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Application of Eringen`s nonlocal elasticity theory for vibration analysis of rotating functionally graded nanobeams
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  • Journal title : Smart Structures and Systems
  • Volume 17, Issue 5,  2016, pp.837-857
  • Publisher : Techno-Press
  • DOI : 10.12989/sss.2016.17.5.837
 Title & Authors
Application of Eringen`s nonlocal elasticity theory for vibration analysis of rotating functionally graded nanobeams
Ebrahimi, Farzad; Shafiei, Navvab;
 Abstract
In the present study, for first time the size dependent vibration behavior of a rotating functionally graded (FG) Timoshenko nanobeam based on Eringen`s nonlocal theory is investigated. It is assumed that the physical and mechanical properties of the FG nanobeam are varying along the thickness based on a power law equation. The governing equations are determined using Hamilton`s principle and the generalized differential quadrature method (GDQM) is used to obtain the results for cantilever boundary conditions. The accuracy and validity of the results are shown through several numerical examples. In order to display the influence of size effect on first three natural frequencies due to change of some important nanobeam parameters such as material length scale, angular velocity and gradient index of FG material, several diagrams and tables are presented. The results of this article can be used in designing and optimizing elastic and rotary type nano-electro-mechanical systems (NEMS) like nano-motors and nano-robots including rotating parts.
 Keywords
bending vibration;Eringen`s nonlocal theory;rotary functionally graded nanobeam;Timoshenko beam theory;
 Language
English
 Cited by
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Wave propagation analysis of size-dependent rotating inhomogeneous nanobeams based on nonlocal elasticity theory, Journal of Vibration and Control, 2017, 107754631771153  crossref(new windwow)
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Thermal effects on wave propagation characteristics of rotating strain gradient temperature-dependent functionally graded nanoscale beams, Journal of Thermal Stresses, 2017, 40, 5, 535  crossref(new windwow)
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Forced Vibration Analysis of Functionally Graded Nanobeams, International Journal of Applied Mechanics, 2017, 09, 07, 1750100  crossref(new windwow)
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Transverse free vibration and stability of axially moving nanoplates based on nonlocal elasticity theory, Applied Mathematical Modelling, 2017, 45, 65  crossref(new windwow)
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Wave propagation analysis of rotating thermoelastically-actuated nanobeams based on nonlocal strain gradient theory, Acta Mechanica Solida Sinica, 2017, 30, 6, 647  crossref(new windwow)
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Thermo-electro-mechanical bending of FG piezoelectric microplates on Pasternak foundation based on a four-variable plate model and the modified couple stress theory, Microsystem Technologies, 2018, 24, 2, 1227  crossref(new windwow)
 References
1.
Akgoz, B. and Civalek, O. (2012), "Modeling and analysis of micro-sized plates resting on elastic medium using the modified couple stress theory", Meccanica, 48(4), 863-873.

2.
Akgoz, B. and Civalek, O. (2014a), "Shear deformation beam models for functionally graded microbeams with new shear correction factors", Compos. Struct., 112, 214-225. crossref(new window)

3.
Akgoz, B. and Civalek, O. (2014b), "Thermo-mechanical buckling behavior of functionally graded microbeams embedded in elastic medium", Int. J. Eng. Sci., 85, 90-104. crossref(new window)

4.
Alshorbagy, A.E., Eltaher, M. and Mahmoud, F. (2011), "Free vibration characteristics of a functionally graded beam by finite element method", Appl. Math. Modell., 35(1), 412-425. crossref(new window)

5.
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)

6.
Aranda-Ruiz, A.J., Loya, J. and Fernandez-Saez, J. (2012), "Bending vibrations of rotating nonuniform nanocantilevers using the Eringen nonlocal elasticity theory", Compos. Struct., 94(9), 2990-3001. crossref(new window)

7.
Asgharl, M., Rahaeifard, M., Kahrobaiyan, M. and Ahmadian, M. (2011), "The modified couple stress functionally graded Timoshenko beam formulation", Mater. Des., 32(3), 1435-1443. crossref(new window)

8.
Avcar, M. (2015), "Effects of rotary inertia shear deformation and non-homogeneity on frequencies of beam", Struct. Eng. Mech., 55(4), 871-884. crossref(new window)

9.
Bath, J. and Turberfield, A. J. (2007), "DNA nanomachines", Nat Nano, 2, 275-284. crossref(new window)

10.
Bellman, R. and Casti, J. (1971), "Differential quadrature and long-term integration", J. Math. Anal. Appl., 34(2), 235-238. crossref(new window)

11.
Bellman, R., Kashef, B. and Casti, J. (1972), "Differential quadrature: a technique for the rapid solution of nonlinear partial differential equations", J. Comput. Phys., 10(1), 40-52. crossref(new window)

12.
Challamel, N. and Wang, C.M. (2008), "The small length scale effect for a non-local cantilever beam: a paradox solved", Nanotechnology, 19(34), 345703. crossref(new window)

13.
Chen, L., Nakamura, M., Schindler, T.D., Parker, D. and Bryant, Z. (2012), "Engineering controllable bidirectional molecular motors based on myosin", Nat Nano, 7, 252-256. crossref(new window)

14.
Civalek, O. and Akgoz, B. (2013), "Vibration analysis of micro-scaled sector shaped graphene surrounded by an elastic matrix", Comput. Mater. Sci., 77, 295-303. crossref(new window)

15.
Civalek, O. and Demir, C. (2011), "Bending analysis of microtubules using nonlocal Euler-Bernoulli beam theory", Appl. Math. Modell., 35(5), 2053-2067. crossref(new window)

16.
Dehrouyeh-Semnani, A. (2015), "The influence of size effect on flapwise vibration of rotating microbeams", Int. J. Eng. Sci., 94, 150-163. crossref(new window)

17.
Dehrouyeh-Semnani, A.M. (2015), "The influence of size effect on flapwise vibration of rotating microbeams", Int. J. Eng. Sci., 94, 150-163. crossref(new window)

18.
Dewey, H. and Hodges, M.J.R. (1981), "Free-vibration analysis of rotating beams by a variable-order finite-element method", AIAA, 19(11).

19.
Ebrahimi, F. and Salari, E. (2015a), "Effect of various thermal loadings on buckling and vibrational characteristics of nonlocal temperature-dependent FG nanobeams", Mech. Adv. Mater. Struct., doi: 10.1080/15376494.2015.1091524. crossref(new window)

20.
Ebrahimi, F. and Salari, E. (2015b), "Thermal buckling and free vibration analysis of size dependent Timoshenko FG nanobeams in thermal environments", Compos. Struct., 128, 363-380. crossref(new window)

21.
Eltaher, M., Emam, S.A. and Mahmoud F. (2012), "Free vibration analysis of functionally graded size-dependent nanobeams", Appl. Math. Comput., 218(14), 7406-7420. crossref(new window)

22.
Eltaher, M., Emam, S.A. and Mahmoud, F. (2013), "Static and stability analysis of nonlocal functionally graded nanobeams", Compos. Struct., 96, 82-88. crossref(new window)

23.
Eringen, A.C. (1972), "Nonlocal polar elastic continua", Int. J. Eng. Sci., 10(1), 1-16. crossref(new window)

24.
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)

25.
Eringen, A.C. and Edelen, D.G.B. (1972), "On nonlocal elasticity", Int. J. Eng. Sci., 10(3), 233-248. crossref(new window)

26.
Ghadiri, M., Hosseni, S. and Shafiei, N. (2015), "A power series for vibration of a rotating nanobeam with considering thermal effect", Mech. Adv. Mater. Struct., doi: 10.1080/15376494.2015.1091527. crossref(new window)

27.
Ghadiri, M. and Shafiei, N. (2015), "Nonlinear bending vibration of a rotating nanobeam based on nonlocal Eringen‟s theory using differential quadrature method", Microsyst. Technol., doi: 10.1007/s00542-015-2662-9. crossref(new window)

28.
Ghadiri, M. and Shafiei, N. (2016), "Vibration analysis of a nano-turbine blade based on Eringen nonlocal elasticity applying the differential quadrature method", J. Vib. Control, doi: 10.1177/1077546315627723. crossref(new window)

29.
Ghadiri, M., Shafiei, N. and Safarpour, H. (2016), "Influence of surface effects on vibration behavior of a rotary functionally graded nanobeam based on Eringen‟s nonlocal elasticity", Microsyst. Technol., doi: 10.1007/s00542-016-2822-6. crossref(new window)

30.
Goel, A. and Vogel, V. (2008), "Harnessing biological motors to engineer systems for nanoscale transport and assembly", Nat Nano, 3, 465-475. crossref(new window)

31.
Kaya, M.O. (2006), "Free vibration analysis of a rotating Timoshenko beam by differential transform method", Aircraft Eng. Aerospace Technol., 78(3), 194-203. crossref(new window)

32.
Ke, L.L. and Wang, Y.S. (2011), "Size effect on dynamic stability of functionally graded microbeams based on a modified couple stress theory", Compos. Struct., 93(2), 342-350. crossref(new window)

33.
Ke, L.L., Wang, Y.S., Yang, J. and Kitipornchai, S. (2012), "Nonlinear free vibration of size-dependent functionally graded microbeams", Int. J. Eng. Sci., 50(1), 256-267. crossref(new window)

34.
Lee, L.K., Ginsburg, M.A., Crovace, C., Donohoe, M. and Stock, D. (2010), "Structure of the torque ring of the flagellar motor and the molecular basis for rotational switching", Nature, 466(7309), 996-1000. crossref(new window)

35.
Lim, C., Li, C. and Yu, J. (2009), "The effects of stiffness strengthening nonlocal stress and axial tension on free vibration of cantilever nanobeams", Interact. Multiscale Mech., 2, 223-233. crossref(new window)

36.
Lubbe, A.S., Ruangsupapichat, N., Caroli, G. and Feringa, B.L. (2011), "Control of rotor function in light-driven molecular motors", J. Organic Chem., 76(21), 8599-8610. crossref(new window)

37.
Metin aydogdu, V.T. (2007), "Free vibration analysis of functionally graded beams with simply supported edges", Mater. Des., 28(5), 1651-1656. crossref(new window)

38.
Murmu, T. and Adhikari, S. (2010), "Scale-dependent vibration analysis of prestressed carbon nanotubes undergoing rotation", J. Appl. Phys., 108(12).

39.
Narendar, S. (2012), "Differential quadrature based nonlocal flapwise bending vibration analysis of rotating nanotube with consideration of transverse shear deformation and rotary inertia", Appl. Math. Comput., 219(3), 1232-1243. crossref(new window)

40.
Narendar, S. and Gopalakrishnan, S. (2011), "Nonlocal wave propagation in rotating nanotube", Result. Phys., 1(1), 17-25. crossref(new window)

41.
Nazemnezhad, R. and Hosseini-Hashemi, S. (2014), "Nonlocal nonlinear free vibration of functionally graded nanobeams", Compos. Struct., 110, 192-199. crossref(new window)

42.
Pradhan, S.C. and Murmu, T. (2010), "Application of nonlocal elasticity and DQM in the flapwise bending vibration of a rotating nanocantilever", Physica E: Low-dimensional Systems and Nanostructures, 42, 1944-1949. crossref(new window)

43.
Rahmani, O. and Pedram, O. (2014), "Analysis and modeling the size effect on vibration of functionally graded nanobeams based on nonlocal Timoshenko beam theory", Int. J. Eng. Sci., 77, 55-70. crossref(new window)

44.
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)

45.
Shafiei, N., Kazemi, M. and Fatahi, L. (2015), "Transverse vibration of rotary tapered microbeam based on modified couple stress theory and generalized differential quadrature element method", Mech. Adv. Mater. Struct., doi: 10.1080/15376494.2015.1128025. crossref(new window)

46.
Shafiei, N., Kazemi, M. and Ghadiri, M. (2016), "On size-dependent vibration of rotary axially functionally graded microbeam", Int. J. Eng. Sci., 101, 29-44. crossref(new window)

47.
Shu, C. (2000), Differential quadrature and its application in engineering, Springer.

48.
Shu, C. and Richards, B.E. (1992), "Application of generalized differential quadrature to solve two-dimensional incompressible Navier-Stokes equations", Int. J. Numer. Meth. Fl., 15, 791-798. crossref(new window)

49.
Simsek, M. (2010), "Fundamental frequency analysis of functionally graded beams by using different higher-order beam theories", Nuclear Eng., 240(4), 697-705. crossref(new window)

50.
Simsek, M. and Yurtcu, H. (2013), "Analytical solutions for bending and buckling of functionally graded nanobeams based on the nonlocal Timoshenko beam theory", Compos. Struct., 97, 378-386. crossref(new window)

51.
Tauchert, T. R. (1974), Energy principles in structural mechanics, McGraw-Hill Companies.

52.
Tierney, H.L., Murphy, C.J., Jewell, A.D., Baber, A.E., Iski, E.V., Khodaverdian, H.Y., Mcguire, A.F., Klebanov, N. and Sykes, E.C.H. (2011), "Experimental demonstration of a single-molecule electric motor", Nat Nano, 6, 625-629. crossref(new window)

53.
Van delden, R.A., Ter wiel, M.K.J., Pollard, M.M., Vicario, J., Koumura, N. and Feringa, B.L. (2005), "Unidirectional molecular motor on a gold surface", Nature, 437, 1337-1340. crossref(new window)

54.
Wang, C.M., Zhang, Y.Y. and He, X.Q. (2007), "Vibration of nonlocal Timoshenko beams", Nanotechnology, 18, 105401. crossref(new window)