Advanced SearchSearch Tips
Nonlocal vibration analysis of FG nano beams with different boundary conditions
facebook(new window)  Pirnt(new window) E-mail(new window) Excel Download
  • Journal title : Advances in nano research
  • Volume 4, Issue 2,  2016, pp.85-111
  • Publisher : Techno-Press
  • DOI : 10.12989/anr.2016.4.2.085
 Title & Authors
Nonlocal vibration analysis of FG nano beams with different boundary conditions
Ehyaei, Javad; Ebrahimi, Farzad; Salari, Erfan;
In this paper, the classical and non-classical boundary conditions effect on free vibration characteristics of functionally graded (FG) size-dependent nanobeams are investigated by presenting a semi analytical differential transform method (DTM) for the first time. Three kinds of mathematical models, namely; power law (P-FGM), sigmoid (S-FGM) and Mori-Tanaka (MT-FGM) distribution are considered to describe the material properties in the thickness direction. The nonlocal Eringen theory takes into account the effect of small size, which enables the present model to become effective in the analysis and design of nanosensors and nanoactuators. Governing equations are derived through Hamilton`s principle and they are solved applying semi analytical differential transform method. The good agreement between the results of this article and those available in literature validated the presented approach. The detailed mathematical derivations are presented and numerical investigations are performed while the emphasis is placed on investigating the effect of the several parameters such as small scale effects, spring constant factors, various material compositions and mode number on the normalized natural frequencies of the FG nanobeams in detail. It is explicitly shown that the vibration of FG nanobeams is significantly influenced by these effects. Numerical results are presented to serve as benchmarks for future analyses of FG nanobeams.
DT method;functionally graded material;non-classical boundary condition;nanobeams;vibration;
 Cited by
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)
On thermal stability of plates with functionally graded coefficient of thermal expansion, Structural Engineering and Mechanics, 2016, 60, 2, 313  crossref(new windwow)
Forced Vibration Analysis of Functionally Graded Nanobeams, International Journal of Applied Mechanics, 2017, 09, 07, 1750100  crossref(new windwow)
Alshorbagy, A.E., Eltaher, M.A. and Mahmoud, F.F. (2011), "Free vibration characteristics of afunctionally graded beam by finite element method", Appl. Math. Model., 35(1), 412-425. crossref(new window)

Ansari, R., Gholami, R. and Sahmani, S. (2011), "Free vibration analysis of size-dependent functionally graded microbeams based on the strain gradient Timoshenko beam theory", Compos. Struct., 94(1), 221-228. crossref(new window)

Asghari, M., Ahmadian, M.T., Kahrobaiyan, M.H.and Rahaeifard, M. (2010), "On the size-dependent behavior of functionally graded micro-beams", Mater. Des., 31(5), 2324-2329. crossref(new window)

Asghari, M., Rahaeifard, M., Kahrobaiyan, M.H. and Ahmadian, M.T. (2011), "The modified couple stressfunctionally graded Timoshenko beam formulation", Mater. Des., 32(3) 1435-1443. crossref(new window)

Aydogdu, M. (2009), "A general nonlocal beam theory: its application to nanobeam bending, buckling and vibration", Physica E: Low-dimen. Syst. Nanostr., 41(9), 1651-1655. crossref(new window)

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

Bennoun, M., Houari, M.S.A. and Tounsi, A. (2016), "A novel five-variable refined plate theory for vibration analysis of functionally graded sandwich plates", Mech. Adv. Mater. Struct., 23(4), 423-431. crossref(new window)

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., 3(1), 029. crossref(new window)

Bounouara, F., Benrahou, K.H., Belkorissat, I. and Tounsi, A. (2016), "A nonlocal zeroth-order shear deformation theory for free vibration of functionally graded nanoscale plates resting on elastic foundation", Steel Compos. Struct., 20(2), 227-249. crossref(new window)

Chemi, A., Heireche, H., Zidour, M., Rakrak, K. and Bousahla, A.A. (2015), "Critical buckling load of chiral double-walled carbon nanotube using non-local theory elasticity", Adv. Nano Res., 3(4), 193-206. crossref(new window)

Civalek, Ö., Cigdem, D., and Bekir, A. (2010), "Free vibration and bending analyses of cantilever microtubules based on nonlocal continuum model", Math. Comput. Appl., 15(2), 289-298.

Eltaher, M.A., Alshorbagy, A.E. and Mahmoud, F.F. (2013), "Determination of neutral axis position andits effect on natural frequencies of functionally graded macro/nanobeams", Compos. Struct., 99, 193-201. crossref(new window)

Eltaher, M.A., Emam, S.A. and Mahmoud, F.F. (2012), "Free vibration analysis of functionally graded size-dependent nanobeams", Appl. Math. Comput., 218(14), 7406-7420.

Eltaher, M.A., Emam, S.A. and Mahmoud, F.F. (2013), "Static and stability analysis of nonlocal functionally graded nanobeams", Compos. Struct., 96, 82-88. crossref(new window)

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

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

Hamidi, A., Houari, M.S.A., Mahmoud, S. 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)

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

Hosseini-Hashemi, S. and Nazemnezhad, R. (2013), "An analytical study on the nonlinear freevibration of functionally graded nanobeams incorporating surface effects", Compos. Part B: Eng., 52, 199-206. crossref(new window)

Ke, L.L. and Wang, Y.S. (2011), "Size effect on dynamic stability of functionally gradedmicrobeams based on a modified couple stress theory", Compos. Struct., 93(2), 342-350. crossref(new window)

Ke, L.L., Wang, Y.S., Yang, J. and Kitipornchai, S. (2012), "Nonlinear free vibration ofsize-dependent functionally graded microbeams", Int. J. Eng. Sci., 50(1), 256-267. crossref(new window)

Ma'en, S.S. and Butcher, E.A. (2012), "Free vibration analysis of non-rotating and rotatingTimoshenko beams with damaged boundaries using the Chebyshev collocation method", Int. J. Mech. Sci., 60(1), 1-11. crossref(new window)

Mahmoud, S., Chaht, F.L., Kaci, A., Houari, M.S.A., Tounsi, A. and Beg, O.A. (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. crossref(new window)

Pradhan, S.C. and Murmu, T. (2010), "Application of nonlocal elasticity and DQM in the flap wise bending vibration of a rotating nano cantilever", Physica E: Low-dimen. Syst. Nanostr., 42(7), 1944-1949. crossref(new window)

Shahba, A., Attarnejad, R., Marvi, M.T. and Hajilar, S. (2011), "Free vibration and stability analysisof axially functionally graded tapered Timoshenko beams with classical and non-classical boundary conditions", Compos. Part B: Eng., 42(4), 801-808.

Sharabiani, P.A. and Yazdi, M.R.H. (2013). (2013), "Nonlinear free vibrations of functionally graded nanobeams with surface effects", Compos. Part B: Eng., 45(1), 581-586. crossref(new window)

Simsek, M. (2010), "Fundamental frequency analysis of functionally graded beams by using different higher-order beam theories", Nucl. Eng. Des., 240(4), 697-705. crossref(new window)

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

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

Wang, Q. (2005), "Wave propagation in carbon nanotubes via nonlocal continuum mechanics", J. Appl. Phys., 98(12), 124301. crossref(new window)

Wang, Q., and Varadan, V.K. (2006), "Vibration of carbon nanotubes studied using nonlocal continuum mechanics", Smart Mater. Struct., 15(2), 659. crossref(new window)

Wattanasakulpong, N. and Variddhi, U. (2014), "Linear and nonlinear vibration analysis ofelastically restrained ends FGM beams with porosities", Aerosp. Sci. Tech., 32(1), 111-120. crossref(new window)

Witvrouw, A. and Mehta, A. (2005), "The use of functionally graded poly-SiGe layers for MEMS applications", Materials science forum, 492, Trans Tech Publications.

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)

Zhang, Y.Q., Liu, G.R. and Wang, J.S. (2004), "Small-scale effects on buckling of multiwalled carbon nanotubes under axial compression", Phys.Rrev. B, 70(20), 205430. crossref(new window)