Abstract
In order to explore the influence of combined gyroscopic coupling effect on the gyroscopic system, the dynamics of a beam undergoing both rotating and spinning motions as a bi-gyroscopic system is studied. The natural frequencies, modes, and stability of such a bi-gyroscopic system have been studied by the standard eigenvalue problems. The bifurcation series of frequencies and corresponding modal motions have been presented to show the gyroscopically coupled motions. The complex modes of the proposed bi-gyroscopic systems, such as whirling motions and in-plane reeling motions, have been illustrated.
Issue Section:
Technical Brief
References
1.
Cheng
, J. L.
, Xu
, H.
, and Yan
, A. Z.
, 2006
, “Frequency Analysis of a Rotating Cantilever Beam Using Assumed Mode Method With Coupling Effect
,” Mech. Based Des. Struct. Machines
, 34
(1
), pp. 25
–47
. 10.1080/153677305005015872.
Hashemi
, S. M.
, and Richard
, M. J.
, 2001
, “Natural Frequencies of Rotating Uniform Beams With Coriolis Effects
,” ASME J. Vib. Acoust.
, 123
(4
), pp. 444
–455
. 10.1115/1.13839693.
Guo
, X. Y.
, Yang
, X. D.
, and Wang
, S. W.
, 2019
, “Dynamic Characteristics of a Rotating Tapered Cantilevered Timoshenko Beam With Preset and Pre-Twist Angles
,” Int. J. Struct. Stability Dyn.
, 19
(4
), p. 1950043
. 10.1142/S02194554195004334.
Huo
, Y. L.
, and Wang
, Z. M.
, 2016
, “Dynamic Analysis of a Rotating Double-Tapered Cantilever Timoshenko Beam
,” Archive Appl. Mech.
, 86
(6
), pp. 1147
–1161
. 10.1007/s00419-015-1084-65.
Banerjee
, J. R.
, and Kennedy
, D.
, 2014
, “Dynamic Stiffness Method for Inplane Free Vibration of Rotating Beams Including Coriolis Effects
,” J. Sound Vib.
, 333
(26
), pp. 7299
–7312
. 10.1016/j.jsv.2014.08.0196.
Anilkumar
, A.
, and Kartik
, V.
, 2020
, “In-Plane Vibration of a Rigid Body Attached to a Flexible Rotating Beam
,” J. Sound Vib.
, 475
, p. 115245
. 10.1016/j.jsv.2020.1152457.
Ma
, H.
, Wang
, D.
, Tai
, X. Y.
, and Wen
, B. C.
, 2017
, “Vibration Response Analysis of Blade-Disk Dovetail Structure Under Blade Tip Rubbing Condition
,” J. Vib. Control
, 23
(2
), pp. 252
–271
. 10.1177/10775463155758358.
Parker
, R. G.
, and Sathe
, P. J.
, 1999
, “Free Vibration and Stability of a Spinning Disk-Spindle System
,” ASME J. Vib. Acoust.
, 121
(3
), pp. 391
–396
. 10.1115/1.28939929.
Parker
, R. G.
, and Sathe
, P. J.
, 1999
, “Exact Solutions for the Free and Forced Vibration of a Rotating Disk-Spindle System
,” J. Sound Vib.
, 223
(3
), pp. 445
–465
. 10.1006/jsvi.1998.209710.
Zu
, J. W. Z.
, and Han
, R. P. S.
, 1992
, “Natural Frequencies and Normal-Modes of a Spinning Timoshenko Beam With General Boundary-Conditions
,” ASME J. Appl. Mech.
, 59
(2
), pp. S197
–S204
. 10.1115/1.289948811.
Sturla
, F. A.
, and Argento
, A.
, 1996
, “Free and Forced Vibrations of a Spinning Viscoelastic Beam
,” ASME J. Vib. Acoust.
, 118
(3
), pp. 463
–468
. 10.1115/1.288820612.
13.
Wu
, J. S.
, Lin
, F. T.
, and Shaw
, H. J.
, 2014
, “Analytical Solution for Whirling Speeds and Mode Shapes of a Distributed-Mass Shaft With Arbitrary Rigid Disks
,” ASME J. Appl. Mech.
, 81
(3
), p. 034503
. 10.1115/1.402467014.
Behzad
, M.
, and Bastami
, A. R.
, 2004
, “Effect of Centrifugal Force on Natural Frequency of Lateral Vibration of Rotating Shafts
,” J. Sound Vib.
, 274
(3–5
), pp. 985
–995
. 10.1016/S0022-460X(03)00659-X15.
Chung
, J.
, Kang
, N. C.
, and Lee
, J. M.
, 1996
, “A Study on Free Vibration of a Spinning Disk
,” KSME Int. J.
, 10
(2
), pp. 138
–145
. 10.1007/BF0295365316.
Liang
, F.
, Yang
, X. D.
, Qian
, Y. J.
, and Zhang
, W.
, 2018
, “Transverse Free Vibration and Stability Analysis of Spinning Pipes Conveying Fluid
,” Int. J. Mech. Sci.
, 137
, pp. 195
–204
. 10.1016/j.ijmecsci.2018.01.01517.
Bahaadini
, R.
, and Saidi
, A. R.
, 2018
, “Stability Analysis of Thin-Walled Spinning Reinforced Pipes Conveying Fluid in Thermal Environment
,” Eur. J. Mech. A/Solids
, 72
, pp. 298
–309
. 10.1016/j.euromechsol.2018.05.01518.
Yang
, X. D.
, Yang
, J. H.
, Qian
, Y. J.
, Zhang
, W.
, and Melnik
, R. V. N.
, 2018
, “Dynamics of a Beam With Both Axial Moving and Spinning Motion: an Example of Bi-Gyroscopic Continua
,” Eur. J. Mech. A/Solids
, 69
, pp. 231
–237
. 10.1016/j.euromechsol.2018.01.00619.
Yang
, X. D.
, Wang
, S. W.
, Zhang
, W.
, Yang
, T. Z.
, and Lim
, C. W.
, 2018
, “Model Formulation and Modal Analysis of a Rotating Elastic Uniform Timoshenko Beam With Setting Angle
,” Eur. J. Mech. A/Solids
, 72
, pp. 209
–222
. 10.1016/j.euromechsol.2018.05.01420.
Zhang
, Y.-W.
, Yang
, X.-D.
, and Zhang
, W.
, 2020
, “Modeling and Dyanmic Analysis of Body-Fixed and Space-Fixed Flexible Rotor
,” J. Vib. Eng. Technol.
, 8
(1
), pp. 59
–66
. 10.1007/s42417-018-0057-921.
Pai
, P. F.
, Qian
, X.
, and Du
, X. W.
, 2013
, “Modeling and Dynamic Characteristics of Spinning Rayleigh Beams
,” Int. J. Mech. Sci.
, 68
, pp. 291
–303
. 10.1016/j.ijmecsci.2013.01.02922.
Ettles
, C.
, 1978
, “Bearing and Rotor Dynamics
,” Tribol. Int.
, 11
(1
), pp. 26
–26
. 10.1016/0301-679X(78)90099-323.
Katz
, R.
, Lee
, C. W.
, Ulsoy
, A. G.
, and Scott
, R. A.
, 1988
, “The Dynamic-Response of a Rotating Shaft Subject to a Moving Load
,” J. Sound Vib.
, 122
(1
), pp. 131
–148
. 10.1016/S0022-460X(88)80011-724.
Chen
, H.-Y.
, Mao
, X.-Y.
, Ding
, H.
, and Chen
, L.-Q.
, 2020
, “Elimination of Multimode Resonances of Composite Plate by Inertial Nonlinear Energy Sinks
,” Mech. Syst. Signal Process.
, 135
, p. 106383
. 10.1016/j.ymssp.2019.10638325.
Young
, T. H.
, and Chen
, M. S.
, 2010
, “Dynamic Stability of a Spinning Timoshenko Beam Subjected to a Moving Mass-Spring-Damper Unit
,” Proceedings of the ASME 10th Biennial Conference on Engineering Systems Design and Analysis
, Istanbul, Turkey
, July 12–24
.26.
Païdoussis
, M. P.
, 1998
, Fluid-Structure Interactions: Slender Structures and Axial Flow
, Vol. 1
, Elsevier Academic Press
, London
.Copyright © 2020 by ASME
You do not currently have access to this content.