Resonance analysis of single DOF parameter-varying system of magnetic-liquid double suspension bearing

Magnetic-liquid double suspension bearing(MLDSB)is mainly supported by electromagnetic suspension and supplemented by hydrostatic supporting.Its bearing capacity and stiffness can be greatly improved,and then it is suitable for the occasions of medium speed,heavy load.When the bearing system is excited by periodic force,the flow q and current i regulated by the double-closed-loop control mechanism change periodically.Then the risk of parametric resonance in MLDSB is greatly aggravated by the change of the parameter system,which seriously affects its operation stabil-ity and reliability.Therefore,this paper intends to study the resonance characteristics of the parame-ter system of MLDSB.Firstly,Marshall-Duffing equation of the parametric system is established by taking the flow q and the current i as variables respectively.Then,by using the asymptotic method,the occurrence condition and variation rule of the principal,1/2 Harmonic and 1/3 Harmonic para-metric resonance are solved.The results show that only the 1/2 Harmonic resonance of the flow q parameter varying system occurs accompanied by the resonance condition of high frequency.The principal,1/2 Harmonic and 1/3 Harmonic parametric resonance of the current i occur accompanied by the resonance condition of high frequency.And the 1/2 Harmonic resonance of the current i oc-curs accompanied by the non-single value bifurcation and dynamic bifurcation.The paper can pro-vide theoretical reference for the parameter design and stable operation of MLDSB.

NONLINEAR INSTABILITY OF WAVETRAIN UNDER INFLUENCES OF SHEAR CURRENT WITH VARYING VORTICITY AND AIR PRESSURE

Under the assumption of weak shear current with varying vorticity in water and weak air pressure the Zakharov theory is extended to include the effects of vorticity and air pressure on the modulation of water waves. This new equation is used to examine the influence of current and wind on the Benjamin-Feir sideband instability and long-time evolution of wavetrain. As strength of the current increases the bandwidth is found broadened, and the maximum growth rate of sidebands decreased. Periodic solution of sidebands in the presence of current is indicated, which means that shear current does not affect the downshift of wave spectrum peak. Energy input by imposing the air pressure leads to the enhancement of the lower sideband, which is in agreement with the finding of Hara and Mei (1991).

Generalized Mean-Flow Theory of Wave-Current-BottomInteractions

The interaction between waves, currents and bottoms in estuarine and coastal regions is ubiquitious, in particular the dynamic mechanism of waves on large-scale slowly varying currents. The wave action concept may be extended and applicated to the study of the mechanism. Considering the effects of moving bottoms and starting from the Navier-Stokes equation of motion of a vinous fluid including the Coriolis force, a generalized mean-flow medel theory for the nearshore region, that is, a set of mean-flow equations and their generalized wave action equation involving the three new kinds of actions termed respectively as the current wave action, the bottom wave action and the dissipative wave action which can be applied to arbitrary depth over moving bottoms and ambient currents with a typical vertical structure, is developed by vertical integration and time-averaglng over a wave peried, thus extending the classical concept, wave action, from the ideal averaged flow conservative system to the real averaged flow dissipative dynamical system, and having a large range of application.

NUMERICAL ANALYSIS AND EXPERI-MENT OF UNSTEADY THERMAL FIELD OF ROTOR PLATE FOR EDDY CURRENT RETARDER

The physical model based on heat transfer theory and virtual boundary method for analyzing unsteady thermal field of rotor plate for eddy current retarder used in automobile is established and boundary conditions are also defined. The finite element governing equation is derived by Galerkin method. The time differential item is discrete based on Galerkin format that is stable at any condition. And a new style of varying time step method is used in iteration process. The thermal field on the rotor plate at the radial and axle directions is analyzed and varying temperature at appointed points on two side-surfaces is measured. The testing and analytical data are uniform approximately. Finite element method can be used for estimating thermal field of the rotor plate at initial design stage of eddy current retarder.

EXTENDED MILD-SLOPE EQUATION

The Hamiltonian formalism for surface waves and the mild-slope approximation were empolyed in handling the case of slowly varying three-dimensional currents and an uneven bottom, thus leading to an extended mild-slope equation. The bottom topography consists of two components: the slowly varying component whose horizontal length scale is longer than the surface wave length, and the fast varying component with the amplitude being smaller than that of the surface wave. ne frequency of the fast varying depth component is, however, comparable to that of the surface waves. The extended mild-slope equation is more widely applicable and contains as special cases famous mild-slope equations below: the classical mild-slope equation of Berkhoff, Kirby's mild-slope equation with current, and Dingemans's mild-slope equation for rippled bed. The extended shallow water equations for ambient currents and rapidly varying topography are also obtained.

Women's Images in Chinese Literature Have Varied During Current Century

●In the early 20th century, awakening women who ran from their feudalistic families found that the male-dominated society, where men managed the exterior affairs and women managed the interior ones, was indestructible.