QUANTITATIVE METHODOLOGY FOR STABILITY ANALYSIS OF NONLINEAR ROTOR SYSTEMS

Rotor-bearings systems applied widely in industry are nonlinear dynamic systems of multi-degree-of-freedom. Modem concepts on design and maintenance call for quantitative stability analysis. Using trajectory based stability-preserving and dimensional-reduction, a quantitative stability analysis method for rotor systems is presented. At first, an n-dimensional nonlinear non-autonomous rotor system is decoupled into n subsystems after numerical integration. Each of them has only onedegree-of-freedom and contains time-varying parameters to represent all other state variables. In this way, n-dimensional trajectory is mapped into a set of one-dimensional trajectories. Dynamic central point （DCP） of a subsystem is then defined on the extended phase plane, namely, force-position plane. Characteristics of curves on the extended phase plane and the DCP＇s kinetic energy difference sequence for general motion in rotor systems are studied. The corresponding stability margins of trajectory are evaluated quantitatively. By means of the margin and its sensitivity analysis, the critical parameters of the period doubling bifurcation and the Hopf bifurcation in a flexible rotor supported by two short journal bearings with nonlinear suspensionare are determined.

Quantitative relationship between channels and bars in a tidal reach of the lower Yangtze River:Implications for river management

Deep-water navigation channels in the tidal reaches of the lower Yangtze River are affected by water and sediment fluxes that produce complex shoals and unstable channel conditions.The Fujiangsha reach is particularly difficult to manage,as it has many braided channels within the tidal fluctuation zone.In this study,hydrologic and topographic data from the Fujiangsha reach from 2012 to 2017 were used to examine the variations in deposition and erosion,flow diversion,shoals,and channel conditions.Since the Three Gorges Dam became operational and water storage was initiated,the Fujiangsha reach has shown an overall tendency toward erosion.Channels deeper than 10 m accounted for 83.7% of the total erosion of the Fujiangsha reach during 2012-2017.Moreover,the dominant channel-forming sediments have gradually changed from suspended sediments to a mixed load of suspended and bed-load sediments.Deposition volumes of these sediments has varied significantly among different channels,but has mainly occurred in the Fubei channel.Furthermore,periodic variations in the Jingjiang point bar have followed a deposition-erosion-deposition pattern,and the downstream Shuangjian shoal mid-channel bar has been scoured and shortened.Approximately 44.0% of the bed load from the upstream Fujiangsha reach is deposited within the 12.5-m deep Fubei channel.The increased erosion and river flow from the Jingjiang point bar and the Shuangjian shoal during the flood season constituted 59.3% and 40.7%,respectively,of the total amount of siltation in the Fubei channel.