Oscillatory Behavior in a Nonlinear Gyroscopic System with Mechanics

Article Preview

Abstract:

In this paper, a nonlinear gyroscopic system is investigated. Two sufficient conditions to ensure the existence of oscillations for the system are proposed. Simulations are demonstrated for the provided results. In the study, the authors has researched the nonlinear gyroscopic system from the mechanics perspective, which will be useful in dynamic mechanical system, especially for parametric vibration. In fact, the nonlinear gyroscopic system is closely connected with mechanics, and they also influences each other during study.

You might also be interested in these eBooks

Info:

Periodical:

Pages:

387-391

Citation:

Online since:

April 2012

Export:

Price:

Permissions CCC:

Permissions PLS:

Сopyright:

© 2012 Trans Tech Publications Ltd. All Rights Reserved

Share:

Citation:

[1] K.M. Liew, Y.G. Hu, X. Zhao, Dynamic stability of rotating cylindrical shells subjected to periodic axial loads, Int. J. Solids and Structures, Vol. 43 (2006), 7553–7570.

DOI: 10.1016/j.ijsolstr.2006.03.016

Google Scholar

[2] S.D. Yu, W.L. Cleghorn, Dynamic instability analysis of high-speed flexible four-bar mechanisms, Mech. Machine Theory, Vol. 37 (2002), 1261–1285.

DOI: 10.1016/s0094-114x(02)00041-1

Google Scholar

[3] C.Y. Lin, L.W. Chen, Dynamic stability of spinning pre-twisted sandwichbeams with a constrained damping layer subjected to periodic axial loads, Composite and Structures Vol. 70 (2005), 275–286.

DOI: 10.1016/j.compstruct.2004.08.033

Google Scholar

[4] O.N. Kirillov, Gyroscopic stabilization of non-conservative systems, Physics Letters A, Vol. 359 (2006), 204–210.

DOI: 10.1016/j.physleta.2006.06.040

Google Scholar

[5] P. Lancaster, A.S. Markus, F. Zhou, A wider class of stable gyroscopic systems, Linear Algebra Appl. Vol. 370 (2003), 257–267

DOI: 10.1016/s0024-3795(03)00395-1

Google Scholar

[6] T.V. Salnikova, The stability of linear potential gyroscopic systems, J. Appl. Math. Mech.,Vol. 70 (2006), 32–35.

Google Scholar

[7] S.A. Agafonov, The stability and stabilization of the motion of non-conservative mechanical Systems, J. Appl. Math. Mech.,Vol. 74 (2010), 401–405.

Google Scholar

[8] V.V. Voronin, V.V. Sazonov, Periodic motions of gyroscopic systems, J. Appl. Math. Mech.,Vol. 52 (1988) 560-569.

DOI: 10.1016/0021-8928(88)90103-7

Google Scholar

[9] R.J. Mcdonald, N.S. Namachchivaya, Global bifurcations in periodically perturbed gyroscopic systems with application to rotating shafts, Chaos, Solitons & Fractals, Vol. 8 (1997), 613-636.

DOI: 10.1016/s0960-0779(96)00116-6

Google Scholar

[10] B. Herve, J.J. Sinoub, H. Mahe, L. Jezequel, Extension of the destabilization paradox to limit cycle amplitudes for a nonlinear self-excited system subject to gyroscopic and circulatory actions, J. Sound Vibration, Vol. 323 (2009), 944-973.

DOI: 10.1016/j.jsv.2009.01.023

Google Scholar

[11] D.N. Vadiraja, A.D. Sahasrabudhe, Vibration analysis and optimal control of rotating pre-twisted thin-walled beams using MFC actuators and sensors, Thin-Walled Structures, Vol. 47 (2009), 555-567.

DOI: 10.1016/j.tws.2008.10.004

Google Scholar