Surface Effects on Free Vibration Analysis of Nanobeams Using Nonlocal Elasticity: A Comparison Between Euler-Bernoulli and Timoshenko

Subject Areas : Engineering

Sh Hosseini – Hashemi ¹ (School of Mechanical Engineering, Iran University of Science and Technology--- Center of Excellence in Railway Transportation, Iran University of Science and Technology)
M Fakher ² (School of Mechanical Engineering, Iran University of Science and Technology)
R Nazemnezhad ³ (School of Mechanical Engineering, Iran University of Science and Technology)

Received: 2013-06-23 Accepted : 2013-08-12 Published : 2013-09-30

Keywords:

References:

 [1] He L., Lim C., Wu B., 2004, A continuum model for size-dependent deformation of elastic films of nano-scale thickness, International Journal of Solids and Structures 41(3):847-857.

[2] Eringen A.C., 1972, Nonlocal polar elastic continua, International Journal of Engineering Science 10(1):1-16.

[3] Eringen A.C., Edelen D., 1972, On nonlocal elasticity, International Journal of Engineering Science 10(3):233-248.

[4] Eringen A.C., 1983, On differential equations of nonlocal elasticity and solutions of screw dislocation and surface waves, Journal of Applied Physics 54(9): 4703-4710.

[5] Eringen A.C., 2002, Nonlocal Continuum Field Theories, Springer.

[6] Gurtin M., Murdoch A.I., 1975, A continuum theory of elastic material surfaces, Archive for Rational Mechanics and Analysis 57(4):291-323.

[7] Gurtin M., Weissmüller J., Larche F., 1998, A general theory of curved deformable interfaces in solids at equilibrium, Philosophical Magazine A 78(5):1093-1109.

[8] Asgharifard Sharabiani P., Haeri Yazdi M.R., 2013, Nonlinear free vibrations of functionally graded nanobeams with surface effects, Composites Part B: Engineering 45(1):581-586.

[9] Wang G., Feng X., Yu S., 2007, Surface buckling of a bending microbeam due to surface elasticity,Europhysics Letters 77(4):44002.

[10] Assadi A., Farshi B., 2011, Size-dependent longitudinal and transverse wave propagation in embedded nanotubes with consideration of surface effects, Acta Mechanica 222(1-2):27-39.

[11] Fu Y., Zhang J., Jiang Y., 2010, Influences of the surface energies on the nonlinear static and dynamic behaviors of nanobeams, Physica E: Low-Dimensional Systems and Nanostructures 42(9):2268-2273.

[12] Gheshlaghi B., Hasheminejad S.M., 2011, Surface effects on nonlinear free vibration of nanobeams, Composites Part B: Engineering 42(4):934-937.

[13] Guo J.-G., Zhao Y.P., 2007, The size-dependent bending elastic properties of nanobeams with surface effects, Nanotechnology 18(29):295701.

[14] Hosseini-Hashemi S., Nazemnezhad R., 2013, An analytical study on the nonlinear free vibration of functionally graded nanobeams incorporating surface effects, Composites Part B: Engineering 52:199-206.

[15] Liu C., Rajapakse R., 2010, Continuum models incorporating surface energy for static and dynamic response of nanoscale beams, Nanotechnology 9(4):422-431.

[16] Nazemnezhad R., Salimi M., Hosseini-Hashemi S., Sharabiani P.A., 2012, An analytical study on the nonlinear free vibration of nanoscale beams incorporating surface density effects, Composites Part B: Engineering 43:2893-2897.

[17] Park H.S., 2012, Surface stress effects on the critical buckling strains of silicon nanowires, Computational Materials Science 51(1):396-401.

[18] Ren Q., Zhao Y.-P., 2004, Influence of surface stress on frequency of microcantilever-based biosensors, Microsystem Technologies 10(4):307-314.

[19] Song F., Huang G., Park H., Liu X., 2011, A continuum model for the mechanical behavior of nanowires including surface and surface-induced initial stresses, International Journal of Solids and Structures 48(14):2154-2163.

[20] Wang G.-F., Feng X.Q., 2009, Timoshenko beam model for buckling and vibration of nanowires with surface effects, Journal of Physics D: Applied Physics 42(15):155411.

[21] Wang L., Hu H., 2005, Flexural wave propagation in single-walled carbon nanotubes, Physical Review B 71(19): 195412-195419.

[22] Wang Q., 2005, Wave propagation in carbon nanotubes via nonlocal continuum mechanics, Journal of Applied physics 98(12):124301-124306.

[23] Ece M., Aydogdu M., 2007, Nonlocal elasticity effect on vibration of in-plane loaded double-walled carbon nano-tubes, Acta Mechanica 190(1-4):185-195.

[24] Lim C., Li C., Yu J.l., 2010, Free vibration of pre-tensioned nanobeams based on nonlocal stress theory, Journal of Zhejiang University Science A 11(1):34-42.

[25] Maachou M., Zidour M., Baghdadi H., Ziane N., Tounsi A., 2011, A nonlocal levinson beam model for free vibration analysis of zigzag single-walled carbon nanotubes including thermal effects, Solid State Communications 151(20): 1467-1471.

[26] Mohammadi B., Ghannadpour S., 2011, Energy approach vibration analysis of nonlocal timoshenko beam theory, Procedia Engineering 10:1766-1771.

[27] Reddy J., 2007, Nonlocal theories for bending, buckling and vibration of beams, International Journal of Engineering Science 45(2):288-307.

[28] Reddy J., 2010, Nonlocal nonlinear formulations for bending of classical and shear deformation theories of beams and plates, International Journal of Engineering Science 48(11):1507-1518.

[29] Wang C., Zhang Y., He X., 2007, Vibration of nonlocal timoshenko beams, Nanotechnology 18(10):105401.

[30] Xu M., 2006, Free transverse vibrations of nano-to-micron scale beams, Proceedings of the Royal Society A: Mathematical, Physical and Engineering Science 462(2074):2977-2995.

[31] Bedroud M., Hosseini-Hashemi S., Nazemnezhad R., 2013, Buckling of circular/annular Mindlin nanoplates via nonlocal elasticity, Acta Mechanica 224(11):2663-2676.

[32] Bedroud M., Hosseini-Hashemi S., Nazemnezhad R., 2013, Axisymmetric/asymmetric buckling of circular/annular nanoplates via nonlocal elasticity, Modares Mechanical Engineering 13(5):144-152.

[33] Hosseini-Hashemi S., Bedroud M., Nazemnezhad R., 2013, An exact analytical solution for free vibration of functionally graded circular/annular Mindlin nanoplates via nonlocal elasticity, Composite Structures 103:108-118.

[34] Hosseini-Hashemi S., Zare M., Nazemnezhad R., 2013, An exact analytical approach for free vibration of Mindlin rectangular nano-plates via nonlocal elasticity, Composite Structures 100:290-299.

[35] Lee H.-L., Chang W.-J., 2010, Surface and small-scale effects on vibration analysis of a nonuniform nanocantilever beam, Physica E: Low-Dimensional Systems and Nanostructures 43(1):466-469.

[36] Wang K., Wang B., 2011, Vibration of nanoscale plates with surface energy via nonlocal elasticity, Physica E: Low-Dimensional Systems and Nanostructures 44(2):448-453.

[37] Lei X.w., Natsuki T., Shi J.x., Ni Q.q., 2012, Surface effects on the vibrational frequency of double-walled carbon nanotubes using the nonlocal timoshenko beam model, Composites Part B: Engineering 43(1):64-69.

[38] Gheshlaghi B., Hasheminejad S.M., 2012, Vibration analysis of piezoelectric nanowires with surface and small scale effects, Current Applied Physics 12(4):1096-1099.

[39] Wang K., Wang B., 2012, The electromechanical coupling behavior of piezoelectric nanowires: Surface and small-scale effects, Europhysics Letters 97(6):66005.

[40] Malekzadeh P., Shojaee M., 2013, Surface and nonlocal effects on the nonlinear free vibration of non-uniform nanobeams, Composites Part B: Engineering 52:82-94.

[41] Mahmoud F., Eltaher M., Alshorbagy A., Meletis E., 2012, Static analysis of nanobeams including surface effects by nonlocal finite element, Journal of Mechanical Science and Technology 26(11):3555-3563.

[42] Gurtin M.E., Ian Murdoch A., 1978, Surface stress in solids, International Journal of Solids and Structures 14(6):431-440.

[43] Shenoy V.B., 2005, Atomistic calculations of elastic properties of metallic fcc crystal surfaces, Physical Review B 71(9):094104-094115.

[44] Gurtin M.E., Murdoch A.I., 1975, A continuum theory of elastic material surfaces, Archive for Rational Mechanics and Analysis 57(4):291-323.

[45] Lu P., He L., Lee H., Lu C., 2006, Thin plate theory including surface effects, International Journal of Solids and Structures 43(16):4631-4647.

[46] Rao S.S., 2007, Vibration of Continuous Systems, John Wiley & Sons.

[47] Timoshenko S.P., Goodier J., 2011, Theory of elasticity, International Journal of Bulk Solids Storage in Silos 1(4): 567-567.

[48] Ogata S., Li J., Yip S., 2002, Ideal pure shear strength of aluminum and copper, Science 298(5594):807-811.

[49] Zhu R., Pan E., Chung P.W., Cai X., Liew K.M., Buldum A., 2006, Atomistic calculation of elastic moduli in strained silicon, Semiconductor Science and Technology 21(7):906.

[50] Miller R.E., Shenoy V.B., 2000, Size-dependent elastic properties of nanosized structural elements, Nanotechnology 11(3):139.