Skip to main content
SpringerLink
Log in

Vibration suppression of a boron nitride nanotube under a moving nanoparticle using a classical optimal control procedure

  • Original Article
  • Published:
Continuum Mechanics and Thermodynamics Aims and scope Submit manuscript

Abstract

The current research investigates the vibration of single-walled boron nitride nanotube (SWBNNT) induced by a moving nanoparticle. In order to decrease the forced vibration of SWBNNT under a moving nanoparticle, a linear classical optimal control procedure is used to manipulate the movement of a nanoparticle as a drug material inside a nano-structure with consideration of various size-dependent procedures based on Rayleigh beam model. The Pasternak substrate is utilized to model the elastic medium. Hamilton, Galerkin and Newmark methods are also employed to solve the motion equations. Different size-dependent beam theories have been considered, such as the classical beam theory, nonlocal beam theory, strain gradient beam theory and nonlocal strain gradient beam theory, in order to reveal small-scale effects. The effects of the small length scale considered herein, the velocity of a moving nanoparticle, electrical potential field, the number of vibration modes and actuators and also resultant control force on the vibration behavior of the SWBNNT are investigated in detail.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Fig. 1
Fig. 2
Fig. 3
Fig. 4
Fig. 5
Fig. 6
Fig. 7

Similar content being viewed by others

References

  1. Ciofani, G., Danti, S., D’Alessandro, D., Moscato, S., Menciassi, A.: Assessing cytotoxicity of boron nitride nanotubes: interference with the MTT assay. Biochem. Biophys. Res. Commun. 394(2), 405–411 (2010)

    Google Scholar 

  2. Bianco, A., Kostarelos, K., Prato, M.: Applications of carbon nanotubes in drug delivery. Curr. Opin. Chem. Biol. 9, 674–679 (2005)

    Google Scholar 

  3. Hilder, T.A., Hill, J.M.: Carbon nanotubes as drug delivery nanocapsules. Curr. Appl. Phys. 8, 258–261 (2008)

    ADS  Google Scholar 

  4. Holt, J.K., et al.: Fast mass transport through sub-2-nanometer carbon nanotubes. Science 312(5776), 1034–1037 (2006)

    ADS  Google Scholar 

  5. Simsek, M.: Dynamic analysis of an embedded microbeam carrying a moving microparticle based on the modified couple stress theory. Int. J. Eng. Sci. 48, 1721–1732 (2010)

    MATH  Google Scholar 

  6. Simsek, M.: Nonlocal effects in the forced vibration of an elastically connected double-carbon nanotube system under a moving nanoparticle. Comput. Mat. Sci. 50, 2112–2123 (2011)

    Google Scholar 

  7. Kiani, K.: Longitudinal and transverse vibration of a single-walled carbon nanotube subjected to a moving nanoparticle accounting for both nonlocal and inertial effects. Physica E 42(9), 2391–2401 (2010)

    ADS  Google Scholar 

  8. Kiani, K., Mehri, B.: Assessment of nanotube structures under a moving nanoparticle using nonlocal beam theories. J. Sound Vib. 329, 2241–2264 (2010)

    ADS  Google Scholar 

  9. Kiani, K.: Nanoparticle delivery via stocky single-walled carbon nanotubes: a nonlinear-nonlocal continuum-based scrutiny. Compos. Struct. 116, 254–272 (2014)

    ADS  Google Scholar 

  10. Kiani, K.: Nonlinear vibrations of a single-walled carbon nanotube for delivering of nanoparticles. Nonlinear Dyn. 76(4), 1885–1903 (2014)

    MathSciNet  MATH  Google Scholar 

  11. Kiani, K., Nikkhoo, A., Mehri, B.: Prediction capabilities of classical and shear deformable beam models excited by a moving mass. J. Sound Vib. 320(3), 632–648 (2009)

    ADS  Google Scholar 

  12. Kiani, K.: Application of nonlocal beam models to double-walled carbon nanotubes under a moving nanoparticle. Part I: theoretical formulations. Acta Mech. 216, 165–195 (2011)

    MATH  Google Scholar 

  13. Kiani, K.: Application of nonlocal beam models to double-walled carbon nanotubes under a moving nanoparticle. Part II: parametric study. Acta Mech. 216, 197–206 (2011)

    MATH  Google Scholar 

  14. Kiani, K.: Vibrations of biaxially tensioned-embedded nanoplates for nanoparticle delivery. Indian J. Sci. Technol. 6(7), 4894–4902 (2013)

    Google Scholar 

  15. Eringen, A.C.: On differential equations of nonlocal elasticity and solutions of screw dislocation and surface waves. J. Appl. Phys. 54(9), 4703–4710 (1983)

    ADS  Google Scholar 

  16. Eringen, A.C.: Linear theory of nonlocal elasticity and dispersion of plane waves. Int. J. Eng. Sci. 10(5), 425–435 (1972)

    MathSciNet  MATH  Google Scholar 

  17. Ghorbanpour Arani, A., Roudbari, M.A., Kiani, K.: Vibration of double-walled carbon nanotubes coupled by temperature-dependent medium under a moving nanoparticle with multi physical fields. Mech. Adv. Mater. Struct. 23, 281–291 (2016)

    Google Scholar 

  18. Nikkhoo, A., Zolfaghari, S., Kiani, K.: A simplified-nonlocal model for transverse vibration of nanotubes acted upon by a moving nanoparticle. J. Braz. Soc. Mech. Sci. Eng. 39(12), 4929–4941 (2017)

    Google Scholar 

  19. Barati, M.R.: Dynamic response of porous functionally graded material nanobeams subjected to moving nanoparticle based on nonlocal strain gradient theory. Mater. Res. Express 4, 115017 (2017)

    ADS  Google Scholar 

  20. Ghorbanpour Arani, A., Roudbari, M.A., Amir, S.: Nonlocal vibration of SWBNNT embedded in bundle of CNTs under a moving nanoparticle. Phys. B 452, 3646–3653 (2014)

    Google Scholar 

  21. Ghorbanpour Arani, A., Roudbari, M.A.: Surface stress, initial stress and Knudsen-dependent flow velocity effects on the electro-thermo nonlocal wave propagation of SWBNNTs. Phys. B 452, 159–165 (2014)

    ADS  Google Scholar 

  22. Nejadsadeghi, N., Placidi, L., Romeo, M., Misra, A.: Frequency band gaps in dielectric granular metamaterials modulated by electric field. Mech. Res. Commun. 95, 96–103 (2019)

    Google Scholar 

  23. Sung, Y.G.: Modeling and control with piezo-actuators for a simply supported beam under a moving mass. J. Sound Vib. 250(4), 617–626 (2002)

    ADS  Google Scholar 

  24. Pirmohammadi, A.A., Pourseifi, M., Rahmani, O., Hoseini, S.A.H.: Modeling and active vibration suppression of a single-walled carbon nanotube subjected to a moving harmonic load based on a nonlocal elasticity theory. Appl. Phys. A 117, 1547–1555 (2014)

    Google Scholar 

  25. Pourseifi, M., Rahmani, O., Hoseini, S.A.H.: Active vibration control of nanotube structures under a moving nanoparticle based on the nonlocal continuum theories. Meccanica 50(5), 1351–1369 (2015)

    MathSciNet  MATH  Google Scholar 

  26. Kiani, K., Wang, Q.: On the interaction of a single-walled carbon nanotube with a moving nanoparticle using nonlocal Rayleigh, Timoshenko, and higher-order beam theories. Eur. J. Mech. A Solids 31, 179–202 (2012)

    ADS  MathSciNet  MATH  Google Scholar 

  27. Ghorbanpour Arani, A., Roudbari, M.A.: Nonlocal piezoelastic surface effect on the vibration of visco-Pasternak coupled boron nitride nanotube system under a moving nanoparticle. Thin Solid Films 542(2), 232–241 (2013)

    ADS  Google Scholar 

  28. Ghorbanpour Arani, A., Hafizi Bidgoli, A., Karamali Ravandi, A., Roudbari, M.A., Amir, S., Azizkhani, M.B.: Induced nonlocal electric wave propagation of boron nitride nanotubes. J. Mech. Sci. Technol. 27(10), 3063–3071 (2013)

    Google Scholar 

  29. Ghorbanpour Arani, A., Jalilvand, A., Ghaffari, M., Talebi Mazraehshahi, M., Kolahchi, R., Roudbari, M.A., Amir, S.: Nonlinear pull-in instability of boron nitride nano-switches considering electrostatic and Casimir forces. Scientia Iranica F 21(3), 1183–1196 (2014)

    Google Scholar 

  30. Ghorbanpour Arani, A., Karamali Ravandi, A., Roudbari, M.A., Azizkhani, M.B., Hafizi Bidgoli, A.: Axial and transverse vibration of SWBNNT system coupled Pasternak foundation under a moving nanoparticle using Timoshenko beam theory. J. Solid Mech. 7(3), 239–254 (2015)

    Google Scholar 

  31. Ghorbanpour Arani, A., Roudbari, M.A., Amir, S.: Longitudinal magnetic field effect on wave propagation of fluid-conveyed SWCNT using Knudsen number and surface considerations. Appl. Math. Modell. 40(3), 2025–2038 (2016)

    MathSciNet  Google Scholar 

  32. Roudbari, M.A., Doroudgar Jorshari, T.: Vibrational control scrutiny of physically affected SWCNT acted upon by a moving nanoparticle in the framework of nonlocal-strain gradient theory. J. Braz. Soc. Mech. Sci. Eng. 40(499), 1–16 (2018)

    Google Scholar 

  33. dell’Isola, F., Andreaus, U., Placidi, L.: At the origins and in the vanguard of peridynamics, non-local and higher-gradient continuum mechanics: an underestimated and still topical contribution of Gabrio Piola. Math. Mech. Solids 20(8), 887–928 (2015)

    MathSciNet  MATH  Google Scholar 

  34. AminPour, H., Rizzi, N.: A one-dimensional continuum with microstructure for single-wall carbon nanotubes bifurcation analysis. Math. Mech. Solids 21(2), 168–181 (2016)

    MathSciNet  MATH  Google Scholar 

  35. Luongo, A., Piccardo, G.: Dynamics of taut strings traveled by train of forces. Contin. Mech. Therm. 28(1–2), 603–616 (2016)

    MathSciNet  MATH  Google Scholar 

  36. Li, L., Hu, Y., Li, X.: Longitudinal vibration of size-dependent rods via nonlocal strain gradient theory. Int. J. Mech. Sci. 115, 135–144 (2016)

    Google Scholar 

  37. Lim, C.W., Zhang, G., Reddy, J.N.: A higher-order nonlocal elasticity and strain gradient theory and its applications in wave propagation. J. Mech. Phys. Solids 78, 298–313 (2015)

    ADS  MathSciNet  MATH  Google Scholar 

  38. Li, L., Hu, Y.: Buckling analysis of size-dependent nonlinear beams based on a nonlocal strain gradient theory. Int. J. Eng. Sci. 97, 84–94 (2015)

    MathSciNet  MATH  Google Scholar 

  39. Li, L., Hu, Y.: Wave propagation in fluid-conveying viscoelastic carbon nanotubes based on nonlocal strain gradient theory. Comput. Mat. Sci. 112, 282–288 (2016)

    Google Scholar 

  40. Li, L., Hu, Y., Ling, L.: Wave propagation in viscoelastic single-walled carbon nanotubes with surface effect under magnetic field based on nonlocal strain gradient theory. Physica E 75, 118–124 (2016)

    ADS  Google Scholar 

  41. Bagheri, A., Roudbari, M.A., Mahmoudabadi, M.J.: Adaptive and sliding mode control for non-linear systems. Int. J. Adv. Des. Manuf. Technol. 3(4), 57–62 (2010)

    Google Scholar 

  42. Burl, J.B.: Linear Optimal Control: H (2) and H (Infinity) Methods. Addison-Wesley, Boston (1998)

    Google Scholar 

  43. Nikkhoo, A., Rofooei, F.R., Shadnam, M.R.: Dynamic behavior and modal control of beams under moving mass. J. Sound Vib. 306, 712–724 (2007)

    ADS  MathSciNet  Google Scholar 

  44. Panchal, M.B., Upadhyay, S.H.: Boron nitride nanotube-based mass sensing of zeptogram scale. Spectrosc. Lett. 48(1), 17–21 (2015)

    Google Scholar 

  45. Adhikari, S.: Boron Nitride Nanotubes in Nanomedicine. A Volume in Micro and Nano Technologies, pp. 149–164. Elsevier, Amsterdam (2016)

    Google Scholar 

  46. Roudbari, M.A., Ansari, R.: Single-walled boron nitride nanotube as nano-sensor. Contin. Mech. Thermodyn. (2018). https://doi.org/10.1007/s00161-018-0719-6

    Article  Google Scholar 

  47. Barchiesi, E., Spagnuolo, M., Placidi, L.: Mechanical metamaterials: a state of the art. Math. Mech. Solids 24(1), 212–234 (2019)

    MathSciNet  Google Scholar 

  48. Milton, G., Briane, M., Harutyunyan, D.: On the possible effective elasticity tensors of 2-dimensional and 3-dimensional printed materials. Math. Mech. Complex Syst. 5(1), 41–94 (2017)

    MathSciNet  MATH  Google Scholar 

  49. Abd-alla, A.E.N.N., Alshaikh, F., Del Vescovo, D., Spagnuolo, M.: Plane waves and eigenfrequency study in a transversely isotropic magneto-thermoelastic medium under the effect of a constant angular velocity. J. Therm. Stresses 40(9), 1079–1092 (2017)

    Google Scholar 

  50. Altenbach, J., Altenbach, H., Eremeyev, V.A.: On generalized Cosserat-type theories of plates and shells: a short review and bibliography. Arch. Appl. Mech. 80(1), 73–92 (2010)

    ADS  MATH  Google Scholar 

  51. Eremeyev, V., Zubov, L.: On constitutive inequalities in nonlinear theory of elastic shells. Z. Angew. Math. Mech. 87(2), 94–101 (2007)

    MathSciNet  MATH  Google Scholar 

  52. Abdoul-Anziz, H., Seppecher, P.: Strain gradient and generalized continua obtained by homogenizing frame lattices. Math. Mech. Complex Syst. 6(3), 213–250 (2018)

    MathSciNet  MATH  Google Scholar 

  53. Misra, A., Poorsolhjouy, P.: Identification of higher-order elastic constants for grain assemblies based upon granular micromechanics. Math. Mech. Complex Syst. 3(3), 285–308 (2015)

    MathSciNet  MATH  Google Scholar 

  54. Alibert, J.J., Seppecher, P., dell’Isola, F.: Truss modular beams with deformation energy depending on higher displacement gradients. Math. Mech. Solids 8(1), 51–73 (2003)

    MathSciNet  MATH  Google Scholar 

  55. Spagnuolo, M., Andreaus, U.: A targeted review on large deformations of planar elastic beams: extensibility, distributed loads, buckling and post-buckling. Math. Mech. Solids 24(1), 258–280 (2019)

    MathSciNet  Google Scholar 

  56. Barchiesi, E., dell’Isola, F., Laudato, M., Placidi, L., Seppecher, P.: A 1D continuum model for beams with pantographic microstructure: asymptotic micro-macro identification and numerical results. In: dell’Isola, F., Eremeyev, V., Porubov, A. (eds.) Advances in Mechanics of Microstructured Media and Structures, vol. 87, pp. 43–74. Springer, Cham (2018) https://doi.org/10.1007/978-3-319-73694-5_4

    Google Scholar 

  57. Niiranen, J., Balobanov, V., Kiendl, J., Hosseini, S.B.: Variational formulations, model comparisons and numerical methods for Euler–Bernoulli micro-and nano-beam models. Math. Mech. Solids 24(1), 312–335 (2019)

    MathSciNet  Google Scholar 

  58. Eremeyev, V.A., Morozov, N.F.: The effective stiffness of a nanoporous rod. In: Doklady Physics, vol. 55(6), pp. 279–282. SP MAIK Nauka/Interperiodica (2010)

  59. Altenbach, H., Bîrsan, M., Eremeyev, V.A.: On a thermodynamic theory of rods with two temperature fields. Acta Mech. 223(8), 1583–1596 (2012)

    MathSciNet  MATH  Google Scholar 

  60. Andreaus, U., Spagnuolo, M., Lekszycki, T., Eugster, S.R.: A Ritz approach for the static analysis of planar pantographic structures modeled with nonlinear Euler–Bernoulli beams. Contin. Mech. Thermodyn. 30(5), 1103–1123 (2018)

    ADS  MathSciNet  MATH  Google Scholar 

  61. Franciosi, P., Spagnuolo, M., Salman, O.U.: Mean Green operators of deformable fiber networks embedded in a compliant matrix and property estimates. Contin. Mech. Thermodyn. 31(1), 101–132 (2019)

    ADS  MathSciNet  Google Scholar 

  62. Khakalo, S., Balobanov, V., Niiranen, J.: Modelling size-dependent bending, buckling and vibrations of 2d triangular lattices by strain gradient elasticity models: applications to sandwich beams and auxetics. Int. J. Eng. Sci. 127, 33–52 (2018)

    MathSciNet  MATH  Google Scholar 

  63. Giorgio, I., dell’Isola, F., Steigmann, D.J.: Axisymmetric deformations of a 2nd grade elastic cylinder. Mech. Res. Commun. 94, 45–48 (2018)

    Google Scholar 

  64. Placidi, L., Barchiesi, E., Turco, E., Rizzi, N.L.: A review on 2D models for the description of pantographic fabrics. Z. Angew. Math. Phys. 67(5), 121 (2016)

    MathSciNet  MATH  Google Scholar 

  65. Placidi, L., Greco, L., Bucci, S., Turco, E., Rizzi, N.L.: A second gradient formulation for a 2D fabric sheet with inextensible fibres. Z. Angew. Math. Phys. 67(5), 114 (2016)

    MathSciNet  MATH  Google Scholar 

  66. Giorgio, I., dell’Isola, F., Steigmann, D.J.: Edge effects in Hypar nets. Comptes Rendus - Mécanique 347, 114–123 (2019). https://doi.org/10.1016/j.crme.2019.01.003

    Article  ADS  Google Scholar 

  67. Altenbach, H., Eremeyev, V.A.: On the effective stiffness of plates made of hyperelastic materials with initial stresses. Int. J. Nonlinear Mech. 45(10), 976–981 (2010)

    ADS  Google Scholar 

  68. Barchiesi, E., Ganzosch, G., Liebold, C., Placidi, L., Grygoruk, R., Müller, W.H.: Out-of-plane buckling of pantographic fabrics in displacement-controlled shear tests: experimental results and model validation. Contin. Mech. Thermodyn. 31(1), 33–45 (2019)

    ADS  MathSciNet  Google Scholar 

  69. Giorgio, I., Rizzi, N.L., Turco, E.: Continuum modelling of pantographic sheets for out-of-plane bifurcation and vibrational analysis. Proc. R. Soc. Lond. A 473(2207), 21 (2017). https://doi.org/10.1098/rspa.2017.0636

    Article  MathSciNet  MATH  Google Scholar 

  70. De Angelo, M., Barchiesi, E., Giorgio, I., Abali, B.E.: Numerical identification of constitutive parameters in reduced order bi-dimensional models for pantographic structures: application to out-of-plane buckling. Appl. Mech. Arch. (2019). https://doi.org/10.1007/s00419-018-01506-9

    Article  Google Scholar 

  71. Avella, M., Dell’Erba, R., Martuscelli, E., Partch, R.: Thermosetting based composites reinforced with silicon carbide whiskers. J. Polym. Mater. 7, 443–456 (2000)

    Google Scholar 

  72. Yildizdag, M.E., Demirtas, M., Ergin, A.: Multipatch discontinuous Galerkin isogeometric analysis of composite laminates. Contin. Mech. Thermodyn. (2018). https://doi.org/10.1007/s00161-018-0696-9

  73. Franciosi, P., Lebail, H.: Anisotropy features of phase and particle spatial pair distributions in various matrix/inclusions structures. Acta Mater. 52(10), 3161–3172 (2004)

    Google Scholar 

  74. Baroudi, D., Giorgio, I., Battista, A., Turco, E., Igumnov, L.A.: Nonlinear dynamics of uniformly loaded elastica: experimental and numerical evidence of motion around curled stable equilibrium configurations. ZAMM - Zeitschrift für Angewandte Mathematik und Mechanik (2019). https://doi.org/10.1002/zamm.201800121

    Article  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Faculty of Mechanical Engineering, Islamic Azad University, Takestan, Qazvin, Iran

    Tahereh Doroudgar Jorshari

  2. Department of Mechanical Engineering, University of Guilan, P.O. Box 3756, Rasht, Iran

    Mir Abbas Roudbari

  3. International Research Center M&MoCS, Università degli studi dell’Aquila, L’Aquila, Italy

    Daria Scerrato

  4. School of Engineering, Deakin University, Geelong, VIC, 3216, Australia

    Abbas Kouzani

Authors
  1. Tahereh Doroudgar Jorshari
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Mir Abbas Roudbari
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Daria Scerrato
    View author publications

    You can also search for this author in PubMed Google Scholar

  4. Abbas Kouzani
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Daria Scerrato.

Additional information

Communicated by Prof. Victor Eremeyev and Prof. Holm Altenbach.

Publisher's Note

Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Jorshari, T.D., Roudbari, M.A., Scerrato, D. et al. Vibration suppression of a boron nitride nanotube under a moving nanoparticle using a classical optimal control procedure. Continuum Mech. Thermodyn. 31, 1825–1842 (2019). https://doi.org/10.1007/s00161-019-00813-y

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s00161-019-00813-y

Keywords

Search

Navigation