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We show the existence of Hopf bifurcation in the delayed Liénard equation. The criterion for the criticality of the Hopf bifurcation is given based on the reduction of the infinite-dimensional problem onto a two-dimensional center manifold. Numerics are provided to verify our theoretical calculation. Application of this technique is discussed via a delayed Liénard oscillator.
A nonlinear self-excited vibration model of main drive system in cold rolling is established. The mechanism of torsional vibration in main drive system stability is discussed within multiple scale method as well as Hopf bifurcation theorem. Then, the periodic solutions and condition of Hopf bifurcation are derived and the influence by subcritical/supercritical bifurcation is analyzed. Based on the...
Torsional vibration generally causes serious instability and great damage in many rotating machinery. Hopf bifurcation control for some nonlinear torsional vibration system with delayed feedbacks is investigated. On the basis of the generalized dissipation Lagrange's equation, the dynamics equation of nonlinear torsional vibration system is established, and a nonlinear time-delayed feedback controller...
The primary objectives of the investigation are to analyze the dynamical behavior of an inertial shaker near the 1:4 strong resonance point by theoretical analyses and numerical simulation. Based on deriving the Poincaré mapping of the inertial shaker, a center manifold theorem technique is applied to reduce the Poincaré mapping to a two-dimensional one, and the normal form mapping associated with...
A dynamic model of the nonlinear elastics rotor-bearing system with coupling faults of pedestal looseness and rub-impact was set up, taking the linearity and cube item as the physics nonlinear factors. The periodic solution of system was analyzed by continuation-shooting algorithm for periodic solution of nonlinear non-autonomous system, and the stability of system periodic motion and unsteady law...
This work explains the hopf bifurcation and stability of self-excited vibration with the variety of vehicle velocity. Polygonal wear of tire is one of the most pressing problems to be solved in the process of a vehicle's research and design. Based on the non-linear character of friction coefficient, which combines the concept of static and kinetic friction, a model of tread-pavement, taking time-delay...
One stochastic nonlinear dynamical model has been proposed to describe the vibration of flexible beam under axial excitation considering the influence of the environment random factors. Firstly, the model has been simplified applying the stochastic average theory of quasi-integral Hamilton system .Secondly, we utilize the methods of Lyapunov exponent and boundary classification associated with diffusion...
The primary objectives of the investigation are to analyze the dynamical behavior of a three-degree-of-freedom vibratory system and choose the suitable system parameters to obtain larger impact velocity or larger regions of periodic motions for engineering application. Stability and local bifurcations of one-impact periodic motion are analyzed by using Jacobian matrix of the Poincareacute mapping...
A nonlinear dynamic model of rub-impact rotor-bearing system with slowly varying mass was set up. The periodic solution of system was analyzed by continuation-shooting algorithm for periodic solution of nonlinear non-autonomous system, and the stability of system periodic motion and unsteady law are discussed by Floquet theory. There exist periodic, quasi-periodic and chaotic motions in the response...
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