Primary parametric resonance of an axially accelerating beam subjected to static loads

• Autorzy: Hu Y. , Rong Y. , Li J.

Identyfikatory

DOI

10.15632/jtam-pl.56.3.815

• Języki publikacji: EN

Abstrakty

EN

Primary parametric resonance and stability of an axially accelerating and current-carrying beam subjected to static loads in magnetic field are investigated. The nonlinear magneto-elastic vibration equation is derived. The approximate solution of the static problem and the disturbance deferential equation of the beam with two sides simply supported are obtained. The frequency-response equation of primary parametric resonance is further achieved by a multi-scale method. According to stability conditions, the stability of the steady-state solution is also discussed. By numerical examples, the amplitude versus different parameter curves and the bifurcation diagrams of the amplitude are acquired. The effects of magnetic induction intensity, axial speed, detuning parameter and static loads on nonlinear vibration characteristics are also analyzed.

Słowa kluczowe

EN

current-carrying beam; primary parametric resonance; magnetic field; axial movement; static loads

• Wydawca: Polskie Towarzystwo Mechaniki Teoretycznej i Stosowanej
• Czasopismo: Journal of Theoretical and Applied Mechanics
• Rocznik: 2018
• Tom: Vol. 56 nr 3
• Strony: 815--828
• Opis fizyczny: Bibliogr. 17 poz., rys.

Twórcy

autor

Hu Y.

• School of Civil Engineering and Mechanics, Yanshan University, Qinhuangdao, China Hebei Provincial Key Laboratory of Mechanical Reliability for Heavy Equipments and Large Structures, Yanshan University, Qinhuangdao, China

autor

Rong Y.

• School of Civil Engineering and Mechanics, Yanshan University, Qinhuangdao, China Hebei Provincial Key Laboratory of Mechanical Reliability for Heavy Equipments and Large Structures, Yanshan University, Qinhuangdao, China

autor

Li J.

• School of Civil Engineering and Mechanics, Yanshan University, Qinhuangdao, China
• Department of Basic Teaching, Tangshan University, Tangshan, China

Bibliografia

• 1. Chakraborty G., Mallik, A.K., 1998, Parametrically excited non-linear traveling beams with and without external forcing, Nonlinear Dynamics, 17, 4, 301-324
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• 3. Chen L.Q., Yang X.D., 2005, Steady-state response of axially moving viscoelastic beams with pulsating speed: comparison of two nonlinear models, International Journal of Solids and Structures, 42, 1, 37-50
• 4. Ghayesh M.H., Balar S., 2008, Non-linear parametric vibration and stability of axially moving visco-elastic Rayleigh beams, International Journal of Solids and Structures, 45, 25-26, 6451-6467
• 5. Ghayesh M.H., Balar S., 2010, Non-linear parametric vibration and stability analysis for two dynamic models of axially moving Timoshenko beams, Applied Mathematical Modelling, 34, 10, 2850-2859
• 6. Hasanyan D.J., Khachaturyan G.M., Piliposyan G.T., 2001, Mathematical modeling and investigation of nonlinear vibration of perfectly conductive plates in an inclined magnetic field, Thin-Walled Structures, 39, 1, 111-123
• 7. Hasanyan D., Librescu L., Qin Z., Ambur D.R., 2005, Nonlinear vibration of finitely-electroconductive plate strips in an axial magnetic field, Computers and Structures, 83, 15, 1205-1216
• 8. Hu Y.D., Hu P., Zhang J.Z., 2015, Strongly nonlinear subharmonic resonance and chaotic motion of axially moving thin plate in magnetic field, Journal of Computational and Nonlinear Dynamics, 10, 2, 1-12
• 9. Hu Y.D, Li J., 2009, The magneto-elastic subharmonic resonance of current-conducting thin plate in magnetic filed, Journal of Sound and Vibration, 319, 3, 1107-1120
• 10. Hu Y.D., Wang T., 2015, Nonlinear resonance of the rotating circular plate under static loads in magnetic field, Chinese Journal of Mechanical Engineering, 28, 6, 1277-1284
• 11. Hu Y.D., Zhang J.Z., 2013, Principal parametric resonance of axially accelerating rectangular thin plate in magnetic field, Applied Mathematics and Mechanics (English Edition), 34, 11, 1405-1420
• 12. Matsner V.I., 1978, Effect of initial deflections on the natural vibration frequencies of shells under axial compressive loads, Soviet Applied Mechanics, 14, 5, 528-531
• 13. Nayfeh A.H., Mook D.T., 1979, Nonlinear Oscillations, Wiley, New York
• 14. Tang Y.Q., Chen L.Q., Yang X.D., 2009, Parametric resonance of axially moving Timoshenko beams with time-dependent speed, Nonlinear Dynamics, 58, 4, 715-724
• 15. Wang J.Y., Chen K.J., 1993, Vibration problems of flexible circular plates with initial deflection, Applied Mathematics and Mechanics (English Edition), 14, 2, 177-184
• 16. Wang X.Z., Lee J.S., Zheng X.J., 2003, Magneto-thermo-elastic instability of ferromagnetic plates in thermal and magnetic fields, International Journal of Solids and Structures, 40, 22, 6125-6142
• 17. Zheng X.J, Zhang J.P., Zhou Y.H., 2005, Dynamic stability of a cantilever conductive plate in transverse impulsive magnetic field, International Journal of Solids and Structures, 42, 8, 2417-2430

Uwagi

PL

Opracowanie rekordu w ramach umowy 509/P-DUN/2018 ze środków MNiSW przeznaczonych na działalność upowszechniającą naukę (2018).