Abstract
The size-dependent free vibrations of nanobeams with axial motion in thermo-magnetic environments are examined using the non-local Rayleigh theory. The vibration equations have been derived using Hamilton's principle. The Galerkin technique has been utilized to determine the backward and forward vibration frequencies as well as the instability thresholds of the system. Comparative studies have been conducted to validate the results of this study. Some key parameters have been evaluated about the vibrations of the nanobeam, such as the magnetic field intensity, the speed of the axial movement, and the ratio of bending stiffness. The results showed that magnetic fields improved the performance of the system. Additionally, it was demonstrated that increasing the rotational inertia parameter reduces vibration frequencies and system stability.
Similar content being viewed by others
Data availability
The authors do not have permissions to share data.
References
Abdelmalek Z, Karbon M, Eyvazian A, Forooghi A, Safarpour H, Tlili I (2021) On the dynamics of a curved microtubule-associated proteins by considering viscoelastic properties of the living biological cells. J Biomol Struct Dyn 39(7):2415–2429
Abdulrazzaq MA, Fenjan RM, Ahmed RA, Faleh NM (2020) Thermal buckling of nonlocal clamped exponentially graded plate according to a secant function based refined theory. Steel Compos Struct 35(1):147–157
Afkhami Z, Farid M (2016) Thermo-mechanical vibration and instability of carbon nanocones conveying fluid using nonlocal Timoshenko beam model. J Vib Control 22(2):604–618
Ahmed RA, Fenjan RM, Faleh NM (2019) Analyzing post-buckling behavior of continuously graded FG nanobeams with geometrical imperfections. Geomech Eng 17(2):175–180
Ahmed RA, Mustafa NM, Faleh NM, Fenjan RM (2020a) Nonlocal nonlinear stability of higher-order porous beams via Chebyshev–Ritz method. Struct Eng Mech 76(3):413–420
Ahmed RA, Fenjan RM, Hamad LB, Faleh NM (2020b) A review of effects of partial dynamic loading on dynamic response of nonlocal functionally graded material beams. Adv Mater Res 9(1):33–48
Al-Toki MH, Ali HA, Faleh NM, Fenjan RM (2022) Numerical assessment of nonlocal dynamic stability of graded porous beams in thermal environment rested on elastic foundation. Geomech Eng 28(5):455–461
Arshid E, Arshid H, Amir S, Mousavi SB (2021) Free vibration and buckling analyses of FG porous sandwich curved microbeams in thermal environment under magnetic field based on modified couple stress theory. Arch Civ Mech Eng 21:1–23
Bai Y, Suhatril M, Cao Y, Forooghi A, Assilzadeh H (2021) Hygro–thermo–magnetically induced vibration of nanobeams with simultaneous axial and spinning motions based on nonlocal strain gradient theory. Eng Comput 38:2509–2526
Bazmi M, Askari S, Ghasemy E, Rashidi A, Ettefaghi E (2019) Nitrogen-doped carbon nanotubes for heat transfer applications: Enhancement of conduction and convection properties of water/N-CNT nanofluid. J Therm Anal Calorim 138:69–79
Chang T-P (2012) Nonlinear vibration analysis of a fixed-fixed beam under oscillating axial load and vibrating magnetic field. J Theor Appl Mech 50(2):441–453
Dehrouyeh-Semnani AM, Dehrouyeh M, Zafari-Koloukhi H, Ghamami M (2015) Size-dependent frequency and stability characteristics of axially moving microbeams based on modified couple stress theory. Int J Eng Sci 97:98–112
Ding H, Zhu M, Chen L (2019) Dynamic stiffness method for free vibration of an axially moving beam with generalized boundary conditions. Appl Math Mech 40(7):911–924
Ebrahimi-Mamaghani A, Forooghi A, Sarparast H, Alibeigloo A, Friswell M (2021) Vibration of viscoelastic axially graded beams with simultaneous axial and spinning motions under an axial load. Appl Math Model 90:131–150
Eslami G, Maleki VA, Rezaee M (2016) Effect of open crack on vibration behavior of a fluid-conveying pipe embedded in a visco-elastic medium. Latin Am J Solids Struct 13:136–154
Fenjan RM, Faleh NM, Ahmed RA (2020a) Geometrical imperfection and thermal effects on nonlinear stability of microbeams made of graphene-reinforced nano-composites. Adv Nano Res 9(3):147–156
Fenjan RM, Ahmed RA, Faleh NM, Hani FM (2020b) Dynamic response of size-dependent porous functionally graded beams under thermal and moving load using a numerical approach. Struct Monit Maint 7(2):69–84
Fenjan RM, Ahmed RA, Faleh NM, Hani FM (2020c) Static stability analysis of smart nonlocal thermo-piezo-magnetic plates via a quasi-3D formulation. Smart Struct Syst 26(1):77–87
Fenjan RM, Ahmed RA, Faleh NM (2020d) Nonlinear vibration characteristics of refined higher-order multi-phase piezo-magnetic nanobeams. Eur Phys J plus 135(5):1–14
Forooghi A, Alibeigloo A (2022) Hygro-thermo-magnetically induced vibration of FG-CNTRC small-scale plate incorporating nonlocality and strain gradient size dependency. Waves Random Complex Media 32(4):1–32
Forooghi A, Safarpour M, Alibeigloo A (2020) Investigation of dynamics and stability behavior of axially moving micro-beams with functionally graded property in the longitudinal direction. J Solid Fluid Mech 10(2):79–94
Forooghi A, Rezaey S, Haghighi SM, Zenkour AM (2021) Thermal instability analysis of nanoscale FG porous plates embedded on Kerr foundation coupled with fluid flow. Eng Comput 38:1–21
Forooghi A, Fallahi N, Alibeigloo A, Forooghi H, Rezaey S (2022) Static and thermal instability analysis of embedded functionally graded carbon nanotube-reinforced composite plates based on HSDT via GDQM and validated modeling by neural network. Mech Based Des Struct Mach 51(6):1–34
Hoseinzadeh M, Pilafkan R, Maleki VA (2023) Size-dependent linear and nonlinear vibration of functionally graded CNT reinforced imperfect microplates submerged in fluid medium. Ocean Eng 268:113257
Karamati A, Hunter N, Lin H, Zobeiri H, Xu S, Wang X (2022) Strong linearity and effect of laser heating location in transient photo/electrothermal characterization of micro/nanoscale wires. Int J Heat Mass Transf 198:123393
Kong S (2022) A review on the size-dependent models of micro-beam and micro-plate based on the modified couple stress theory. Arch Comput Methods Eng 29(1):1–31
Liu H, Lv Z, Wu H (2019) Nonlinear free vibration of geometrically imperfect functionally graded sandwich nanobeams based on nonlocal strain gradient theory. Compos Struct 214:47–61
Liu S, Tang Y-Q, Chen L (2021) Multi-scale analysis and Galerkin verification for dynamic stability of axially translating viscoelastic Timoshenko beams. Appl Math Model 93:885–897
Minaei M, Rezaee M, Arab Maleki V (2021) Vibration analysis of viscoelastic carbon nanotube under electromagnetic fields based on the nonlocal Timoshenko beam theory. Iran J Mech Eng Trans ISME 23(2):176–198
Nejadsadeghi N, Misra A (2019) Axially moving materials with granular microstructure. Int J Mech Sci 161:105042
Pourreza T, Alijani A, Maleki VA, Kazemi A (2021) Nonlinear vibration of nanosheets subjected to electromagnetic fields and electrical current. Adv Nano Res 10(5):481–491
Pourreza T, Alijani A, Maleki VA, Kazemi A (2022) The effect of magnetic field on buckling and nonlinear vibrations of Graphene nanosheets based on nonlocal elasticity theory. Int J Nano Dimens 13(1):54–70
Rezaee M, Arab Maleki V (2017) Vibration analysis of fluid conveying viscoelastic pipes rested on non-uniform Winkler elastic foundation. Modares Mech Eng 16(12):87–94
Rezaee M, Maleki VA (2015) An analytical solution for vibration analysis of carbon nanotube conveying viscose fluid embedded in visco-elastic medium. Proc Inst Mech Eng C J Mech Eng Sci 229(4):644–650
Rezaee M, Sharafkhani N (2019) Nonlinear dynamic analysis of an electrostatically actuated cylindrical micro-beam subjected to cross fluid flow. Int J Appl Mech 11(06):1950061
Sahoo B (2021) Nonlinear vibration analysis of a hinged–clamped beam moving with pulsating speed and subjected to internal resonance. Int J Struct Stab Dyn 21(08):2150117
Sahoo SK, Das H, Panda L (2019) An overview of transverse vibration of axially travelling string. Recent Trends Appl Math Sel Proc AMSE 2021:427–446
Sarparast H, Alibeigloo A, Borjalilou V, Koochakianfard O (2022) Forced and free vibrational analysis of viscoelastic nanotubes conveying fluid subjected to moving load in hygro-thermo-magnetic environments with surface effects. Arch Civ Mech Eng 22(4):172
Shariati A, Jung DW, Mohammad-Sedighi H, Żur KK, Habibi M, Safa M (2020) On the vibrations and stability of moving viscoelastic axially functionally graded nanobeams. Materials 13(7):1707
Tahmasebi E, Ashrafi Khorasani N, Imam A (2020) Nonlinear vibration behavior of a carry current ferromagnetic beam plate under magnetic fields and thermal loads. J Vib Control 26(15–16):1276–1285
VahidiPashaki P, Pouya M, Maleki VA (2018) High-speed cryogenic machining of the carbon nanotube reinforced nanocomposites: finite element analysis and simulation. Proc Inst Mech Eng Part C J Mech Eng Sci 232(11):1927–1936
Wang J, Shen H (2019) Nonlinear vibrations of axially moving simply supported viscoelastic nanobeams based on nonlocal strain gradient theory. J Phys Condens Matter 31(48):485403
Wu Q, Qi G (2020) Homoclinic bifurcations and chaotic dynamics of non-planar waves in axially moving beam subjected to thermal load. Appl Math Model 83:674–682
Yan Y, Li J-X, Wang W-Q (2023) Time-delay feedback control of an axially moving nanoscale beam with time-dependent velocity. Chaos Solitons Fractals 166:112949
Zhao X, Wang C, Zhu W, Li Y, Wan X (2021) Coupled thermoelastic nonlocal forced vibration of an axially moving micro/nano-beam. Int J Mech Sci 206:106600
Zhu K, Chung J (2019) Vibration and stability analysis of a simply-supported Rayleigh beam with spinning and axial motions. Appl Math Model 66:362–382
Author information
Authors and Affiliations
Contributions
LG: Writing Original draft preparation, Conceptualization, Supervision, Project administration. HH: Methodology, Software, Formal analysis, Language review.
Corresponding author
Ethics declarations
Conflict of interest
The authors declare no competing interests.
Additional information
Publisher's Note
Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.
Rights and permissions
Springer Nature or its licensor (e.g. a society or other partner) holds exclusive rights to this article under a publishing agreement with the author(s) or other rightsholder(s); author self-archiving of the accepted manuscript version of this article is solely governed by the terms of such publishing agreement and applicable law.
About this article
Cite this article
Guo, L., Huang, H. Size-dependent vibrations of axially moving carbon nanobeam located in the magnetic field. Multiscale and Multidiscip. Model. Exp. and Des. 6, 553–560 (2023). https://doi.org/10.1007/s41939-023-00163-y
Received:
Accepted:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s41939-023-00163-y