Surface Effect on Nonlinear Free Vibration Analysis of Nanotubes
الموضوعات : فصلنامه شبیه سازی و تحلیل تکنولوژی های نوین در مهندسی مکانیکجعفر اسکندری جم 1 , یاسر میرزایی 2 , بهنام قشلاقی 3
1 - دانشیار، مرکز کامپوزیت، تهران.
2 - استادیار، گروه مکانیک، دانشگاه آزاد اسلامی، واحد دماوند
3 - کارشناس ارشد، گروه مکانیک، دانشگاه آزاد اسلامی، واحد دماوند.
الکلمات المفتاحية: Nonlinear vibration, Nanotubes, Surface effect,
ملخص المقالة :
In this work,The free nonlinear vibrations of nanotubes using the Euler-Bernoulli beam theory along with the von Kármán geometric nonlinearity in presence of surface effects has been investigated. Natural frequencies of a simply-supported nanotube in terms of the Jacobi elliptic functions are obtained by using the free vibration modes of the corresponding linear problem. The numerical results describe the imperative influence of surface effect, mode number, vibration amplitude, and the length and thickness of the nanotubes on the vibrational characteristics of the nanotubes. In addition the influence of surface effects on the system phase trajectory is considered. Finally, it is observed that the surface effects diminish by increasing in the dimension of nanotubes. The present study may be used to improve the design of different types of micro-nano sensors.
[1] Fennimore A.M., Yuzvinsky T.D., Han W.Q., Fuhrer M.S., Cumings J., Zettl A., Rotational actuators based on carbon nanotubes, Nature, 424, 2003, pp. 408-410.
[2] Williams P.A., Papadakis S.J., Patel A.M., Falvo M.R., Washburn S., Superfine R., Fabrication of nanometer-scale mechanical devices incorporating individual multiwalled carbon nanotubes as torsional springs, Applied Physics Letters, 82, 2003, pp. 805-807.
[3] Papadakis S.J., Hall A.R., Williams P.A., Vicci L., Falvo M.R., Superfine R., Washburn S., Resonant oscillators with carbon-nanotube torsion springs, Physics Review Letters, 93, 2004, pp. 1461011, 1461014.
[4] Williams P.A., Papadakis S.J., Patel A.M., Falvo M.R., Washburn S., Superfine R, Torsional response and stiffening of individual multiwalled carbon nanotubes, Physics Review Letters, 89, 2002, pp. 2555021-2555025.
[5] Lagowski J., Gatos H.C., Sproles Jr E.S., Surface stress and the normal mode of vibration of thin crystals: GaAs, Applied Physics Letters, 26, 1975, pp. 493-495.
[6] Sader J. E., Surface stress induced deflections of cantilever plates with applications to the atomic force microscope: rectangular plates, Journal of Applied Physics, 89, 2001, pp. 2911-2921.
[7] Lee J.H., Kim T. S., Yoon K. H., Effect of mass and stress on resonant frequency shift of functionalized Pb(Zr0.52Ti0.48)O3 thin film microcantilever for the detection of C-reactiveprotein, Applied Physic Letters, 84, 2004, pp. 3187-3189.
[8] He J., Lilley C.M., Surface Effect on the Elastic Behavior of Static Bending Nanowires, Nano Letters, 2008, pp. 1798–1802.
[9] Wang G.F, Feng X.Q., Effects of surface elasticity and residual surface tension on the natural frequency of microbeams, Applied Physic Letters, 90, 2007, pp. 2319041-2319044.
[10] Abbasion S., Rafsanjani A., Avazmohammadi R., Farshidianfar A., Free vibration of microscaled Timoshenko beams, Applied Physic Letters, 95, 2009, pp. 1431221-1431224.
[11] Zhang Y.Y., Wang C.M., Tan V.B.C., Assessment of Timoshenko beam models for vibrational behaviour of single-walled carbon nanotubes using molecular dynamics, Advances in Applied Mathematics and Mechanics, 1, 2009, pp. 89-106.
[12] Fu Y. M., Hong J. W., Wang X. Q., Analysis of nonlinear vibration for embedded carbon nanotubes, Journal of Sound and Vibration, 96, 2006, pp. 746-756.
[13] Gibbs J. W., The Scientific Papers of J. Willard Gibbs, Vol. 1: Thermodynamics: Longmans and Green, New York, 1906.
[14] Cammarata R.C., Surface and interface stresses effects in thin films, Prog. Surf. Sci, 46, 1994, pp. 1–38 .
[15] Gurtin ME, Murdoch AI, A continuum theory of elastic material surfaces, Arch Rat Mech Anal, 57, 1975, pp. 291-323.
[16] Gurtin ME, Struthers A., Multiphase thermomechanics with interfacial structure, Arch Rat Mech Anal,112, 1990, PP. 97-160.
[17] Wang G.F., Feng X.Q., Effects of surface elasticity and residual surface tension on the natural frequency of microbeams, Applied Physics Letters, 90, 2007, pp. 231904.
[18] Ke L.L., Yang J., Kitipornchai S., An analytical study on the nonlinear vibration of functionally graded beams, Meccanica, 45, 2009, pp. 743-752.
[19] Byrd P.F., Friedman M.D., Handbook of Elliptic Integrals for Engineers and Scientists, Springer, Berlin, 1991.
[20] Miller R.E., Shenoy V.B., Size-dependent elastic properties of nanosized structural elements, Nanotechnology, 11, 2000, pp. 139-147.
[21] Shenoy V.B., Atomistic calculations of elastic properties of metallic fcc crystal surfaces, Phys. Rev. B 71, 2005, pp. 0941041-09410411.
