.
Hebali, H., Tounsi, A., Houari, M.S.A., Bessaim, A. and Adda Bedia, E.A. (2014), "New quasi-3D hyperbolic shear deformation theory for the static and free vibration analysis of functionally graded plates", J. Eng. Mech. (ASCE), 140(2), 374-383. crossref(new window)

35.
Heireche, H., Tounsi, A., Benzair, A., Maachou, M. and Adda Bedia, E.A. (2008a), "Sound wave propagation in single-walled carbon nanotubes using nonlocal elasticity", Physica E., 40(8), 2791-2799. crossref(new window)

36.
Heireche, H., Tounsi, A. and Benzair, A. (2008b), "Scale Effect on wave propagation of double-walled carbon nanotubes with initial axial loading", Nanotechnology, 19(18), 185703. crossref(new window)

37.
Hosseini-Hashemi, S., Bedroud, M. and Nazemnezhad, R. (2013), "An exact analytical solution for free vibration of functionally graded circular/annular Mindlin nanoplates via nonlocal elasticity", Compos. Struct., 103, 108-118. crossref(new window)

38.
Jung, W.-Y. and Han, S.-C. (2013), "Analysis of sigmoid functionally graded material (S-FGM) nanoscale plates using the nonlocal elasticity theory", Math. Probl. Eng. DOI: http://dx.doi.org/10.1155/2013/476131 crossref(new window)

39.
Katsnelson, M.I. and Novoselov, K.S. (2007), "Graphene: New bridge between condensed matter physics and quantum electrodynamics", Solid State Commun., 143(1-2), 3-13. crossref(new window)

40.
Khalfi, Y., Houari, M.S.A. and Tounsi, A. (2014), "A refined and simple shear deformation theory for thermal buckling of solar functionally graded plates on elastic foundation", Int. J. Computat. Method., 11(5), 135007.

41.
Larbi Chaht, F., Kaci, A., Houari, M.S.A., Tounsi, A., Anwar Beg, O. and Mahmoud, S.R. (2015), "Bending and buckling analyses of functionally graded material (FGM) size-dependent nanoscale beams including the thickness stretching effect", Steel Compos. Struct., Int. J., 18(2), 425-442. crossref(new window)

42.
Lee, Z., Ophus, C., Fischer, L., Nelson-Fitzpatrick, N., Westra, K., Evoy, S., Radmilovic, V., Dahmen, U. and Mitlin, D. (2006), "Metallic NEMS components fabricated from nanocomposite Al-Mo films", Nanotechnology, 17(12), 3063. crossref(new window)

43.
Liang, X., Wang, Z., Wang, L. and Liu, G. (2014), "Semi-analytical solution for three-dimensional transient response of functionally graded annular plate on a two parameter viscoelastic foundation", J. Sound Vib., 333(12), 2649-2663. crossref(new window)

44.
Lu, P., Zhang, P.Q., Lee, H.P., Wang, C.M. and Reddy, J.N. (2008), "Non-local elastic plate theories", Proceedings of the Royal Society A., 463(2088), 3225-3240.

45.
Lu, C., Wu, D. and Chen, W. (2011), "Nonlinear responses of nanoscale FGM films including the effects of surface energies", IEEE Transactions on Nanotechnology, 10, 1321-1327. crossref(new window)

46.
Lun, F., Zhang, P., Gao, F. and Jia, H. (2006), "Design and fabrication of micro-optomechanical vibration sensor", Microfabrication Technology, 120(1), 61-64.

47.
Mahi, A., Adda Bedia, E.A. and Tounsi, A. (2015), "A new hyperbolic shear deformation theory for bending and free vibration analysis of isotropic, functionally graded, sandwich and laminated composite plates", Appl. Math. Model., 39(9), 2489-2508. crossref(new window)

48.
Moser, Y. and Gijs, M.A. (2007), "Miniaturized flexible temperature sensor", J. Microelectromech. Syst., 16(6), 1349-1354. crossref(new window)

49.
Nami, M.R. and Janghorban, M. (2013), "Static analysis of rectangular nanoplates using trigonometric shear deformation theory based on nonlocal elasticity theory", Beilstein J. Nanotech., 4(1), 968-973. crossref(new window)

50.
Natarajan, S., Baiz, P., Ganapathi, M., Kerfriden, P. and Bordas, S. (2011), "Linear free flexural vibration of cracked functionally graded plates in thermal environment", Comput. Struct., 89(15-16), 1535-1546. crossref(new window)

51.
Natarajan, S., Chakraborty, S., Thangavel, M., Bordas, S. and Rabczuk, T. (2012), "Size-dependent free flexural vibration behavior of functionally graded nanoplates", Computat. Mater. Sci., 65, 74-80. crossref(new window)

52.
Nedri, K., El Meiche, N. and Tounsi, A. (2014), "Free vibration analysis of laminated composite plates resting on elastic foundations by using a refined hyperbolic shear deformation theory" Mech. Compos. Mater., 49(6), 641-650. crossref(new window)

53.
Ould Larbi, L., Kaci, A., Houari, M.S.A. and Tounsi, A. (2013), "An efficient shear deformation beam theory based on neutral surface position for bending and free vibration of functionally graded beams", Mech. Based Des. Struct. Mach., 41(4), 421-433. crossref(new window)

54.
Phan-Dao, H., Nguyen-Xuan, H., Thai-Hoang, C., Nguyen-Thoi, T. and Rabczuk, T. (2013), "An edgebased smoothed finite element method for analysis of laminated composite plates", Int. J. Computat. Method., 10(1), 1340005. crossref(new window)

55.
Pradhan, S.C. (2009), "Buckling of single layer graphene sheet based on nonlocal elasticity and higher order shear deformation theory", Phys. Lett. A, 373(45), 4182-4188. crossref(new window)

56.
Pradhan, S.C. and Kumar, A. (2010), "Vibration analysis of orthotropic graphene sheets embedded in Pasternak elastic medium using nonlocal elasticity theory and differential quadrature method", Comput. Mater. Sci., 50(1), 239-245. crossref(new window)

57.
Pradhan, S.C. and Phadikar, J.K. (2009), "Small scale effect on vibration of embedded multilayered graphene sheets based on nonlocal continuum models", Phys. Lett. A, 373(11), 1062-1069. crossref(new window)

58.
Qian, L., Batra, R. and Chen, L. (2004), "Static and dynamic deformations of thick functionally graded elastic plates by using higher-order shear and normal deformable plate theory and meshless local Petrov-Galerkin method", Compos. Part B: Eng., 35(6-8), 685-697. crossref(new window)

59.
Rahaeifard, M., Kahrobaiyan, M. and Ahmadian, M. (2009), "Sensitivity analysis of atomic force microscope cantilever made of functionally graded materials", Proceedings of the 3rd International Conference on Micro-and Nanosystems, San Diego, CA, USA, August-September.

60.
Ray, M.C. (2003), "Zeroth-order shear deformation theory for laminated composite plates", J. Appl. Mech., 70(3), 374-380. crossref(new window)

61.
Reddy, J.N. (2007), "Nonlocal theories for bending, buckling and vibration of beams", Int. J. Eng. Sci., 45(2-8), 288-307. crossref(new window)

62.
Reddy, J.N. and Pang, S.D. (2008), "Nonlocal continuum theories of beams for the analysis of carbon nanotubes", J. Appl. Phys., 103(2), 023511. crossref(new window)

63.
Samaei, A.T., Abbasion, S. and Mirsayar, M.M. (2011), "Buckling analysis of a single-layer grapheme sheet embedded in an elastic medium based on nonlocal Mindlin plate theory", Mech. Res. Commun., 38(7), 481-485. crossref(new window)

64.
Samaei, A.T., Aliha, M.R.M. and Mirsayar, M.M. (2015), "Frequency analysis of a graphene sheet embedded in an elastic medium with consideration of small scale", Mater. Phys. Mech., 22, 125-135.

65.
Sobhy, M. (2014), "Generalized two-variable plate theory for multi-layered graphene sheets with arbitrary boundary conditions", Acta Mechanica, 225(9), 2521-2538. crossref(new window)

66.
Stolken, J. and Evans, A. (1998), "A microbend test method for measuring the plasticity length scale", Acta Materialia, 46(14), 5109-5115. crossref(new window)

67.
Thai, C.H., Nguyen-Xuan, H., Nguyen-Thanh, N., Le, T.H., Nguyen-Thoi, T. and Rabczuk, T. (2012), "Static, free vibration and buckling analysis of laminated composite Reissner-Mindlin plates using NURBS-based isogeometric approach", Int. J. Numer. Method. Eng., 91(6), 571-603. crossref(new window)

68.
Tounsi, A., Semmah, A. and Bousahla, A.A. (2013a),"Thermal buckling behavior of nanobeam usin an efficient higher-order nonlocal beam theory", J. Nanomech. Micromech. (ASCE), 3(3), 37-42. crossref(new window)

69.
Tounsi, A, Benguediab, S., Adda Bedia, E.A., Semmah, A. and Zidour, M. (2013b), "Nonlocal effects on thermal buckling properties of double-walled carbon nanotubes", Adv. Nano Res., Int. J., 1(1), 1-11. crossref(new window)

70.
Tounsi, A., Houari, M.S.A., Benyoucef, S. and Adda Bedia, E.A. (2013c), "A refined trigonometric shear deformation theory for thermoelastic bending of functionally graded sandwich plates", Aerosp. Sci. Technol., 24(1), 209-220. crossref(new window)

71.
Valizadeh, N., Natarajan, S., Gonzalez-Estrada, O.A., Rabczuk, T., Bui, T.Q. and Bordas, S.P.A. (2013), "NURBS-based finite element analysis of functionally graded plates: static bending, vibration, buckling and flutter", Compos. Struct., 99, 309-326. crossref(new window)

72.
Witvrouw, A. and Mehta, A. (2005), "The use of functionally graded poly-SiGe layers for MEMS applications", In: Materials Science Forum, Volume 492-493, pp. 255-260. crossref(new window)

73.
Yaghoobi, H. and Torabi, M. (2013), "Exact solution for thermal buckling of functionally graded plates resting on elastic foundations with various boundary conditions", J. Therm. Stresses, 36(9), 869-894. crossref(new window)

74.
Zemri, A., Houari, M.S.A., Bousahla, A.A. and Tounsi, A. (2015), "A mechanical response of functionally graded nanoscale beam: an assessment of a refined nonlocal shear deformation theory beam theory", Struct. Eng. Mech., Int. J., 54(4), 693-710. crossref(new window)

75.
Zhuang, X., Huang, R., Zhu, H., Askes, H. and Mathisen, K. (2013), "A new and simple locking-free triangular thick plate element using independent shear degrees of freedom", Finite Elem. Anal. Des., 75, 1-7. crossref(new window)

76.
Ziane, N., Meftah, S.A., Ruta, G., Tounsi, A. and Adda Bedia, E.A. (2015), "Investigation of the Instability of FGM box beams", Struct. Eng. Mech., Int. J., 54(3), 579-595. crossref(new window)

77.
Zidi, M., Tounsi, A., Houari, M.S.A., Adda Bedia, E.A. and Anwar Beg, O. (2014), "Bending analysis of FGM plates under hygro-thermo-mechanical loading using a four variable refined plate theory", Aerosp. Sci. Technol., 34, 24-34. crossref(new window)

78.
Zidour, M., Daouadji, T.H., Benrahou, K.H., Tounsi, A., Adda Bedia, E.A. and Hadji, L. (2014), "Buckling analysis of chiral single-walled carbon nanotubes by using the nonlocal Timoshenko beam theory", Mech. Compos. Mater., 50(1), 95-104. crossref(new window)