..., 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...

... to solve this model. The bifurcation and chaos in the proposed dynamic model with the change of the operating time and the excitation frequency are investigated by bifurcation and spectrum waterfall diagrams to analyze the bifurcation characteristics and the dimensionless mesh force. It is found...

... form and the bifurcation behaviors for the single- and two-degree-of-freedom systems are studied in detail. A new type of bifurcation, which we refer to as a star bifurcation, has been observed for the symmetric two-degree-of-freedom system. This bifurcation is of codimension-four for the undamped case...

.... Moreover, the stability and bifurcation features of the system and the nonlinear dynamic stress of the rotor cannot be investigated. In this paper, the shooting method, path-following technique, and Floquet theory are chosen to evaluate the stability and bifurcation characteristics of a 3D rotor system...

... balance method and direct numerical simulation. Chaotic behavior is presented via the bifurcation diagrams and corresponding Lyapunov exponent. Some implications of the results on the applications of the devices are discussed. 28 04 2009 19 03 2010 28 11 2011 28 11 2011...

... of periodical change in contact position between balls and races. The numerical integration method is used to obtain the nonlinear dynamic responses; the effects of the rotating speed and the bearing clearance on dynamic responses are analyzed; and the bifurcation plots, the phase plane plots, the frequency...

... . Lu , Q. S. , To , C. W. S. , and Huang , K. L. , 1995 , “ Dynamic Stability and Bifurcation of an Alternating Load and Magnetic Field Excited Magneto-Elastic Beam ,” J. Sound Vib. , 181 , pp. 873 – 891 . 0022-460X Shih , Y. S. , Wu , G. Y. , and Chen , J. S...

... probability density of amplitude and phase difference, the stochastic jump of the Duffing oscillator and P-bifurcation as the system parameters change are examined for the first time. The agreement between the analytical results and those from Monte Carlo simulation of original system shows that the proposed...

... of the beam are initially obtained in the frequency domain and then represented as integrations of complex function in the space-time domain. A bifurcation is found in critical speed against resonance frequency. When the dimensionless frequency is high, there is a single critical speed that increases...

... of Coulomb friction makes the trivial equilibrium, which is an unstable focus in the system without friction, into a locally asymptotically stable equilibrium set. The branch of stable nontrivial steady states is not bifurcated from the trivial steady state by the effect of Coulomb friction and is different...

.... Because the rotor is slender, the natural frequency p f n of a forward whirling mode and p b n of a backward whirling mode have the relation of internal resonance p f n : p b n = 1 : ( − 1 ) . Due to the influence of the internal resonance, various phenomena occur, such as Hopf bifurcation, an almost...

...Albert C. J. Luo; Lidi Chen The grazing bifurcation and periodic motion switching of the harmonically forced, piecewise linear system with impacting are investigated. The generic mappings relative to the discontinuous boundaries of this piecewise system are introduced. Based on such mappings...

...J. C. Chedjou; K. Kyamakya; I. Moussa; H.-P. Kuchenbecker; W. Mathis This paper studies the dynamics of a self-sustained electromechanical transducer. The stability of fixed points in the linear response is examined. Their local bifurcations are investigated and different types of bifurcation...

... to the nonlinear dynamical behavior analysis of a rigid rotor in the elliptical bearing support. Both balanced and unbalanced rotors are taken into consideration. Numerical simulations show that the balanced rotor undergoes a supercritical Hopf bifurcation as the rotor spin speed increases. The investigation...

... chaotic vibration, due to the 1 to ( − 1 ) type internal resonance at the major critical speed and twice the major critical speed are investigated. The following are clarified theoretically and experimentally: (a) the Hopf bifurcation and consecutive period doubling bifurcations possible route to chaos...

...Albert C. J. Luo The criteria for the grazing bifurcation of a periodically forced, piecewise linear system are developed and the initial grazing manifolds are obtained. The initial grazing manifold is invariant. The grazing flows are illustrated to verify the analytic prediction of grazing...

...J. K. Wang; M. M. Khonsari A method is developed for predicting the stability envelope of a rotor-bearing system using the Hopf bifurcation theory. Results are compared to published literature obtained using a trial-and-error method. Newkirk , B. L. and Taylor , H. D. , 1925...

... to the fact that the conditions for resonances between breathers and linear modes are much less restrictive in the former than the latter case. Furthermore, the bifurcation properties are quite different in the two cases: For example, the phenomenon of complex instability, observed only for the “soft spring...

...Baozhong Yang; C. Steve Suh Spectral analysis has been widely applied to the detection of bifurcation and the determination of the extent to which dynamic instability and chaotic responses develop. However, because spectral analysis employs stationary sinusoids in representing time-varying signals...

... the response of the rotor are a set of two-degree-of-freedom nonlinear differential equations with time delay coupling in nonlinear terms. It is found that as the time delay increases beyond a critical value, the equilibrium position of the rotor motion becomes unstable and may bifurcate into two qualitatively...