DOI QR코드

DOI QR Code

Surface effects on flutter instability of nanorod under generalized follower force

  • Xiao, Qiu-Xiang (School of Civil Engineering, Central South University) ;
  • Zou, Jiaqi (School of Civil Engineering, Central South University) ;
  • Lee, Kang Yong (State Key Laboratory of Structural Analysis for Industrial Equipment and Department of Engineering Mechanics, Dalian University of Technology) ;
  • Li, Xian-Fang (School of Civil Engineering, Central South University)
  • 투고 : 2017.05.03
  • 심사 : 2017.07.13
  • 발행 : 2017.12.25

초록

This paper studies on dynamic and stability behavior of a clamped-elastically restrained nanobeam under the action of a nonconservative force with an emphasis on the influence of surface properties on divergence and flutter instability. Using the Euler-Bernoulli beam theory incorporating surface effects, a governing equation for a clamped-elastically restrained nanobeam is derived according to Hamilton's principle. The characteristic equation is obtained explicitly and the force-frequency interaction curves are displayed to show the influence of the surface effects, spring stiffness of the elastic restraint end on critical loads including divergence and flutter loads. Divergence and flutter instability transition is analyzed. Euler buckling and stability of Beck's column are some special cases of the present at macroscale.

키워드

과제정보

연구 과제 주관 기관 : National Natural Science Foundation of China, Dalian University of Technology

참고문헌

  1. Akgoz, B. and Civalek, O. (2015), "Bending analysis of FG microbeams resting on Winkler elastic foundation via strain gradient elasticity", Compos. Struct., 134, 294-301. https://doi.org/10.1016/j.compstruct.2015.08.095
  2. Ansari, R., Gholami, R. and Sahmani, S. (2013), "Size-dependent vibration of functionally graded curved microbeams based on the modified strain gradient elasticity theory", Arch. Appl. Mech., 83(10), 1439-1449. https://doi.org/10.1007/s00419-013-0756-3
  3. Asthana, A., Momeni, K., Prasad, A., Yap, Y.K. and Yassar, R.S. (2011), "In situ observation of size-scale effects on the mechanical properties of ZnO nanowires", Nanotechnol., 22(26), 265712. https://doi.org/10.1088/0957-4484/22/26/265712
  4. Chen, Y.Z. (2003), "Interaction between compressive force and vibration frequency for a varying cross-section cantilever under action of generalized follower force", J. Sound Vib., 259(4), 991-999. https://doi.org/10.1006/jsvi.2002.5205
  5. Cheng, C.H. and Chen, T. (2015), "Size-dependent resonance and buckling behavior of nanoplates with high-order surface stress effects", Physica E, 67, 12-17. https://doi.org/10.1016/j.physe.2014.10.040
  6. Choi, J., Cho, M. and Kim, W. (2010), "Surface effects on the dynamic behavior of nanosized thin film resonator", Appl. Phys. Lett., 97(97), 171901. https://doi.org/10.1063/1.3502486
  7. Civalek, O. and Demir, C. (2016), "A simple mathematical model of microtubules surrounded by an elastic matrix by nonlocal finite element method", Appl. Math. Comput., 289, 335-352.
  8. Cuenot, S., Fretigny, C., Demoustier-Champagne, S. and Nysten, B. (2004), "Surface tension effect on the mechanical properties of nanomaterials measured by atomic force microscopy", Phys. Rev. B, 69(16), 165410. https://doi.org/10.1103/PhysRevB.69.165410
  9. Ebrahimi, F., Shaghaghi, G.R. and Boreiry, M. (2016), "An investigation into the influence of thermal loading and surface effects on mechanical characteristics of nanotubes", Struct. Eng. Mech., 57(1), 179-200. https://doi.org/10.12989/sem.2016.57.1.179
  10. Elishakoff, I. (2005), "Controversy associated with the so-called "follower forces": Critical overview", Appl. Mech. Rev., 58(2), 117-142. https://doi.org/10.1115/1.1849170
  11. Gurtin, M.E. and Murdoch, A.I. (1975), "A continuum theory of elastic material surfaces", Arch. Ration. Mech. Anal., 57(4), 291-323. https://doi.org/10.1007/BF00261375
  12. Gurtin, M.E. and Murdoch, A.I. (1978), "Surface stress in solids", Int. J. Solid. Struct., 14(6), 431-440. https://doi.org/10.1016/0020-7683(78)90008-2
  13. Hasheminejad, B.S.M., Gheshlaghi, B., Mirzaei, Y. and Abbasion, S. (2011), "Free transverse vibrations of cracked nanobeams with surface effects", Thin Solid Film., 519(8), 2477-2482. https://doi.org/10.1016/j.tsf.2010.12.143
  14. Ibach, H. (1997), "The role of surface stress in reconstruction, epitaxial growth and stabilization of mesoscopic structures", Surf. Sci. Rep., 29(5-6), 195-263. https://doi.org/10.1016/S0167-5729(97)00010-1
  15. Jing, G.Y., Duan, H.L., Sun, X.M., Zhang, Z.S., Xu, J., Li, Y.D., Wang, J.X. and Yu, D.P. (2006), "Surface effects on elastic properties of silver nanowires: Contact atomic-force microscopy", Phys. Rev. B, 73(23), 235409. https://doi.org/10.1103/PhysRevB.73.235409
  16. Lachut, M.J. and Sader, J.E. (2007), "Effect of surface stress on the stiffness of cantilever plates", Phys. Rev. Lett., 99(20), 206102. https://doi.org/10.1103/PhysRevLett.99.206102
  17. Langthjem, M.A. and Sugiyama, Y. (2000), "Dynamic stability of columns subjected to follower loads: A survey", J. Sound Vib., 238(5), 809-851. https://doi.org/10.1006/jsvi.2000.3137
  18. Leung, A.Y.T. (2008), "Exact spectral elements for follower tension buckling by power series", J. Sound Vib., 309(3-5), 718-729. https://doi.org/10.1016/j.jsv.2007.07.058
  19. Li, L., Li, X. and Hu, Y. (2016a), "Free vibration analysis of nonlocal strain gradient beams made of functionally graded material", Int. J. Eng. Sci., 102, 77-92. https://doi.org/10.1016/j.ijengsci.2016.02.010
  20. Li, X.F., Jiang, S.N. and Lee, K.Y. (2016b), "Surface effect on dynamic stability of microcantilevers on an elastic foundation under a subtangential follower force", Int. J. Mech. Mater. Des., doi:10.1007/s10999-016-9362-1.
  21. Li, X.F., Wang, B.L., Tang, G.J. and Lee, K.Y. (2011), "Size effect in transverse mechanical behavior of one-dimensional nanostructures", Physica E, 44(1), 207-214. https://doi.org/10.1016/j.physe.2011.08.016
  22. Li, X.F., Zhang, H. and Lee, K.Y. (2014), "Dependence of Young's modulus of nanowires on surface effect", Int. J. Mech. Sci., 81, 120-125. https://doi.org/10.1016/j.ijmecsci.2014.02.018
  23. Li, X.F., Zou, J., Jiang, S.N. and Lee, K.Y. (2016c), "Resonant frequency and flutter instability of a nanocantilever with the surface effects", Compos. Struct., 153, 645-653. https://doi.org/10.1016/j.compstruct.2016.06.065
  24. Mercan, K. and Civalek, O. (2016), "Dsc method for buckling analysis of boron nitride nanotube (BNNT) surrounded by an elastic matrix", Compos. Struct., 143, 300-309. https://doi.org/10.1016/j.compstruct.2016.02.040
  25. Mercan, K. and Civalek, O. (2017), "Buckling analysis of Silicon carbide nanotubes (SiCNTs) with surface effect and nonlocal elasticity using the method of HDQ", Compos. Part B, 114, 34-45. https://doi.org/10.1016/j.compositesb.2017.01.067
  26. Moon, W. and Hwang, H. (2008), "Atomistic study of structures and elastic properties of single crystalline ZnO nanotubes", Nanotechnol., 19(22), 225703. https://doi.org/10.1088/0957-4484/19/22/225703
  27. Mutyalarao, M., Bharathi, D. and Rao, B.N. (2013), "Dynamic stability of cantilever columns under a tip-concentrated subtangential follower force", Math. Mech. Solid., 18(5), 449-463. https://doi.org/10.1177/1081286512442436
  28. Park, H.S. (2008), "Surface stress effects on the resonant properties of silicon nanowires", J. Appl. Phys., 103(12), 123504. https://doi.org/10.1063/1.2939576
  29. Pedersen, P. (1977), "Influence of boundary conditions on the stability of a column under non-conservative load", Int. J. Solid. Struct., 13(5), 445-455. https://doi.org/10.1016/0020-7683(77)90039-7
  30. Pilkey, W.D. (1994), Formulas for Stress, Strain, and Structural Matrices, John Wiley & Sons, Inc.
  31. Shaat, M. and Mahmoud, F.F. (2015), "A new Mindlin FG plate model incorporating microstructure and surface energy effects", Struct. Eng. Mech., 53(1), 105-130. https://doi.org/10.12989/sem.2015.53.1.105
  32. Shen, J., Wu, J.X., Song, J., Li, X.F. and Lee, K.Y. (2012), "Flexural waves of carbon nanotubes based on generalized gradient elasticity", Phys. Stat. Sol. B, 249(1), 50-57. https://doi.org/10.1002/pssb.201147006
  33. Shenoy, V.B. (2005), "Atomistic calculations of elastic properties of metallic fcc crystal surfaces", Phys. Rev. B, 71(9), 094104. https://doi.org/10.1103/PhysRevB.71.094104
  34. Shi, M.X., Liu, B., Zhang, Z.Q., Zhang, Y.W. and Gao, H.J. (2012), "Direct influence of residual stress on the bending stiffness of cantilever beams", Proc. R. Soc. A, 468(2145), 2595-2613. https://doi.org/10.1098/rspa.2011.0662
  35. Sundararajan, C. (1976), "Influence of an elastic end support on the vibration and stability of Beck's column", Int. J. Mech. Sci., 18(5), 239-241. https://doi.org/10.1016/0020-7403(76)90005-9
  36. Wang, G.F. and Feng, X.Q. (2007), "Effects of surface elasticity and residual surface tension on the natural frequency of microbeams", Appl. Phys. Lett., 90(23), 231904. https://doi.org/10.1063/1.2746950
  37. Wang, J., Huang, Z., Duan, H., Yu, S., Feng, X., Wang, G., Zhang, W. and Wang, T. (2011), "Surface stress effect in mechanics of nanostructured materials", Acta Mech. Solida Sin., 24(1), 52-82. https://doi.org/10.1016/S0894-9166(11)60009-8
  38. Wang, K. and Wang, B. (2015), "Timoshenko beam model for the vibration analysis of a cracked nanobeam with surface energy", J. Vib. Control, 21(12), 2452-2464. https://doi.org/10.1177/1077546313513054
  39. Wang, K.F. and Wang, B. (2014), "Effect of surface energy on the sensing performance of bridged nanotube-based micro-mass sensors", J. Intell. Mater. Syst. Struct., 25(17), 2177-2186. https://doi.org/10.1177/1045389X13517317
  40. Wu, J.X., Li, X.F., Tang, A.Y. and Lee, K.Y. (2017), "Free and forced transverse vibration of nanowires with surface effects", J. Vib. Control, 23(13), 2064-2077. https://doi.org/10.1177/1077546315610302
  41. Xiang, Y., Wang, C.M., Kitipornchai, S. and Wang, Q. (2010), "Dynamic instability of nanorods/nanotubes subjected to an end follower force", J. Eng. Mech., 136(8), 1054-1058. https://doi.org/10.1061/(ASCE)EM.1943-7889.0000135
  42. Yao, H., Yun, G., Bai, N. and Li, J. (2012), "Surface elasticity effect on the size-dependent elastic property of nanowires", J. Appl. Phys., 111(8), 083506. https://doi.org/10.1063/1.3703671
  43. Zang, X., Zhou, Q., Chang, J., Liu, Y. and Lin, L. (2015), "Graphene and carbon nanotube (CNT) in MEMS/NEMS applications", Microelectron. Eng., 132, 192-206. https://doi.org/10.1016/j.mee.2014.10.023
  44. Zhang, Y.Q., Pang, M. and Chen, W.Q. (2015), "Transverse vibrations of embedded nanowires under axial compression with high-order surface stress effects", Physica E, 66, 238-244. https://doi.org/10.1016/j.physe.2014.10.027
  45. Zheng, X.P., Cao, Y.P., Li, B., Feng, X.Q. and Wang, G.F. (2010), "Surface effects in various bending-based test methods for measuring the elastic property of nanowires", Nanotechnol., 21(20), 205702. https://doi.org/10.1088/0957-4484/21/20/205702
  46. Zhu, J., Yang, J.S. and Ru, C.Q. (2014), "Buckling of an elastic plate due to surface-attached thin films with intrinsic stresses", Struct. Eng. Mech., 52(1), 89-95. https://doi.org/10.12989/sem.2014.52.1.089

피인용 문헌

  1. Fluid-conveying piezoelectric nanosensor: Nonclassical effects on vibration-stability analysis vol.76, pp.5, 2017, https://doi.org/10.12989/sem.2020.76.5.619