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The Hamiltonian principle is applied to the nonlinear vibration equation of an axially moving conductive beam in the magnetic field with consideration of the axial velocity, axial tension, electromagnetic coupling effect and complex boundary conditions. Nonlinear vibration characteristics of the free vibrating beam under 1:3 internal resonances are studied based on our approach. For beams with one end fixed and the other simply supported, the nonlinear vibration equation is dispersed by the Galerkin method, and the vibration equations are solved by the multiple-scales method. As a result, the coupled relations between the first-order and second-order vibration modes are obtained in the internal resonance system. Firstly, the influence of initial conditions, axial velocity and the external magnetic field strength on the vibration modes is analysed in detail. Secondly, direct numerical calculation on the vibration equations is carried out in order to evaluate the accuracy of the perturbation approach. It is found that through numerical calculations, in the undamped system, the vibration modes are more sensitive to the initial value of vibration amplitude. The amplitude changes of the first-order and second-order modes resulting from the increase of the initial amplitude value of the vibration modes respectively are very special, and present a “reversal behaviour”. Lastly, in the damped system, the vibration modes exhibit a trend of coupling attenuation with time. Its decay rate increases when the applied magnetic field strength becomes stronger.
Czasopismo
Rocznik
Tom
Strony
179--191
Opis fizyczny
Bibliogr. 17 poz., rys.
Twórcy
autor
- Key Laboratory of Mechanical Reliability for Heavy Equipments and Large Structures of Hebei Province, Yanshan University, Qinhuangdao, P.R. China
- Department of Mechanics, School of Aerospace Engineering, Beijing Institute of Technology, Beijing, P.R. China
autor
- Key Laboratory of Mechanical Reliability for Heavy Equipments and Large Structures of Hebei Province, Yanshan University, Qinhuangdao, P.R. China
autor
- Department of Mechanics, School of Aerospace Engineering, Beijing Institute of Technology, Beijing, P.R. China
autor
- State Key Laboratory of Explosion Science and Technology, Beijing Institute of Technology, Beijing, P.R. China
autor
- Department of Mechanics, School of Aerospace Engineering, Beijing Institute of Technology, Beijing, P.R. China
Bibliografia
- 1. Chen L.Q., Tang Y.Q., Lim C.W., 2010, Dynamic stability in parametric resonance of axially accelerating viscoelastic Timoshenko beams, Journal of Sound and Vibration, 329, 5, 547-565
- 2. Ding H., Chen L.Q., 2010, Galerkin methods for natural frequencies of high-speed axially moving beams, Journal of Sound and Vibration, 329, 17, 3484-3494
- 3. Hu Y., Hu P., Zhang J., 2015, Strongly nonlinear subharmonic resonance and chaotic motion of axially moving thin plate in magnetic field, Journal of Computational and Nonlinear Dynamics, 10, 2, 021010
- 4. Hu Y., Wang J., 2017, Principal-internal resonance of an axially moving current-carrying beam in magnetic field, Nonlinear Dynamics, 90, 1, 683-695
- 5. Li J., Hu Y.D., Wang Y.N., 2017, The magneto-elastic internal resonances of rectangular conductive thin plate with different size ratios, Journal of Mechanics, 34, 5, 711-723
- 6. Mao X.Y., Ding H., Chen L.Q., 2016, Steady-state response of a fluid-conveying pipe with 3:1 internal resonance in supercritical regime, Nonlinear Dynamics, 86, 2, 795-809
- 7. Mao X.Y., Ding H., Lim C.W., Chen L.Q., 2016, Super-harmonic resonance and multifrequency responses of a super-critical translating beam, Journal of Sound and Vibration, 385, 267-283
- 8. Nayfeh A.H., Mook D.T., 1979, Nonlinear Oscillation, John Wiley & Sons, New York
- 9. Pellicano F., 2005, On the dynamic properties of axially moving systems, Journal of Sound and Vibration, 281, 3-5, 593-609
- 10. Pratiher B., 2011, Non-linear response of a magneto-elastic translating beam with prismatic joint for higher resonance conditions, International Journal of Non-Linear Mechanics, 46, 5, 685-692
- 11. Pratiher B., Dwivedy S.K., 2009, Non-linear dynamics of a soft magneto-elastic Cartesian manipulator, International Journal of Non-Linear Mechanics, 44, 7, 757-768
- 12. Sahoo B., Panda L.N., Pohit G., 2015, Two-frequency parametric excitation and internal resonance of a moving viscoelastic beam, Nonlinear Dynamics, 82, 4, 1721-1742
- 13. Sahoo B., Panda L.N., Pohit G., 2016, Combination, principal parametric and internal resonances of an accelerating beam under two frequencies parametric excitation, International Journal of Non-Linear Mechanics, 78, 35-44
- 14. Tang Y.Q., Zhang D.B., Gao J.M., 2016, Parametric and internal resonance of axially accelerating viscoelastic beams with the recognition of longitudinally varying tensions, Nonlinear Dynamics, 83, 1-2, 401-418
- 15. Wang L., Chen H.H., He X.D., 2011, Active H control of the vibration of an axially moving cantilever beam by magnetic force, Mechanical Systems and Signal Processing, 25, 8, 2863-2878
- 16. Wu G.Y., 2007, The analysis of dynamic instability on the large amplitude vibrations of a beam with transverse magnetic fields and thermal loads, Journal of Sound and Vibration, 302, 1-2, 167-177
- 17. Yan Q., Ding H., Chen L., 2015, Nonlinear dynamics of axially moving viscoelastic Timoshenko beam under parametric and external excitations, Applied Mathematics and Mechanics, 36, 8, 971-984
Uwagi
Opracowanie rekordu w ramach umowy 509/P-DUN/2018 ze środków MNiSW przeznaczonych na działalność upowszechniającą naukę (2019).
Typ dokumentu
Bibliografia
Identyfikator YADDA
bwmeta1.element.baztech-4193e319-993d-4ac7-a283-85b2453deaeb
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