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The generalized Bagley–Torvik system is a linear oscillator whose damping force is described by fractional-order derivative with order between 0 and 2. This paper shows that as a sequential fractional-order differential equation with constant coefficients whose general solution depends on more than two free (independent) constants, the generalized Bagley–Torvik equation actually admits a general solution...
An analytic method to prove the sensitivity of chaotic motion to initial states and perturbations is proposed in this paper. With the fundamental perturbation method, a second order nonlinear differential equation is expanded into a series of perturbation equations, and by means of variation of constants, the general solutions of the perturbation equations are obtained. Based on these general solutions,...
Due to the singularity in the Local Area Network (LAN) traffic, the multifractal spectrums are used to study the characteristics of network traffic from the viewpoint of nonlinear dynamic system. First, the multifractal spectrums of the LAN traffic are introduced and established to investigate the complex features of the systems. Then, the distributions of spectrum parameter vs. the network traffic...
A crisis is investigated in high dimensional chaotic systems by means of generalized cell mapping digraph (GCMD) method. The crisis happens when a hyperchaotic attractor collides with a chaotic saddle in its fractal boundary, and is called a hyperchaotic boundary crisis. In such a case, the hyperchaotic attractor together with its basin of attraction is suddenly destroyed as a control parameter passes...
In this paper, a methodology to analytically predict the stable and unstable periodic solutions forn-dimensional discrete dynamical systems is applied to investigate the Henon map. The positive and negative iterative mappings of discrete maps are introduced for the mapping structure of the periodic solutions. The complete bifurcation and stability of the stable and unstable periodic solutions with...
The nonlinear dynamics and the vibration isolation effectiveness of a two-degree-of-freedom nonlinear vibration isolation system are numerically studied. The complex nonlinear behavior in the force-frequency plane of the system is analyzed. Cascades of bifurcation of the system with different excitation amplitude are also obtained. The power flow transmissibility is analyzed to validate the performance...
With the consideration of thermal effect, an improved panel flutter model equation is established to study the dynamic behaviors of panel structures on supersonic aircrafts. The governing equation is approached byGalerkinMethod, and then the resulting ordinary differential equations of the panel are obtained. By the numerical simulation, some essential nonlinear phenomena are discovered, and they...
The parameter study of a machine-tool with intermittent cutting is completed for eccentricity frequency and amplitude. The effects with respect to chip length are also incorporated, such that comparisons of the parameter maps can be accomplished. Specific areas within the parameter maps are studied, via switching components, to explain the complicated motions within. In such a case, the switching...
Being lighter and stiffer than traditional metallic materials, nanocomposites have great potential to be used as structural damping materials for a variety of applications. Studies of friction damping in the nanocomposites are largely experimental, and there has been a lack of understanding of the damping mechanism in nanocomposites. A new friction model is developed to study the energy dissipation...
This chapter deals with the nonlinear analysis of a system with two rigid rotors connected by a spline coupling and mounted on isotropic bearings. The coupling has Coulomb friction. The system is found to have three unstable fixed points and a limit cycle above a certain critical speed. The response of the system at the limit cycle indicates transient chaos, which is usually an artifact of the crisis...
In this chapter, the influence of cross-coupling effects on the rubbing-related dynamics of rotor/stator systems is investigated. The model considered in this chapter is a four-dof rotor/stator system, which takes into account the dynamics of the stator and the deformation on the contact surface as well as the cross-coupling effects. The stability of the synchronous full annular rub solution of the...
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