Investigation of surface effects on free torsional vibration of nanobeams

Document Type : Research Article

Author

School of Engineering, Damghan University, Damghan, Iran

Abstract

In this study, surface effects on the free torsional vibration of nanobeams are investigated. To this end, equations of motion of nanobeams incorporating the surface effects are derived using the Hamilton’s principle and based on the surface elasticity theory. Then, equations of motion are analytically solved for three types of boundary conditions: clamped-clamped, clamped-free, and free-free, and associated mode shapes and natural frequencies are obtained. Nanobeams made of aluminum and silicon are selected as case studies. A detailed study is performed to examine the surface effects on the free torsional vibration of nanobeams for various nanobeam lengths, nanobeam radii, and mode numbers. In addition, influences of each of the surface parameters on torsional natural frequencies are separately investigated. The results show that influences of the surface effects on the free torsional vibration of nanobeams are completely different from those on the free transverse vibration of nanobeams. Results of the present study can be useful in design of nano-electro-mechanical systems like nano-bearings and rotary servomotors.

Keywords

Main Subjects


[1] A.C. Eringen, D. Edelen, On nonlocal elasticity,International Journal of Engineering Science, 10(3)(1972) 233-248.
[2] M.E. Gurtin, A.I. Murdoch, A continuum theory of elastic material surfaces, Archive for Rational Mechanics and Analysis, 57(4) (1975) 291-323.
[3] M. Gurtin, J. Weissmüller, F. Larche, A general theory of curved deformable interfaces in solids at equilibrium, Philosophical Magazine A, 78(5) (1998) 1093-1109.
[4] R. Nazemnezhad, S. Hosseini-Hashemi, Nonlinear free vibration analysis of Timoshenko nanobeams with surface energy, Meccanica, 50(4) (2015) 1027-1044.
[5] S. Hosseini-Hashemi, R. Nazemnezhad, H. Rokni,Nonlocal nonlinear free vibration of nanobeams with surface effects, European Journal of Mechanics-A/Solids, 52 (2015) 44-53.
[6] A.G. Arani, S. Amir, P. Dashti, M. Yousefi, Flow-induced vibration of double bonded visco-CNTs under magnetic fields considering surface effect, Computational Materials Science, 86 (2014) 144-154.
[7] A.G. Arani, M. Roudbari, Nonlocal piezoelastic surface effect on the vibration of visco-Pasternak coupled boron nitride nanotube system under a moving nanoparticle,Thin Solid Films, 542 (2013) 232-241.
[8] A.G. Arani, S. Amir, A. Shajari, M. Mozdianfard, Z.K.Maraghi, M. Mohammadimehr, Electro-thermal nonlocal vibration analysis of embedded DWBNNTs,Proceedings of the Institution of Mechanical Engineers,Part C: Journal of Mechanical Engineering Science,(2011) 0954406211422619.
[9] M. Zare, R. Nazemnezhad, S. Hosseini-Hashemi, Natural frequency analysis of functionally graded rectangular nanoplates with different boundary conditions via an analytical method, Meccanica, (2015) 1-18.
[10] S. Hosseini-Hashemi, M. Kermajani, R. Nazemnezhad,An analytical study on the buckling and free vibration of rectangular nanoplates using nonlocal third-order shear deformation plate theory, European Journal of Mechanics-A/Solids, 51 (2015) 29-43.
[11] S. Hosseini-Hashemi, M. Bedroud, R. Nazemnezhad, An exact analytical solution for free vibration of functionally graded circular/annular Mindlin nanoplates via nonlocal elasticity, Composite Structures, 103 (2013) 108-118.
[12] C. Li, C.W. Lim, J. Yu, Twisting statics and dynamics for circular elastic nanosolids by nonlocal elasticity theory, Acta Mechanica Solida Sinica, 24(6) (2011) 484-494.
[13] C.W. Lim, C. Li, J. Yu, Free torsional vibration of nanotubes based on nonlocal stress theory, Journal of Sound and Vibration, 331(12) (2012) 2798-2808.
[14] M. Aydogdu, M. Arda, Torsional vibration analysis of double walled carbon nanotubes using nonlocal elasticity,International Journal of Mechanics and Materials in Design, (2014) 1-14.
[15] J. Loya, J. Aranda-Ruiz, J. Fernandez-Saez, Torsion of cracked nanorods using a nonlocal elasticity model,Journal of Physics D: Applied Physics, 47(11) (2014)115304.
[16] M. Arda, M. Aydogdu, Torsional statics and dynamics of nanotubes embedded in an elastic medium, omposite Structures, 114 (2014) 80-91.
[17] S.S. Rao, Vibration of continuous systems, John Wiley & Sons, 2007.
[18] P. Lee, Y. Wang, X. Markenscoff, High-frequency vibrations of crystal plates under initial stresses, The Journal of the Acoustical Society of America, 57(1)(1975) 95-105.
[19] C. Liu, R. Rajapakse, Continuum models incorporating surface energy for static and dynamic response of nanoscale beams, Nanotechnology, IEEE Transactions on, 9(4) (2010) 422-431.
[20] S. Hosseini-Hashemi, M. Fakher, R. Nazemnezhad,Surface effects on free vibration analysis of nanobeams using nonlocal elasticity: a comparison between Euler-Bernoulli and Timoshenko, J Solid Mech, 5(3) (2013)290-304.
[21] R. Nazemnezhad, M. Salimi, S.H. Hashemi, P.A.Sharabiani, An analytical study on the nonlinear free vibration of nanoscale beams incorporating surface density effects, Composites Part B: Engineering, 43(8)(2012) 2893-2897.
[22] S. Hosseini-Hashemi, M. Fakher, R. Nazemnezhad, M.H.S. Haghighi, Dynamic behavior of thin and thick cracked nanobeams incorporating surface effects,Composites: Part B, 61 (2014) 66-72
[23] S. Hosseini-Hashemi, R. Nazemnezhad, An analytical study on the nonlinear free vibration of functionally graded nanobeams incorporating surface effects,Composites Part B: Engineering, 52 (2013) 199-206.
[24] M. Gurtin, X. Markenscoff, R. Thurston, Effect of surface stress on the natural frequency of thin crystals,Applied Physics Letters, 29(9) (1976) 529-530.