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Erschienen in: Acta Mechanica 1/2021

02.11.2020 | Original Paper

Vibrations and stability analysis of double current-carrying strips interacting with magnetic field

verfasst von: A. R. Hosseinian, R. D. Firouz-Abadi

Erschienen in: Acta Mechanica | Ausgabe 1/2021

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Abstract

Interactive vibrations and buckling of double current-carrying strips (DCCS) are investigated in this study. Considering the rotational and transverse deformation of the strip, four coupled equations of motion are obtained using Hamilton’s principle. Using the Galerkin method, mass and stiffness matrices are extracted and the stability of the system is determined by solving the eigenvalue problem. Effects of pretension and elevated temperature on the stability of DCCS are studied for three types of materials and various arrangements. Finally, the effect of horizontal or vertical distance between strips on the critical current value is investigated. According to the results, the effects of temperature rise, pretension, and the relative distance of the strips on the instability of DCCS are found to be significant.
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Literatur
1.
Zurück zum Zitat Van de Ven, A.: Magnetoelastic buckling of a beam of elliptic cross-section. Acta Mech. 51, 119–138 (1984)CrossRef Van de Ven, A.: Magnetoelastic buckling of a beam of elliptic cross-section. Acta Mech. 51, 119–138 (1984)CrossRef
2.
Zurück zum Zitat Van de Ven, A., Tani, J., Otomo, K., Shindo, Y.: Magnetoelastic buckling of two nearby ferromagnetic rods in a magnetic field. Acta Mech. 75, 191–209 (1988)CrossRef Van de Ven, A., Tani, J., Otomo, K., Shindo, Y.: Magnetoelastic buckling of two nearby ferromagnetic rods in a magnetic field. Acta Mech. 75, 191–209 (1988)CrossRef
3.
Zurück zum Zitat Lu, Q., To, C., Huang, K.: Dynamic stability and bifurcation of an alternating load and magnetic field excited magnetoelastic beam. J. Sound Vib. 181, 873–891 (1995)CrossRef Lu, Q., To, C., Huang, K.: Dynamic stability and bifurcation of an alternating load and magnetic field excited magnetoelastic beam. J. Sound Vib. 181, 873–891 (1995)CrossRef
4.
Zurück zum Zitat Wei, L., Yapeng, S., Daining, F.: Magnetoelastic coupling on soft ferromagnetic solids with an interface crack. Acta Mech. 154, 1–9 (2002)CrossRef Wei, L., Yapeng, S., Daining, F.: Magnetoelastic coupling on soft ferromagnetic solids with an interface crack. Acta Mech. 154, 1–9 (2002)CrossRef
5.
Zurück zum Zitat Korobkov, Y.S., Krasova, N., Khromatov, V.: The influence of a magnetic field on the vibration frequency spectra of rectangular plates. Russ. Electr. Eng. 78, 198–201 (2007)CrossRef Korobkov, Y.S., Krasova, N., Khromatov, V.: The influence of a magnetic field on the vibration frequency spectra of rectangular plates. Russ. Electr. Eng. 78, 198–201 (2007)CrossRef
6.
Zurück zum Zitat Wang, X.-Z.: Changes in the natural frequency of a ferromagnetic rod in a magnetic field due to magnetoelastic interaction. Appl. Math. Mech. 29, 1023 (2008)MathSciNetCrossRef Wang, X.-Z.: Changes in the natural frequency of a ferromagnetic rod in a magnetic field due to magnetoelastic interaction. Appl. Math. Mech. 29, 1023 (2008)MathSciNetCrossRef
7.
Zurück zum Zitat Gao, Y.: Study on magneto-elastic-plastic deformation characteristics of ferromagnetic rectangular plate with simple supports. Acta. Mech. Sin. 25, 139–147 (2009)CrossRef Gao, Y.: Study on magneto-elastic-plastic deformation characteristics of ferromagnetic rectangular plate with simple supports. Acta. Mech. Sin. 25, 139–147 (2009)CrossRef
8.
Zurück zum Zitat Hu, N., Burgueño, R.: Buckling-induced smart applications: recent advances and trends. Smart Mater. Struct. 24, 063001 (2015)CrossRef Hu, N., Burgueño, R.: Buckling-induced smart applications: recent advances and trends. Smart Mater. Struct. 24, 063001 (2015)CrossRef
9.
Zurück zum Zitat An, S., Kim, B., Kwon, S., Moon, G., Lee, M., Jhe, W.: Buckling-based non-linear mechanical sensor. Sensors 18, 2637 (2018)CrossRef An, S., Kim, B., Kwon, S., Moon, G., Lee, M., Jhe, W.: Buckling-based non-linear mechanical sensor. Sensors 18, 2637 (2018)CrossRef
10.
Zurück zum Zitat Liu, S., Burgueño, R.: Self-sensing solid materials via delamination buckling. In: ASME 2017 Conference on Smart Materials, Adaptive Structures and Intelligent Systems (2017) Liu, S., Burgueño, R.: Self-sensing solid materials via delamination buckling. In: ASME 2017 Conference on Smart Materials, Adaptive Structures and Intelligent Systems (2017)
11.
Zurück zum Zitat Grimes, C.A., Roy, S.C., Rani, S., Cai, Q.: Theory, instrumentation and applications of magnetoelastic resonance sensors: a review. Sensors 11, 2809–2844 (2011)CrossRef Grimes, C.A., Roy, S.C., Rani, S., Cai, Q.: Theory, instrumentation and applications of magnetoelastic resonance sensors: a review. Sensors 11, 2809–2844 (2011)CrossRef
12.
Zurück zum Zitat Dolbin, N., Morozov, A.: Elastic bending vibrations of a rod carrying electric current. J. Appl. Mech. Tech. Phys. 7, 59–62 (1966)CrossRef Dolbin, N., Morozov, A.: Elastic bending vibrations of a rod carrying electric current. J. Appl. Mech. Tech. Phys. 7, 59–62 (1966)CrossRef
13.
Zurück zum Zitat Chattopadhyay, S., Moon, F.C.: Magnetoelastic buckling and vibration of a rod carrying electric current. J. Appl. Mech. 42, 809–814 (1975)CrossRef Chattopadhyay, S., Moon, F.C.: Magnetoelastic buckling and vibration of a rod carrying electric current. J. Appl. Mech. 42, 809–814 (1975)CrossRef
14.
Zurück zum Zitat Firouz-Abadi, R., Hosseinian, A.: Resonance frequencies and stability of a current-carrying suspended nanobeam in a longitudinal magnetic field. Theor. Appl. Mech. Lett. 2, 031012 (2012)CrossRef Firouz-Abadi, R., Hosseinian, A.: Resonance frequencies and stability of a current-carrying suspended nanobeam in a longitudinal magnetic field. Theor. Appl. Mech. Lett. 2, 031012 (2012)CrossRef
15.
Zurück zum Zitat Kiani, K.: Forced vibrations of a current-carrying nanowire in a longitudinal magnetic field accounting for both surface energy and size effects. Physica E 63, 27–35 (2014)CrossRef Kiani, K.: Forced vibrations of a current-carrying nanowire in a longitudinal magnetic field accounting for both surface energy and size effects. Physica E 63, 27–35 (2014)CrossRef
16.
Zurück zum Zitat Kiani, K.: Surface effect on free transverse vibrations and dynamic instability of current-carrying nanowires in the presence of a longitudinal magnetic field. Phys. Lett. A 378, 1834–1840 (2014)MathSciNetCrossRef Kiani, K.: Surface effect on free transverse vibrations and dynamic instability of current-carrying nanowires in the presence of a longitudinal magnetic field. Phys. Lett. A 378, 1834–1840 (2014)MathSciNetCrossRef
17.
Zurück zum Zitat Kiani, K.: Vibrations and instability of pretensioned current-carrying nanowires acted upon by a suddenly applied three-dimensional magnetic field. Mater. Chem. Phys. 162, 531–541 (2015)CrossRef Kiani, K.: Vibrations and instability of pretensioned current-carrying nanowires acted upon by a suddenly applied three-dimensional magnetic field. Mater. Chem. Phys. 162, 531–541 (2015)CrossRef
18.
Zurück zum Zitat Kiani, K.: Vibrations and instability of double-nanowire-systems as electric current carriers. Mod. Phys. Lett. B 29, 1550144 (2015)MathSciNetCrossRef Kiani, K.: Vibrations and instability of double-nanowire-systems as electric current carriers. Mod. Phys. Lett. B 29, 1550144 (2015)MathSciNetCrossRef
19.
Zurück zum Zitat Wang, L., Liu, W.-B., Dai, H.-L.: Dynamics and instability of current-carrying microbeams in a longitudinal magnetic field. Physica E 66, 87–92 (2015)CrossRef Wang, L., Liu, W.-B., Dai, H.-L.: Dynamics and instability of current-carrying microbeams in a longitudinal magnetic field. Physica E 66, 87–92 (2015)CrossRef
20.
Zurück zum Zitat Kiani, K.: Dynamic interactions between double current-carrying nanowires immersed in a longitudinal magnetic field: novel integro-surface energy-based models. Int. J. Eng. Sci. 107, 98–133 (2016)MathSciNetCrossRef Kiani, K.: Dynamic interactions between double current-carrying nanowires immersed in a longitudinal magnetic field: novel integro-surface energy-based models. Int. J. Eng. Sci. 107, 98–133 (2016)MathSciNetCrossRef
21.
Zurück zum Zitat Kiani, K.: A refined integro-surface energy-based model for vibration of magnetically actuated double-nanowire-systems carrying electric current. Physica E 86, 225–236 (2017)CrossRef Kiani, K.: A refined integro-surface energy-based model for vibration of magnetically actuated double-nanowire-systems carrying electric current. Physica E 86, 225–236 (2017)CrossRef
22.
Zurück zum Zitat Hong, Y., Wang, L.: Stability and nonplanar buckling analysis of a current-carrying mircowire in three-dimensional magnetic field. Microsyst. Technol. 25, 4053–4066 (2019)CrossRef Hong, Y., Wang, L.: Stability and nonplanar buckling analysis of a current-carrying mircowire in three-dimensional magnetic field. Microsyst. Technol. 25, 4053–4066 (2019)CrossRef
23.
Zurück zum Zitat Hasanyan, D.J., Librescu, L., Ambur, D.R.: Buckling and postbuckling of magnetoelastic flat plates carrying an electric current. Int. J. Solids Struct. 43, 4971–4996 (2006)CrossRef Hasanyan, D.J., Librescu, L., Ambur, D.R.: Buckling and postbuckling of magnetoelastic flat plates carrying an electric current. Int. J. Solids Struct. 43, 4971–4996 (2006)CrossRef
24.
Zurück zum Zitat Hasanyan, D.: Mathematical modeling and analysis of magneto thermoelastic plate. J. Therm. Stress. 32, 65–78 (2008)CrossRef Hasanyan, D.: Mathematical modeling and analysis of magneto thermoelastic plate. J. Therm. Stress. 32, 65–78 (2008)CrossRef
25.
Zurück zum Zitat Yuda, H., Jing, L.: The magneto-elastic subharmonic resonance of current-conducting thin plate in magnetic filed. J. Sound Vib. 319, 1107–1120 (2009)CrossRef Yuda, H., Jing, L.: The magneto-elastic subharmonic resonance of current-conducting thin plate in magnetic filed. J. Sound Vib. 319, 1107–1120 (2009)CrossRef
26.
Zurück zum Zitat Rao, S.S.: Vibration of Continuous Systems, vol. 464. Wiley, New York (2007) Rao, S.S.: Vibration of Continuous Systems, vol. 464. Wiley, New York (2007)
27.
Zurück zum Zitat Li, S.: Introduction to electrochemical reaction engineering. In: Li, E. (ed.) Reaction Engineering, vol. 13, pp. 599–651. Butterworth-Heinemann, Boston (2017)CrossRef Li, S.: Introduction to electrochemical reaction engineering. In: Li, E. (ed.) Reaction Engineering, vol. 13, pp. 599–651. Butterworth-Heinemann, Boston (2017)CrossRef
28.
Zurück zum Zitat Kasap, S.: Essential Heat Transfer for Electrical Engineers. Web-Materials, Saskatchewan (2003) Kasap, S.: Essential Heat Transfer for Electrical Engineers. Web-Materials, Saskatchewan (2003)
29.
Zurück zum Zitat Amba-Rao, C.L.: Effect of end conditions on the lateral frequencies of uniform straight columns. J. Acoust. Soc. Am. 42, 900–901 (1967)CrossRef Amba-Rao, C.L.: Effect of end conditions on the lateral frequencies of uniform straight columns. J. Acoust. Soc. Am. 42, 900–901 (1967)CrossRef
30.
Zurück zum Zitat Galef, A.: Bending frequencies of compressed beams. J. Acoust. Soc. Am. 44, 643–643 (1968)CrossRef Galef, A.: Bending frequencies of compressed beams. J. Acoust. Soc. Am. 44, 643–643 (1968)CrossRef
Metadaten
Titel
Vibrations and stability analysis of double current-carrying strips interacting with magnetic field
verfasst von
A. R. Hosseinian
R. D. Firouz-Abadi
Publikationsdatum
02.11.2020
Verlag
Springer Vienna
Erschienen in
Acta Mechanica / Ausgabe 1/2021
Print ISSN: 0001-5970
Elektronische ISSN: 1619-6937
DOI
https://doi.org/10.1007/s00707-020-02814-4

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