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Three-dimensional nonlocal-surface energy-based statics, dynamics, and divergence instability of movable cable-like nanostructures with arbitrary translational motion

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Abstract

Previous studies were concerned with transverse vibrations of axially moving nanowires; however, their statics as well as lateral and transverse vibrations and potential instabilities for the most general form of the translational motion in the presence of axially, laterally, and transversely distributed and pointed loads have not been explained yet. To scrutinize this interesting problem simply, but effectively, the authors develop a fairly comprehensive cable-like model for three-dimensionally moving pretensioned wire-like nanostructures in vacuum under static loads accounting for both nonlocality and surface energy. By decomposing the total deformations into the statics and dynamics parts, the continuum-based governing equations pertinent to purely linear static and dynamic states are presented for the first time. The explicit expressions of static deformations and potential divergence instability of the movable nanowire with general translation motion are displayed and discussed. Subsequently, Galerkin methodology based on admissible modes is employed for dynamic analysis of laterally loaded nanowires in the movable manner. The influences of crucial factors on the free vibration response as well as dynamic instability are investigated for various types of motions.

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References

  1. Nafari, A., Bowland, C.C., Sodano, H.A.: Ultra-long vertically aligned lead titanate nanowire arrays for energy harvesting in extreme environments. Nano Energy 31, 168–73 (2017)

    Google Scholar 

  2. Liu, X., Gao, H., Ward, J.E., Liu, X., Yin, B., Fu, T., Chen, J., Lovley, D.R., Yao, J.: Power generation from ambient humidity using protein nanowires. Nature 578, 550–4 (2020)

    Google Scholar 

  3. Zheng, G., Patolsky, F., Cui, Y., Wang, W.U., Lieber, C.M.: Multiplexed electrical detection of cancer markers with nanowire sensor arrays. Nat. Biotechnol. 23, 1294–301 (2005)

    Google Scholar 

  4. Xie, P., Xiong, Q., Fang, Y., Qing, Q., Lieber, C.M.: Local electrical potential detection of DNA by nanowire–nanopore sensors. Nat. Nanotechnol. 7, 119 (2012)

    Google Scholar 

  5. Prashanthi, K., Thundat, T.: Nanowire sensors using electrical resonance. J. Electrochem. Soc. 167, 037538 (2020)

    Google Scholar 

  6. Ghosh, R., Ghosh, J., Das, R., Mawlong, L.P., Paul, K.K., Giri, P.K.: Multifunctional Ag nanoparticle decorated Si nanowires for sensing, photocatalysis and light emission applications. J. Colloid Interface Sci. 532, 464–73 (2018)

    Google Scholar 

  7. Nateghi, M.R., Shateri-Khalilabad, M.: Silver nanowire-functionalized cotton fabric. Carbohydr. Polym. 117, 160–8 (2015)

    Google Scholar 

  8. Javey, A., Nam, S., Friedman, R.S., Yan, H., Lieber, C.M.: Layer-by-layer assembly of nanowires for three-dimensional, multifunctional electronics. Nano Lett. 7, 773–7 (2007)

    Google Scholar 

  9. Yang, C., Gu, H., Lin, W., Yuen, M.M., Wong, C.P., Xiong, M., Gao, B.: Silver nanowires: from scalable synthesis to recyclable foldable electronics. Adv. Mater. 23, 3052–6 (2011)

    Google Scholar 

  10. Liu, Z., Xu, J., Chen, D., Shen, G.: Flexible electronics based on inorganic nanowires. Chem. Soc. Rev. 44, 161–92 (2015)

    Google Scholar 

  11. Chen, X.Z., Hoop, M., Shamsudhin, N., Huang, T., Özkale, B., Li, Q., Siringil, E., Mushtaq, F., Di Tizio, L., Nelson, B.J., Pané, S.: Hybrid magnetoelectric nanowires for nanorobotic applications: fabrication, magnetoelectric coupling, and magnetically assisted in vitro targeted drug delivery. Adv. Mater. 29, 1605458 (2017)

    Google Scholar 

  12. Chen, X.Z., Hoop, M., Mushtaq, F., Siringil, E., Hu, C., Nelson, B.J., Pane, S.: Recent developments in magnetically driven micro- and nanorobots. Appl. Mater. Today 9, 37–48 (2017)

    Google Scholar 

  13. Yang, J., Zhang, C., Wang, X., Wang, W., Xi, N., Liu, L.: Development of micro-and nanorobotics: a review. Sci. China Technol. Sci. 62, 1–20 (2019)

    Google Scholar 

  14. Puigmarti-Luis, J., Pellicer, E., Jang, B., Chatzipirpiridis, G., Sevim, S., Chen, X.Z., Nelson, B.J., Pané, S.: Magnetically and chemically propelled nanowire-based swimmers. In: Magnetic Nano-and Microwires (pp. 777–99). Woodhead publishing (2020)

  15. Eringen, A.C.: Linear theory of nonlocal elasticity and dispersion of plane waves. Int. J. Eng. Sci. 10, 425–35 (1972)

    MATH  Google Scholar 

  16. Eringen, A.C.: On differential equations of nonlocal elasticity and solutions of screw dislocation and surface waves. J. Appl. Phys. 54, 4703–10 (1983)

    Google Scholar 

  17. Eringen, A.C.: Nonlocal Continuum Field Theories. Springer, New York (2002)

    MATH  Google Scholar 

  18. Demir, Ç., Civalek, Ö.: On the analysis of microbeams. Int. J. Eng. Sci. 121, 14 (2017)

    MathSciNet  MATH  Google Scholar 

  19. Jalaei, M.H., Civalek, Ö.: On dynamic instability of magnetically embedded viscoelastic porous FG nanobeam. Int. J. Eng. Sci. 143, 14 (2019)

    MathSciNet  MATH  Google Scholar 

  20. Fakher, M., Hosseini-Hashemi, S.: Nonlinear vibration analysis of two-phase local/nonlocal nanobeams with size-dependent nonlinearity by using Galerkin method. J. Vib. Control (2020). https://doi.org/10.1177/1077546320927619

    Article  Google Scholar 

  21. Barretta, R., Caporale, A., Faghidian, S.A., Luciano, R., de Sciarra, F.M., Medaglia, C.M.: A stress-driven local-nonlocal mixture model for Timoshenko nano-beams. Compos. Part B Eng. 164, 590–598 (2019)

    Google Scholar 

  22. Barretta, R., Canadija, M., de Sciarra, F.M.: Nonlocal mechanical behavior of layered nanobeams. Symmetry 12, 717 (2020)

    Google Scholar 

  23. Kiani, K., Roshan, M.: Nonlocal dynamic response of double-nanotube-systems for delivery of lagged-inertial-nanoparticles. Int. J. Mech. Sci. 152, 576–95 (2019)

    Google Scholar 

  24. Kiani, K., Soltani, S.: Nonlocal longitudinal, flapwise, and chordwise vibrations of rotary doubly coaxial/non-coaxial nanobeams as nanomotors. Int. J. Mech. Sci. 168, 105291 (2020)

    Google Scholar 

  25. Jin, L., Li, L.: Nonlinear dynamics of silicon nanowire resonator considering nonlocal effect. Nanoscale Res. Lett. 12, 331 (2017)

    Google Scholar 

  26. Uzun, B., Civalek, Ö.: Nonlocal FEM formulation for vibration analysis of nanowires on elastic matrix with different materials. Math. Comput. Appl. 24, 38 (2019)

    MathSciNet  Google Scholar 

  27. Sedighi, H.M., Malikan, M.: Stress-driven nonlocal elasticity for nonlinear vibration characteristics of carbon/boron-nitride hetero-nanotube subject to magneto-thermal environment. Phys. Scr. 95, 055218 (2020)

    Google Scholar 

  28. Ouakad, H.M., Valipour, A., Żur, K.K., Sedighi, H.M., Reddy, J.N.: On the nonlinear vibration and static deflection problems of actuated hybrid nanotubes based on the stress-driven nonlocal integral elasticity. Mech. Mater. 148, 103532 (2020)

    Google Scholar 

  29. Jankowski, P., Żur, K.K., Kim, J., Reddy, J.N.: On the bifurcation buckling and vibration of porous nanobeams. Compos. Struct. 250, 112632 (2020)

    Google Scholar 

  30. Sedighi, H.M., Malikan, M., Valipour, A., Żur, K.K.: Nonlocal vibration of carbon/boron-nitride nano-hetero-structure in thermal and magnetic fields by means of nonlinear finite element method. J. Comput. Des. Eng. 7(5), 591–602 (2020)

    Google Scholar 

  31. Shariati, A., Mohammad-Sedighi, H., Żur, K.K., Habibi, M., Safa, M.: On the vibrations and stability of moving viscoelastic axially functionally graded nanobeams. Materials 13(7), 1707 (2020)

    Google Scholar 

  32. Akgöz, B., Civalek, Ö.: A novel microstructure-dependent shear deformable beam model. Int. J. Mech. Sci. 99, 10 (2015)

    MATH  Google Scholar 

  33. Civalek, Ö., Dastjerdi, S., Akbas, S.D., Akgöz, B.: Vibration analysis of carbon nanotube-reinforced composite microbeams. Math. Methods Appl. Sci. (2021). https://doi.org/10.1002/mma.7069

    Article  Google Scholar 

  34. Lim, C.W., Li, C., Yu, J.L.: Dynamic behaviour of axially moving nanobeams based on nonlocal elasticity approach. Acta Mech. Sin. 26, 755–65 (2010)

    MathSciNet  MATH  Google Scholar 

  35. Li, C.: Nonlocal thermo-electro-mechanical coupling vibrations of axially moving piezoelectric nanobeams. Mech. Based Des. Struct. Mach. 45, 463–78 (2017)

    Google Scholar 

  36. Kiani, K.: Longitudinal, transverse, and torsional vibrations and stabilities of axially moving single-walled carbon nanotubes. Curr. Appl. Phys. 13, 1651–60 (2013)

    Google Scholar 

  37. Kiani, K.: Longitudinal and transverse instabilities of moving nanoscale beam-like structures made of functionally graded materials. Compos. Struct. 107, 610–9 (2014)

    Google Scholar 

  38. Mokhtari, A., Mirdamadi, H.R., Ghayour, M., Sarvestan, V.: Time/wave domain analysis for axially moving pre-stressed nanobeam by wavelet-based spectral element method. Int. J. Mech. Sci. 105, 58–69 (2016)

    Google Scholar 

  39. Liu, J., Li, C., Yang, C., Shen, J., Xie, F.: Dynamical responses and stabilities of axially moving nanoscale beams with time-dependent velocity using a nonlocal stress gradient theory. J. Vib. Control 23, 3327–44 (2017)

    MathSciNet  Google Scholar 

  40. Wang, J., Shen, H., Zhang, B., Liu, J., Zhang, Y.: Complex modal analysis of transverse free vibrations for axially moving nanobeams based on the nonlocal strain gradient theory. Physica E 101, 85–93 (2018)

    Google Scholar 

  41. Guo, S., He, Y., Liu, D., Lei, J., Li, Z.: Dynamic transverse vibration characteristics and vibro-buckling analyses of axially moving and rotating nanobeams based on nonlocal strain gradient theory. Microsys. Technol. 24, 963–77 (2018)

    Google Scholar 

  42. Wang, J., Shen, H.: Nonlinear vibrations of axially moving simply supported viscoelastic nanobeams based on nonlocal strain gradient theory. J. Phys. Condens. Matter 31, 485403 (2019)

    Google Scholar 

  43. Gurtin, M.E., Murdoch, A.I.: A continuum theory of elastic material surfaces. Arch. Ration. Mech. Anal. 57, 291–323 (1975)

    MathSciNet  MATH  Google Scholar 

  44. Gurtin, M.E., Murdoch, A.I.: Effect of surface stress on wave propagation in solids. J. Appl. Phys. 47, 4414–21 (1976)

    Google Scholar 

  45. Gurtin, M.E., Murdoch, A.I.: Surface stress in solids. Int. J. Solid Struct. 14, 431–40 (1978)

    MATH  Google Scholar 

  46. Wang, G.F., Feng, X.Q.: Timoshenko beam model for buckling and vibration of nanowires with surface effects. J. Phys. D Appl. Phys. 42, 155411 (2009)

    Google Scholar 

  47. Su, G.Y., Li, Y.X., Li, X.Y., Muller, R.: Free and forced vibrations of nanowires on elastic substrates. Int. J. Mech. Sci. 138, 62–73 (2018)

    Google Scholar 

  48. Wu, J.X., Li, X.F., Tang, A.Y., Lee, K.Y.: Free and forced transverse vibration of nanowires with surface effects. J. Vib. Control 23, 2064–77 (2017)

    MathSciNet  Google Scholar 

  49. Wang, B., Bi, H., Wang, Y., Ouyang, H., Deng, Z.: Nonlinear vibration of buckled nanowires on a compliant substrate. Appl. Math. Model. 79, 230–42 (2020)

    MathSciNet  MATH  Google Scholar 

  50. Lei, X., Narsu, B., Yun, G., Li, J., Yao, H.: Axial buckling and transverse vibration of ultrathin nanowires: low symmetry and surface elastic effect. J. Phys. D Appl. Phys. 49, 175305 (2016)

    Google Scholar 

  51. Yuan, Y., Xu, K., Kiani, K.: Torsional vibration of nonprismatically nonhomogeneous nanowires with multiple defects: surface energy-nonlocal-integro-based formulations. Appl. Math. Model. 82, 17–44 (2020)

    MathSciNet  MATH  Google Scholar 

  52. Dai, H.L., Zhao, D.M., Zou, J.J., Wang, L.: Surface effect on the nonlinear forced vibration of cantilevered nanobeams. Physica E 80, 25–30 (2016)

    Google Scholar 

  53. Kiani, K.: Elasto-dynamic analysis of spinning nanodisks via a surface energy-based model. J. Phys. D Appl. Phys. 49, 275306 (2016)

    Google Scholar 

  54. Ebrahimi, F., Barati, M.R.: Vibration analysis of size-dependent flexoelectric nanoplates incorporating surface and thermal effects. Mech. Adv. Mater. Struct. 25, 611–21 (2018)

    Google Scholar 

  55. Zhao, D., Liu, J., Wang, L.: Nonlinear free vibration of a cantilever nanobeam with surface effects: semi-analytical solutions. Int. J. Mech. Sci. 113, 184–95 (2016)

    Google Scholar 

  56. Xu, X.J., Deng, Z.C., Zhang, K., Meng, J.M.: Surface effects on the bending, buckling and free vibration analysis of magneto-electro-elastic beams. Acta Mech. 227, 1557–73 (2016)

    MathSciNet  MATH  Google Scholar 

  57. Uzun, B., Civalek, Ö.: Nonlocal FEM formulation for vibration analysis of nanowires on elastic matrix with different materials. Math. Comput. Appl. 24, 38 (2019)

    MathSciNet  Google Scholar 

  58. Kiani, K.: Divergence and flutter instabilities of nanobeams in moving state accounting for surface and shear effects. Math. Comput. Appl. 77, 2764–85 (2019)

    MathSciNet  MATH  Google Scholar 

  59. Aichun, L., Kiani, K.: Bilaterally flexural vibrations and instabilities of moving piezoelectric nanowires with surface effect. Eur. Phys. J. Plus 135, 191 (2020)

    Google Scholar 

  60. Nelson, B.J., Peyer, K.E.: Micro-and nanorobots swimming in heterogeneous liquids. ACS Nano 8(9), 8718–8724 (2014)

    Google Scholar 

  61. Chen, X.Z., Hoop, M., Mushtaq, F., Siringil, E., Hu, C., Nelson, B.J., Pane, S.: Recent developments in magnetically driven micro-and nanorobots. Appl. Mater. Today 9, 37–48 (2017)

    Google Scholar 

  62. Wu, Z., Chen, Y., Mukasa, D., Pak, O.S., Gao, W.: Medical micro/nanorobots in complex media. Chem. Soc. Rev. 49(22), 8088–8112 (2020)

    Google Scholar 

  63. Wang, W., Wu, Z., He, Q.: Swimming nanorobots for opening a cell membrane mechanically. View 1(3), 20200005 (2020)

    Google Scholar 

  64. Al-Yasiri, M.S., Al-Sallami, W.T.: How the drilling fluids can be made more efficient by using nanomaterials. Am. J. Nano Res. Appl. 3(3), 41–45 (2015)

    Google Scholar 

  65. Sajjadian, M., Sajjadian, V.A., Rashidi, A.: Experimental evaluation of nanomaterials to improve drilling fluid properties of water-based muds HP/HT applications. J. Petrol. Sci. Eng. 190, 107006 (2020)

    Google Scholar 

  66. Shahnazar, S., Bagheri, S., Abd Hamid, S.B.: Enhancing lubricant properties by nanoparticle additives. Int. J. Hydrog. Energy 41(4), 3153–3170 (2016)

    Google Scholar 

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

    Google Scholar 

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  1. Department of Civil Engineering, K.N. Toosi University of Technology, Valiasr Ave., P.O. Box 15875-4416, Tehran, Iran

    Keivan Kiani & Mahdi Efazati

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  1. Keivan Kiani
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  2. Mahdi Efazati
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Correspondence to Keivan Kiani.

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Dedicated to the honorable memory of my beloved mother, Kobra Ahmadi (1950-July 21, 2020).

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Kiani, K., Efazati, M. Three-dimensional nonlocal-surface energy-based statics, dynamics, and divergence instability of movable cable-like nanostructures with arbitrary translational motion. Arch Appl Mech 91, 3095–3123 (2021). https://doi.org/10.1007/s00419-021-01955-9

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