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Studies of Nonlinear Vibration Responses of Bearing-Supported Shaft Systems Subjected to Collision Constraints
|關鍵字:||Vibration;碰撞;Bearing;Collision;Constraint;撓性軸承;非線性;振動||出版社:||機械工程學系所||引用:|| G. Ioannou, A. Woowat and R. Gohar “Multiple Roller Bearing-Shaft Systems” Wear, Vol. 81, 1982, PP. 47-58.  C.W. Lee, Y.G. Jei“Modal Analysis of Continuous Rotor-Bearing Systems” Journal of Sound and Vibration, Vol. 126, Issue 2, 1988, PP. 345-361.  N. H. Shabaneh, Jean W. Zu“Dynamic Analysis of Rotor Shaft Systems with Viscoelastically Supported Bearings”Mechanism and Machine Theory, Vol. 35, 2000, PP. 1313-1330.  S.P. Harsha“Nonlinear Dynamic Analysis of a High-Speed Rotor Supported by Rolling Element Bearings”Journal of Sound and Vibration, Vol. 290, 2006, PP. 65-100.  M.H. Eissa, U.H. Hegazy, Y.A. Amer“Dynamic Behavior of an AMB Supported Rotor Subject to Harmonic Excitation”Applied Mathematical Modelling, Vol. 32, 2008, PP. 1370-1380.  Mohammed F. Abdul Azeez, Alexander F. Vakakis,“Numerical and Experimental Analysis of a Continuous Overhung Rotor Undergoing Vibro-Impacts”International Journal of Non-Linear Mechanics, Vol. 34, 1999, PP.415-435.  J.Zapomel, C.H.J.Fox, and EMalenovsky, “Numerical Investigation of a Rotor System with Disc-Housing Impact”Journal of Sound and Vibration, Vol. 2, No.243, 2001, PP.215-240.  Q. -S. Lu, Q. -H. Li, E. H. Twizell“The Existence of Periodic Motions in Rub-Impact Rotor Systems”Journal of Sound and Vibration, Vol. 264, 2003, PP. 1127-1137.  O. Grapis, V. Tamuzsb, N.-G. Ohlson, J. Andersonsb,“Overcritical High-Speed Rotor Systems, Full Annular Rub and Accident” Journal of Sound and Vibration, Vol. 290, 2006, PP. 910-927.  S. Popprath, H. Ecker“Nonlinear Dynamics of a Rotor Contacting an Elastically Suspended Stator”Journal of Sound and Vibration, Vol. 308, 2007, PP. 767-784.  S. Popprath, H. Ecker“The Effect of Bearing Cage Run-Out on the Nonlinear Dynamics of a Rotating Shaft”Journal of Sound and Vibration, Vol. 308, 2007, PP. 767-784.||摘要:||
The objective of this thesis is to develop a model for studying of nonlinear vibration of bearing-supported rigid shaft systems subjected to collision constraints. The system consists of a rigid shaft and a rigid disk. The shaft is supported by bearings which are modeled as springs and dampers. The kinetic energy and the potentail energy of the system are derived. The work done by supported forces of bearings are also considered. By using the Lagrange equations, the equations of motion of the bearing-supported shaft systems are derived. Next, the geometrical constraints when the collision occurs are found. At last, the relations between the velocities of the shaft before and after impact are determind.
Analyses of transient responses of systems with and without collision are carried out, and are compared with those obtained using linearized equations of motion. Then, the individual influence of the parameters such as coefficient of restitution, bearing stiffness, the locations of bearings and collision constraints on the dynamic responses are investigated.
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