Skip to main content
Top

27-04-2024 | Original Paper

Nonlocal stability of curved carbon nanotubes conveying fluid based on Eringen’s nonlocal elasticity theory in a thermomagnetic environment

Authors: Hossein Ramezani, Majid Haji Ali Koohpayeh, Alireza Tajedini, Ghazaleh Ramezani, Amirhossein Mohseni

Published in: Acta Mechanica

Login to get access

Activate our intelligent search to find suitable subject content or patents.

search-config
loading …

Abstract

Curved carbon nanotubes (CCNT) can exhibit both in-plane and out-of-plane vibrations, and their curvature can give rise to additional vibrational modes. The vibrational modes of CCNT can be influenced by various factors, including diameter, chirality and curvature. In this study, in-plane and out-of-plane vibration and stability of CCNT conveying fluid are carried out using nonlocal elasticity and Euler–Bernoulli beam theory. Additionally, to improve the system's stability, a model of Kelvin–Voigt has been used to form an enclosed elastic medium. The inextensibility of the tube is assumed to extract the in-plane and out-of-plane nonlocal equations of motion and boundary conditions, solved by a numerical solution to obtain the natural frequencies of the CCNT. The purpose of this study is to investigate the influence of different parameters, including nonlocal parameters, temperature changes, magnetic field intensity and fluid velocity on the in-plane and out-of-plane stability of CCNT. The results show that the critical flow velocity decreases by increasing the thermal loading through which the stable zone is reduced. Also, by comparing the stable zone of the classic and nonlocal continuum theories, one can conclude that the largest stable zone is associated with the nonlocal elasticity.
Literature
1.
go back to reference Wang, J., et al.: Large π-extended and curved carbon nanorings as carbon nanotube segments. Acc. Chem. Res. 54(22), 4178–4190 (2021)CrossRef Wang, J., et al.: Large π-extended and curved carbon nanorings as carbon nanotube segments. Acc. Chem. Res. 54(22), 4178–4190 (2021)CrossRef
2.
go back to reference Kleinherbers, E., Stegmann, T., Szpak, N.: Electronic transport in bent carbon nanotubes. Phys. Rev. B 107(19), 195424 (2023)CrossRef Kleinherbers, E., Stegmann, T., Szpak, N.: Electronic transport in bent carbon nanotubes. Phys. Rev. B 107(19), 195424 (2023)CrossRef
3.
go back to reference Malikan, M., et al.: Dynamic modeling of non-cylindrical curved viscoelastic single-walled carbon nanotubes based on the second gradient theory. Mater. Res. Express 6, 075041 (2019)CrossRef Malikan, M., et al.: Dynamic modeling of non-cylindrical curved viscoelastic single-walled carbon nanotubes based on the second gradient theory. Mater. Res. Express 6, 075041 (2019)CrossRef
4.
go back to reference Çoban Kayıkçı, F., Köşker, R.: Stress distribution in an elastic body with a locally curved double-walled carbon nanotube. J. Braz. Soc. Mech. Sci. Eng. 43, 1–16 (2021)CrossRef Çoban Kayıkçı, F., Köşker, R.: Stress distribution in an elastic body with a locally curved double-walled carbon nanotube. J. Braz. Soc. Mech. Sci. Eng. 43, 1–16 (2021)CrossRef
5.
go back to reference Hosseini, M., Dini, A., Eftekhari, M.: Strain gradient effects on the thermoelastic analysis of a functionally graded micro-rotating cylinder using generalized differential quadrature method. Acta Mech. 228(5), 1563–1580 (2017)MathSciNetCrossRef Hosseini, M., Dini, A., Eftekhari, M.: Strain gradient effects on the thermoelastic analysis of a functionally graded micro-rotating cylinder using generalized differential quadrature method. Acta Mech. 228(5), 1563–1580 (2017)MathSciNetCrossRef
6.
go back to reference Dini, A., et al.: Size-dependent analysis of a functionally graded piezoelectric micro-cylinder based on the strain gradient theory with the consideration of flexoelectric effect: plane strain problem. J. Braz. Soc. Mech. Sci. Eng. 42(8), 410 (2020)CrossRef Dini, A., et al.: Size-dependent analysis of a functionally graded piezoelectric micro-cylinder based on the strain gradient theory with the consideration of flexoelectric effect: plane strain problem. J. Braz. Soc. Mech. Sci. Eng. 42(8), 410 (2020)CrossRef
7.
go back to reference Karami, H., Farid, M.: A new formulation to study in-plane vibration of curved carbon nanotubes conveying viscous fluid. J. Vib. Control 21, 2360–2371 (2015)MathSciNetCrossRef Karami, H., Farid, M.: A new formulation to study in-plane vibration of curved carbon nanotubes conveying viscous fluid. J. Vib. Control 21, 2360–2371 (2015)MathSciNetCrossRef
8.
go back to reference Eshraghi, I., Jalali, S.K., Pugno, N.M.: Imperfection sensitivity of nonlinear vibration of curved single-walled carbon nanotubes based on nonlocal Timoshenko beam theory. Materials (Basel) 9(9), 786 (2016)CrossRef Eshraghi, I., Jalali, S.K., Pugno, N.M.: Imperfection sensitivity of nonlinear vibration of curved single-walled carbon nanotubes based on nonlocal Timoshenko beam theory. Materials (Basel) 9(9), 786 (2016)CrossRef
9.
go back to reference Dini, A., Hosseini, M., Nematollahi, M.A.: On the size-dependent dynamics of curved single-walled carbon nanotubes conveying fluid based on nonlocal theory. Acta Mech. 232, 4729–4745 (2021)MathSciNetCrossRef Dini, A., Hosseini, M., Nematollahi, M.A.: On the size-dependent dynamics of curved single-walled carbon nanotubes conveying fluid based on nonlocal theory. Acta Mech. 232, 4729–4745 (2021)MathSciNetCrossRef
10.
11.
go back to reference Wang, S., et al.: A size-dependent quasi-3D model for bending and buckling of porous functionally graded curved nanobeam. Int. J. Eng. Sci. 193, 103962 (2023)MathSciNetCrossRef Wang, S., et al.: A size-dependent quasi-3D model for bending and buckling of porous functionally graded curved nanobeam. Int. J. Eng. Sci. 193, 103962 (2023)MathSciNetCrossRef
12.
go back to reference Malikan, M., Eremeyev, V.A., Sedighi, H.M.: Buckling analysis of a non-concentric double-walled carbon nanotube. Acta Mech. 231(12), 5007–5020 (2020)MathSciNetCrossRef Malikan, M., Eremeyev, V.A., Sedighi, H.M.: Buckling analysis of a non-concentric double-walled carbon nanotube. Acta Mech. 231(12), 5007–5020 (2020)MathSciNetCrossRef
13.
go back to reference Ebrahimi, F., Salari, E.: Thermo-mechanical vibration analysis of a single-walled carbon nanotube embedded in an elastic medium based on higher-order shear deformation beam theory. J. Mech. Sci. Technol. 29, 3797–3803 (2015)CrossRef Ebrahimi, F., Salari, E.: Thermo-mechanical vibration analysis of a single-walled carbon nanotube embedded in an elastic medium based on higher-order shear deformation beam theory. J. Mech. Sci. Technol. 29, 3797–3803 (2015)CrossRef
14.
go back to reference Nematollahi, M.A., Dini, A., Hosseini, M.: Thermo-magnetic analysis of thick-walled spherical pressure vessels made of functionally graded materials. Appl. Math. Mech. 40(6), 751–766 (2019)MathSciNetCrossRef Nematollahi, M.A., Dini, A., Hosseini, M.: Thermo-magnetic analysis of thick-walled spherical pressure vessels made of functionally graded materials. Appl. Math. Mech. 40(6), 751–766 (2019)MathSciNetCrossRef
15.
go back to reference Dini, A., Abolbashari, M.H.: Hygro-thermo-electro-elastic response of a functionally graded piezoelectric cylinder resting on an elastic foundation subjected to non-axisymmetric loads. Int. J. Press. Vessels Pip. 147, 21–40 (2016)CrossRef Dini, A., Abolbashari, M.H.: Hygro-thermo-electro-elastic response of a functionally graded piezoelectric cylinder resting on an elastic foundation subjected to non-axisymmetric loads. Int. J. Press. Vessels Pip. 147, 21–40 (2016)CrossRef
16.
go back to reference Hosseini, M., Dini, A.: Magneto-thermo-elastic response of a rotating functionally graded cylinder. Struct. Eng. Mech. Int. J. 56(1), 137–156 (2015)CrossRef Hosseini, M., Dini, A.: Magneto-thermo-elastic response of a rotating functionally graded cylinder. Struct. Eng. Mech. Int. J. 56(1), 137–156 (2015)CrossRef
17.
go back to reference Dini, A., Nematollahi, M.A., Hosseini, M.: Analytical solution for magneto-thermo-elastic responses of an annular functionally graded sandwich disk by considering internal heat generation and convective boundary condition. J. Sandwich Struct. Mater. 23(2), 542–567 (2019)CrossRef Dini, A., Nematollahi, M.A., Hosseini, M.: Analytical solution for magneto-thermo-elastic responses of an annular functionally graded sandwich disk by considering internal heat generation and convective boundary condition. J. Sandwich Struct. Mater. 23(2), 542–567 (2019)CrossRef
18.
go back to reference Dini, A., Zandi-Baghche-Maryam, A., Shariati, M.: Effects of van der Waals forces on hygro-thermal vibration and stability of fluid-conveying curved double-walled carbon nanotubes subjected to external magnetic field. Physica E 106, 156–169 (2019)CrossRef Dini, A., Zandi-Baghche-Maryam, A., Shariati, M.: Effects of van der Waals forces on hygro-thermal vibration and stability of fluid-conveying curved double-walled carbon nanotubes subjected to external magnetic field. Physica E 106, 156–169 (2019)CrossRef
19.
go back to reference Zandi-Baghche-Maryam, A., Dini, A., Hosseini, M.: Wave propagation analysis of inhomogeneous multi-nanoplate systems subjected to a thermal field considering surface and flexoelectricity effects. Waves Random Complex Media 2, 1–28 (2022)CrossRef Zandi-Baghche-Maryam, A., Dini, A., Hosseini, M.: Wave propagation analysis of inhomogeneous multi-nanoplate systems subjected to a thermal field considering surface and flexoelectricity effects. Waves Random Complex Media 2, 1–28 (2022)CrossRef
20.
go back to reference Ninh, D.G., Tien, N.D.: Investigation for electro-thermo-mechanical vibration of nanocomposite cylindrical shells with an internal fluid flow. Aerosp. Sci. Technol. 92, 501–519 (2019)CrossRef Ninh, D.G., Tien, N.D.: Investigation for electro-thermo-mechanical vibration of nanocomposite cylindrical shells with an internal fluid flow. Aerosp. Sci. Technol. 92, 501–519 (2019)CrossRef
21.
go back to reference Soltani, P., Dastjerdi, H.A., Farshidianfar, A.: Thermo-Mechanical Vibration of a Single-Walled Carbon Nanotube Embedded in a Pasternak Medium Based on Nonlocal Elasticity Theory. Citeseer (2010) Soltani, P., Dastjerdi, H.A., Farshidianfar, A.: Thermo-Mechanical Vibration of a Single-Walled Carbon Nanotube Embedded in a Pasternak Medium Based on Nonlocal Elasticity Theory. Citeseer (2010)
22.
go back to reference Russillo, A.F., et al.: On the dynamics of 3D nonlocal solids. Int. J. Eng. Sci. 180, 103742 (2022)CrossRef Russillo, A.F., et al.: On the dynamics of 3D nonlocal solids. Int. J. Eng. Sci. 180, 103742 (2022)CrossRef
23.
go back to reference Dastjerdi, S., et al.: On the deformation and frequency analyses of SARS-CoV-2 at nanoscale. Int. J. Eng. Sci. 170, 103604 (2022)MathSciNetCrossRef Dastjerdi, S., et al.: On the deformation and frequency analyses of SARS-CoV-2 at nanoscale. Int. J. Eng. Sci. 170, 103604 (2022)MathSciNetCrossRef
24.
go back to reference Malikan, M., SadraeeFar, M.N.: Differential quadrature method for dynamic buckling of graphene sheet coupled by a viscoelastic medium using neperian frequency based on nonlocal elasticity theory. J. Appl. Comput. Mech. 4(3), 147–160 (2018) Malikan, M., SadraeeFar, M.N.: Differential quadrature method for dynamic buckling of graphene sheet coupled by a viscoelastic medium using neperian frequency based on nonlocal elasticity theory. J. Appl. Comput. Mech. 4(3), 147–160 (2018)
25.
go back to reference Yang, J., Rafiee, M., Kitipornchai, S., Jia, X.: Nonlinear thermo-electrical free vibration of functionally graded CNT-reinforced piezoelectric composite beams resting on an elastic foundation. In: 20th International Congress on Sound and Vibration 2013, ICSV 2013, vol. 2, pp. 1804–1811. International Institute of Acoustics & Vibration (2013) Yang, J., Rafiee, M., Kitipornchai, S., Jia, X.: Nonlinear thermo-electrical free vibration of functionally graded CNT-reinforced piezoelectric composite beams resting on an elastic foundation. In: 20th International Congress on Sound and Vibration 2013, ICSV 2013, vol. 2, pp. 1804–1811. International Institute of Acoustics & Vibration (2013)
26.
go back to reference Yinusa, A., Sobamowo, M.G.: Nonlinear thermal-magneto-mechanical vibration analysis of single-walled embedded branched carbon nanotubes conveying nanofluid. ASME Open J. Eng. 2, 32 (2023)CrossRef Yinusa, A., Sobamowo, M.G.: Nonlinear thermal-magneto-mechanical vibration analysis of single-walled embedded branched carbon nanotubes conveying nanofluid. ASME Open J. Eng. 2, 32 (2023)CrossRef
27.
go back to reference Malikan, M.: On the plastic buckling of curved carbon nanotubes. Theor. Appl. Mech. Lett. 10(1), 46–56 (2020)CrossRef Malikan, M.: On the plastic buckling of curved carbon nanotubes. Theor. Appl. Mech. Lett. 10(1), 46–56 (2020)CrossRef
28.
go back to reference Ghayesh, M.H., Farajpour, A., Farokhi, H.: Viscoelastic local dynamics of microtubes conveying fluid. Microfluid. Nanofluid. 22, 1–17 (2018)CrossRef Ghayesh, M.H., Farajpour, A., Farokhi, H.: Viscoelastic local dynamics of microtubes conveying fluid. Microfluid. Nanofluid. 22, 1–17 (2018)CrossRef
29.
go back to reference Farajpour, A., Ghayesh, M., Farokhi, H.: Size-dependent bifurcations of microtubes conveying fluid flow embedded in a nonlinear elastic medium. In: Proceedings of the 21st Australasian Fluid Mechanics Conference (AFMC 2018), pp. 1–4 (2018) Farajpour, A., Ghayesh, M., Farokhi, H.: Size-dependent bifurcations of microtubes conveying fluid flow embedded in a nonlinear elastic medium. In: Proceedings of the 21st Australasian Fluid Mechanics Conference (AFMC 2018), pp. 1–4 (2018)
30.
go back to reference Bakis, K.N., Srinil, N.: Internal flow-induced instability analysis of catenary risers. In: MARINE VIII: Proceedings of the VIII International Conference on Computational Methods in Marine Engineering, pp. 525–536. CIMNE (2019) Bakis, K.N., Srinil, N.: Internal flow-induced instability analysis of catenary risers. In: MARINE VIII: Proceedings of the VIII International Conference on Computational Methods in Marine Engineering, pp. 525–536. CIMNE (2019)
32.
go back to reference Dai, H.L., Fu, Y.M., Dong, Z.M.: Exact solutions for functionally graded pressure vessels in a uniform magnetic field. Int. J. Solids Struct. 43(18–19), 5570–5580 (2006)CrossRef Dai, H.L., Fu, Y.M., Dong, Z.M.: Exact solutions for functionally graded pressure vessels in a uniform magnetic field. Int. J. Solids Struct. 43(18–19), 5570–5580 (2006)CrossRef
33.
go back to reference Mohammadi, M., et al.: Hygro-mechanical vibration analysis of a rotating viscoelastic nanobeam embedded in a visco-Pasternak elastic medium and in a nonlinear thermal environment. Acta Mech. 227(8), 2207–2232 (2016)MathSciNetCrossRef Mohammadi, M., et al.: Hygro-mechanical vibration analysis of a rotating viscoelastic nanobeam embedded in a visco-Pasternak elastic medium and in a nonlinear thermal environment. Acta Mech. 227(8), 2207–2232 (2016)MathSciNetCrossRef
34.
go back to reference Eringen, A.C.: On differential equations of nonlocal elasticity and solutions of screw dislocation and surface waves. J. Appl. Phys. 54(9), 4703 (1983)CrossRef Eringen, A.C.: On differential equations of nonlocal elasticity and solutions of screw dislocation and surface waves. J. Appl. Phys. 54(9), 4703 (1983)CrossRef
35.
go back to reference Eringen, A.C.: Nonlocal Continuum Field Theories. Springer (2002) Eringen, A.C.: Nonlocal Continuum Field Theories. Springer (2002)
36.
go back to reference Ke, L.-L., Wang, Y.-S.: Thermoelectric-mechanical vibration of piezoelectric nanobeams based on the nonlocal theory. Smart Mater. Struct. 21(2), 025018 (2012)CrossRef Ke, L.-L., Wang, Y.-S.: Thermoelectric-mechanical vibration of piezoelectric nanobeams based on the nonlocal theory. Smart Mater. Struct. 21(2), 025018 (2012)CrossRef
37.
go back to reference Ebrahimi, F., Reza Barati, M.: Magneto-electro-elastic buckling analysis of nonlocal curved nanobeams. Eur. Phys. J. Plus 131(9), 1–13 (2016)CrossRef Ebrahimi, F., Reza Barati, M.: Magneto-electro-elastic buckling analysis of nonlocal curved nanobeams. Eur. Phys. J. Plus 131(9), 1–13 (2016)CrossRef
38.
go back to reference Chen, S.S.: Vibration and stability of a uniformly curved tube conveying fluid. J. Acoust. Soc. Am. 51(1), 223–232 (1972)CrossRef Chen, S.S.: Vibration and stability of a uniformly curved tube conveying fluid. J. Acoust. Soc. Am. 51(1), 223–232 (1972)CrossRef
39.
go back to reference Chen, S.-S.: Out-of-plane vibration and stability of curved tubes conveying fluid. J. Appl. Mech. 40(2), 362–368 (1973)CrossRef Chen, S.-S.: Out-of-plane vibration and stability of curved tubes conveying fluid. J. Appl. Mech. 40(2), 362–368 (1973)CrossRef
40.
go back to reference Bellman, R., Kashef, B.G., Casti, J.: Differential quadrature—a technique for the rapid solution of nonlinear partial differential equation. J. Comput. Phys. 10, 40–52 (1972)MathSciNetCrossRef Bellman, R., Kashef, B.G., Casti, J.: Differential quadrature—a technique for the rapid solution of nonlinear partial differential equation. J. Comput. Phys. 10, 40–52 (1972)MathSciNetCrossRef
41.
go back to reference Wu, T.Y., Liu, G.R.: A differential quadrature as a numerical method to solve differential equations. Comput. Mech. 24, 197–205 (1999)MathSciNetCrossRef Wu, T.Y., Liu, G.R.: A differential quadrature as a numerical method to solve differential equations. Comput. Mech. 24, 197–205 (1999)MathSciNetCrossRef
42.
go back to reference Wu, T.Y., Liu, G.R.: The generalized differential quadrature rule for initial-value differential equations. J. Sound Vib. 233(2), 195–213 (2000)MathSciNetCrossRef Wu, T.Y., Liu, G.R.: The generalized differential quadrature rule for initial-value differential equations. J. Sound Vib. 233(2), 195–213 (2000)MathSciNetCrossRef
43.
go back to reference Bert, C.W., Malik, M.: Differential quadrature method in computational mechanics—a review. Appl. Mech. Rev. 49, 1–28 (1996)CrossRef Bert, C.W., Malik, M.: Differential quadrature method in computational mechanics—a review. Appl. Mech. Rev. 49, 1–28 (1996)CrossRef
44.
go back to reference Tang, M., et al.: Nonlinear modeling and size-dependent vibration analysis of curved microtubes conveying fluid based on modified couple stress theory. Int. J. Eng. Sci. 84, 1–10 (2014)MathSciNetCrossRef Tang, M., et al.: Nonlinear modeling and size-dependent vibration analysis of curved microtubes conveying fluid based on modified couple stress theory. Int. J. Eng. Sci. 84, 1–10 (2014)MathSciNetCrossRef
Metadata
Title
Nonlocal stability of curved carbon nanotubes conveying fluid based on Eringen’s nonlocal elasticity theory in a thermomagnetic environment
Authors
Hossein Ramezani
Majid Haji Ali Koohpayeh
Alireza Tajedini
Ghazaleh Ramezani
Amirhossein Mohseni
Publication date
27-04-2024
Publisher
Springer Vienna
Published in
Acta Mechanica
Print ISSN: 0001-5970
Electronic ISSN: 1619-6937
DOI
https://doi.org/10.1007/s00707-024-03938-7

Premium Partners