JOURNAL BROWSE
Search
Advanced SearchSearch Tips
A nonlocal quasi-3D trigonometric plate model for free vibration behaviour of micro/nanoscale plates
facebook(new window)  Pirnt(new window) E-mail(new window) Excel Download
 Title & Authors
A nonlocal quasi-3D trigonometric plate model for free vibration behaviour of micro/nanoscale plates
Bessaim, Aicha; Houari, Mohammed Sid Ahmed; Bernard, Fabrice; Tounsi, Abdelouahed;
 Abstract
In this work, a nonlocal quasi-3D trigonometric plate theory for micro/nanoscale plates is proposed. In order to introduce the size influences, the Eringen`s nonlocal elasticity theory is utilized. In addition, the theory considers both shear deformation and thickness stretching effects by a trigonometric variation of all displacements within the thickness, and respects the stress-free boundary conditions on the top and bottom surfaces of the plate without considering the shear correction factor. The advantage of this theory is that, in addition to considering the small scale and thickness stretching effects (), the displacement field is modelled with only 5 unknowns as the first order shear deformation theory (FSDT). Analytical solutions for vibration of simply supported micro/nanoscale plates are illustrated, and the computed results are compared with the available solutions in the literature and finite element model using ABAQUS software package. The influences of the nonlocal parameter, shear deformation and thickness stretching on the vibration behaviors of the micro/nanoscale plates are examined.
 Keywords
trigonometric shear deformation theory;nanoplates;nonlocal elasticity theory;navier solution;stretching effect;vibration;
 Language
English
 Cited by
1.
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)
2.
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)
1.
Size-dependent mechanical behavior of functionally graded trigonometric shear deformable nanobeams including neutral surface position concept, Steel and Composite Structures, 2016, 20, 5, 963  crossref(new windwow)
2.
Damping vibration analysis of smart piezoelectric polymeric nanoplates on viscoelastic substrate based on nonlocal strain gradient theory, Smart Materials and Structures, 2017, 26, 6, 065018  crossref(new windwow)
3.
Damping vibration analysis of graphene sheets on viscoelastic medium incorporating hygro-thermal effects employing nonlocal strain gradient theory, Composite Structures, 2018, 185, 241  crossref(new windwow)
4.
A review of continuum mechanics models for size-dependent analysis of beams and plates, Composite Structures, 2017, 177, 196  crossref(new windwow)
5.
Damping vibration behavior of visco-elastically coupled double-layered graphene sheets based on nonlocal strain gradient theory, Microsystem Technologies, 2017  crossref(new windwow)
6.
Vibration analysis of nonlocal strain gradient embedded single-layer graphene sheets under nonuniform in-plane loads, Journal of Vibration and Control, 2017, 107754631773408  crossref(new windwow)
7.
A novel quasi-3D trigonometric plate theory for free vibration analysis of advanced composite plates, Composite Structures, 2018, 184, 688  crossref(new windwow)
8.
A Nonlocal Strain Gradient Mass Sensor Based on Vibrating Hygro-Thermally Affected Graphene Nanosheets, Iranian Journal of Science and Technology, Transactions of Mechanical Engineering, 2017  crossref(new windwow)
9.
Thermal stability of functionally graded sandwich plates using a simple shear deformation theory, Structural Engineering and Mechanics, 2016, 58, 3, 397  crossref(new windwow)
 References
1.
Aagesen, M. and Sorensen, C.B. (2008), "Nanoplates and their suitability for use as solar cells", Proceedings of Clean Technology, 109-112.

2.
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", Braz. J. Phys., 45, 225-233. crossref(new window)

3.
Aghababaei, R. and Reddy, J.N. (2009), "Non-local third-order shear deformation plate theory with application to bending and vibration of plates", J. Sound Vib., 326, 227-289.

4.
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., 55(4), 743-762. crossref(new window)

5.
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)

6.
Aksencer, T. and Aydogdu, M. (2011), "Levy type solution for vibration and buckling of nanoplates using nonlocal elasticity theory", Physica E, 43(4), 954959.

7.
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., 53(6), 1143-1165. crossref(new window)

8.
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)

9.
Alibeigloo, A. (2011), "Free vibration analysis of nano-plate using three-dimensional theory of elasticity", Acta Mechanica, 222(1-2), 149-159. crossref(new window)

10.
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, 3933-3942. crossref(new window)

11.
Babaei, H. and Shahidi, A.R. (2010), "Small-scale effects on the buckling of quadrilateral nanoplates based on nonlocal elasticity theory using the Galerkin method", Arch. Appl. Mech., 81(8), 1051-1062.

12.
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", Compos. Part B. 60, 274-283. crossref(new window)

13.
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. 18(4), 1063-1081. crossref(new window)

14.
Benachour, A., Daouadji, H.I., 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", Compos. Part B. 42, 1386-1394. crossref(new window)

15.
Benguediab, S., Tounsi, A., Zidour, M. and Semmah, A. (2014), "Chirality and scale effects on mechanical buckling properties of zigzag double-walled carbon nanotubes", Compos. Part B. 57, 21-24. crossref(new window)

16.
Bennai, R., Ait Atmane, H. and Tounsi, A. (2015), "Anew higher-order shear and normal deformation theory for functionally graded sandwich beams", Steel Compos. Struct., 19(3), 521-546. crossref(new window)

17.
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, 225404. crossref(new window)

18.
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., 48(3), 351-365. crossref(new window)

19.
Bessaim, A., Houari, M.S.A., Tounsi, A., Mahmoud, S.R., and Adda Bedia, E.A. (2013), "Anew higher-order shear and normal deformation theory for the static and free vibration analysis of sandwich plates with functionally graded isotropic face sheets", J. Sandw. Struct. Mater., 15(6), 671-703. crossref(new window)

20.
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. Nono Res. 3(1), 29-37. crossref(new window)

21.
Bourada, M., Kaci, A., Houari, M.S.A. and Tounsi, A. (2015), "Anew simple shear and normal deformations theory for functionally graded beams", Steel Compos. Struct., 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. Comput. Meth., 11(6), 1350082. crossref(new window)

23.
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. 17(1), 69-81. crossref(new window)

24.
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, 237-247. crossref(new window)

25.
Eringen, A.C. and Edelen, D.G.B. (1972), "On nonlocal elasticity", Int J. Eng Sci., 10, 233-48. crossref(new window)

26.
Eringen, A.C. (1983), "On differential equations of nonlocal elasticity and solutions of screw dislocation and surface waves", J. Appl. Phys., 54, 4703-10. crossref(new window)

27.
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, 795-810. crossref(new window)

28.
Fritz, J., Baller, M.K., Lang, H.P., Rothuizen, H., Vettiger, P., Meyer, E., Guntherodt, H.J., Gerber, C. and and Gimzewski, J.K. (2000), "Translating biomolecular recognition into nanomechanics", Science, 288(5464),316-318. crossref(new window)

29.
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., 18(1), 235-253. crossref(new window)

30.
Hebali, H., Tounsi, A., Houari, M.S.A., Bessaim, A. and Adda Bedia, E.A. (2014), "A new quasi-3D hyperbolic shear deformation theory for the static and free vibration analysis of functionally graded plates", ASCE J. Eng. Mech., 140, 374-383. crossref(new window)

31.
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, 2791-2799. crossref(new window)

32.
Houari, M.S.A., Tounsi, A. and Anwar Beg, O. (2013), "Thermoelastic bending analysis of functionally graded sandwich plates using a new higher order shear and normal deformation theory", Int. J. Mech. Sci., 76, 102-111. crossref(new window)

33.
Huang, D.W. (2008), "Size-dependent response of ultra-thin films with surface effects", Int. J. Solid Struct., 45(2), 568-579. crossref(new window)

34.
Janghorban, M. and Zare, A. (2011), "Free vibration analysis of functionally graded carbon nanotubes with variable thickness by differential quadrature method", Physica E, 43, 1602-1604. crossref(new window)

35.
Janghorban, M. (2012), "Two different types of differential quadrature methods for static analysis of microbeams based on nonlocal thermal elasticity theory in thermal environment", Arch. Appl. Mech., 82, 669-675. crossref(new window)

36.
Karimi, M., Haddad, H.A., Shahidi, A.R. (2015), "Combining surface effects and non local two variable refined plate theories on the shear/biaxial buckling and vibration of silver nanoplates", Micro Nano Lett., 10(6),276-281. crossref(new window)

37.
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. Comput. Meth., 11(5), 135007.

38.
Kiani, K. (2011a), "Small-scale effect on the vibration of thin nanoplates subjected to a moving nanoparticle via nonlocal continuum theory", J. Sound Vib., 330(20), 4896-4914. crossref(new window)

39.
Kiani, K. (2011b), "Nonlocal continuum-based modeling of a nanoplate subjected to a moving nanoparticle. Part I: theoretical formulations", Physica E, 44(1), 229-248. crossref(new window)

40.
Kiani, K. (2011c), "Nonlocal continuum-based modeling of a nanoplate subjected to a moving nanoparticle. Part II: parametric studies", Physica E, 44(1), 249-269. crossref(new window)

41.
Kiani, K. (2013a), "Free vibration of conducting nanoplates exposed to unidirectional in-plane magnetic fields using nonlocal shear deformable plate theories", Physica E: Low-dimens. Syst. Nanostruct., 57, 179-192.

42.
Kiani, K. (2013b), "Vibrations of biaxially tensioned embedded nanoplates for nanoparticle delivery", Indi. J. Sci. Tech., 6(7), 48944902.

43.
Kiani, K. (2015), "Free vibrations of elastically embedded stocky single-walled carbon nanotubes acted upon by a longitudinally varying magnetic field", Meccanica. (accepted paper)

44.
Kitipornchai, S., He, X.Q. and Liew K.M. (2005), "Continuum model for the vibration of multilayered graphene sheets", Phys. Rev. B, 72, 075443. crossref(new window)

45.
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., 18(2), 425-442. crossref(new window)

46.
Lee, W.H., Han, S.C. and Park, W.T. (2012), "Nonlocal elasticity theory for bending and free vibration analysis of nano plates", J. Korea Acad. Indus. Coop. Soc., 13(7), 3207-3215.

47.
Liew, K.M., Hung. K.C. and Lim, M.K. (1993), "A continuum three-dimensional vibration analysis of thick rectangular plates", Int. J. Solid Struct., 30(24), 3357-3379. crossref(new window)

48.
Liu, C. and Rajapakse, R.K.N.D. (2010), "Continuum models incorporating surface energy for static and dynamic response of nanoscale beams", IEEE Tran. Nanotechnol., 9(4), 422-431. crossref(new window)

49.
Lu, P., He. L.H., Lee, H.P. and Lu, C. (2006), "Thin plate theory including surface effects", Int. J. Solid Struct., 43(16), 4631-4647. crossref(new window)

50.
Ma, Q. and Clarke, D.R. (1995), "Size dependent hardness of silver single crystals", J. Mater. Res., 10, 853-863. crossref(new window)

51.
Ma, M., Tu, J.P., Yuan, Y.F., Wang, X.L., Li, K.F., Mao, F. and Zeng, Z.Y. (2008), "Electrochemical performance of ZnO nanoplates as anode materials for Ni/Zn secondary batteries", J. Power Sour., 179, 395-400. crossref(new window)

52.
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. 2489-2508. crossref(new window)

53.
Malekzadeh, P., Setoodeh, A.R. and Beni, A.A. (2011), "Small scale effect on the free vibration of orthotropic arbitrary straight straightsided quadrilateral nanoplates", Compos. Struct., 93(7), 16311639. crossref(new window)

54.
Mohammadi, M., Ghayour, M. and Farajpour, A. (2013), "Free transverse vibration analysis of circular and annular grapheme sheets with various boundary conditions using the nonlocal continuum plate model", Compos. Part E: Eng., 45(1), 32-42. crossref(new window)

55.
Murmu, T., and Pradhan, S.C. (2009), "Vibration analysis of nanoplates under uniaxial prestressed conditions via nonlocal elasticity", J. Appl. Phys., 106, 104301. crossref(new window)

56.
Murmu, T. and Pradhan, S.C. (2010), "Small scale effect on the free in-plane vibration of nanoplates by nonlocal continuum model", Physica E, 41(8), 1628-1633.

57.
Murmu, T. and Adhikari, S. (2011), "Nonlocal vibration of bonded double-nanoplate-systems", Compos. Part E: Eng., 42(7), 1901-1911. crossref(new window)

58.
Nami, M.R. and Janghorban, M. (2013), "Static analysis of rectangular nanoplates using trigonometric shear deformation theory based on nonlocal elasticity theory", Beil. J. Nanotech., 4, 968-973. crossref(new window)

59.
Nami, M.R. and Janghorban, M. (2014), "Resonance behavior of FG rectangular micro/nano plate based on nonlocal elasticity theory and strain gradient theory with one gradient constant", Compos. Struct., 111, 349-353. crossref(new window)

60.
Nami, M.R. and Janghorban, M. (2015), "Free vibration of functionally graded size dependent nanoplates based on second order shear deformation theory using nonlocal elasticity theory", Iran. J. Sci. Tech., 39, 15-28.

61.
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. Bas. Des. Struct. Mach., 41, 421-433. 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,. 023511. crossref(new window)

63.
Phadikar, J.K. and Pradhan, S.C. (2010), "Variational formulation and finite element analysis for nonlocal elastic nanobeams and nanoplates", Computat. Mater. Sci., 49(3), 492-499. crossref(new window)

64.
Pradhan, S.C. and Murmu, I. (2009), "Small scale effect on the buckling of single-layered graphene sheets under biaxial compression via nonlocal continuum mechanics", Comput. Mater. Sci., 47, 268-274. crossref(new window)

65.
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.

66.
Sheng, H.Y., Li. H.P., Lu, P. and Xu, H.Y. (2010), "Free vibration analysis for micro-structures used in MEMS considering surface effects", J. Sound Vib., 329(2), 236-246. crossref(new window)

67.
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)

68.
Tounsi, A., Benguediab, S., Adda Bedia, E.A., Semmah, A. and Zidour, M. (2013a), "Nonlocal effects on thermal buckling properties of double-walled carbon nanotubes", Adv. Nano Res., 1(1), 1-11. crossref(new window)

69.
Tounsi, A., Benguediab, S., Houari, M.S.A. and Semmah, A. (2013b), "A new nonlocal beam theory with thickness stretching effect for nanobeams", Int. J. Nanosci., 12, 1350025. crossref(new window)

70.
Tounsi, A., Semmah, A. and Bousahla, A.A. (2013c), "Thermal buckling behavior of nanobeams using an efficient higher-order nonlocal beam theory", ASCE J. Nanomech. Micromech., 3, 37-42. crossref(new window)

71.
Tounsi, A., Houari, M.S.A., Benyoucef, S. and Adda Bedia, E.A. (2013d), A refined trigonometric shear deformation theory for thermoelastic bending of functionally graded sandwich plates", Aerosp. Sci. Techn., 24, 209-220. crossref(new window)

72.
Wang, G.F. and Feng, X.Q. (2009), "Timoshenko beam model for buckling and vibration of nan ow ires with surface effects", J. Phys. D. Appl. Phys., 42,155411. crossref(new window)

73.
Yguerabide, J. and Yguerabide, E.E. (2001), "Resonance light scattering particles as ultrasensitive labels for detection of analytes in a wide range of applications", J. Cell. Biochem. Suppl., 37, 71-81.

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., 54(4), 693-710. crossref(new window)

75.
Zhang, Z., Wang, C. and Challamel, N. (2015), "Eringen's length-scale coefficients for vibration and buckling of nonlocal rectangular plates with simply supported edges", ASCE J. Eng. Mech., 141(2), 04014117. crossref(new window)

76.
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. Tech., 34, 24-34. crossref(new window)