碰摩裂纹转子轴承系统的周期运动稳定性及实验研究

根据碰摩裂纹耦合故障转子轴承系统的非线性动力学方程，利用求解非线性非自治系统周期解的延拓打靶法，研究了系统周期运动的稳定性。研究发现，小偏心量下系统周期运动发生Hopf分岔，大偏心量下系统周期运动发生倍周期分岔，偏心量的加大使周期解的稳定性明显降低；系统碰摩间隙变小，碰摩影响了油膜涡动的形成，使失稳转速有所提高；裂纹深度的加大降低了系统周期运动的稳定性。本文的研究为转子轴承系统的安全稳定运行提供了理论参考。     

受外激励二阶参变系统的周期解及其稳定性

给出受外激励二阶参变系统周期解的新的计算方法，它对于相当广泛一类方程均可适用，并可对解的稳定性作出判断。     

Periodic,almost periodic and chaotic motions of forced self-sustained oscillators

Steady motions of the Van der Pol oscillator and an oscillator with hysteresis are studied numerically in this paper. Some features of periodic, almost periodic and chaotic motions of forced self-sustained oscillators are investigated. This paper has been presented at the ICTAM XVI Lyngby.     

The displacement discontinuity method in the analysis of open cracks

The application of the displacement discontinuity numerical technique to the solution of some problems of fracture mechanics is demonstrated in the hypothesis of homogeneous and elastic material. The fracture is supposed to be free from traction and is represented by a set of constant displacement discontinuity elements, except for two parabolic elements, located at each crack tip, in order to simulate the singularity of the solution near the crack tips. On the basis of the stress and displacement field determined by the displacement discontinuity method, the stress intensity factors for mode I and II are computed according to the method of the displacements. Three examples are provided to verify the validity of the formulation.

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Sommario Lo scopo del presente lavore è di illustrare l'applicazione del metodo numerico della Displacement Discontinuity alla soluzione di alcuni problemi di meccanica della frattura, nell'ipotesi di materiale omogeneo ed elastico. La frattura è supposta aperta ed è rappresentata da una linea di elementi a discontinuità di spostamento costante, con l'eccezione di due speciali elementi parabolici, ubicati agli apici, al fine di simulare la singolarita' del campo tensionale. Sulla base del campo degli sforzi e degli spostamenti cosi determinati, vengono ricavati i fattori di concentrazione degli sforzi in modo I e II mediante il metodo degli spostamenti. Vengono inoltre riportati tre esempi di calcolo, effettuati al fine di verificare la validità del procedimento proposto.

     

3D Coupled Displacement Discontinuity and Finite Element Analysis of Reservoir Behavior during Production in Semi-infinite Domain

In this paper, we apply a DDM-FEM coupling method to reservoir simulation to evaluate the reservoir behavior over a compacting oil reservoir in half space. We use displacement discontinuity methods to account for the reservoir surroundings, and finite element methods in the fully coupled simulation of the reservoir itself.     

Unsteady Motion of a Maxwellian Fluid Droplet in a Maxwellian Medium under the Action of Monotonic and Periodic Forces

Unsteady motion of a Maxwellian fluid droplet, which arises in a quiescent Maxwellian medium under the action of monotonic and periodic forces, is considered. In the initial period of time smaller than the relaxation time, the droplet is affected by elastic forces on the part of the fluid; moreover, the droplet itself is a viscoelastic material. A solution of the problem in the first approximation is found. The dependence of the amplitude of droplet velocity and the shift of the phase of oscillations on the relaxation time of the external and internal media and also on the frequency of oscillations of the driving force is analyzed. The passage to the limit in terms of density and viscosity of the internal medium is performed.__________Translated from Prikladnaya Mekhanika i Tekhnicheskaya Fizika, Vol. 46, No. 4, pp. 55–65, July–August, 2005.     

Asymptotic Technical Stability in Measure of the Nonlinear Controllable Motion of an Elastic Flight Vehicle

The asymptotic technical stability conditions for the nonlinear controllable motion of an elongated elastic flight vehicle are formulated. A longitudinal vertical flight at constant velocity is considered. The variation in the cross section, transverse strains, and vibrations of the vehicle are taken into account. The asymptotic technical stability criteria formulated depend on the key parameters of the controlled process, including the contribution of the weight due to curving of the vehicle axis to the transverse load and the aerodynamic force during a vertical flight     

Effect of Longitudinal Forced Motion on the Stability of Convection in a Plane Vertical Layer with Internal Heat Sources

The effect of longitudinal forced fluid motion on the mechanisms of instability of a convection flow developing in a plane vertical layer in the presence of internal heat sources is considered. It is found that forced motion which intensifies the central stream of the convection flow can lead to moderate stabilization of the hydrodynamic and thermal crisis mechanisms. In the presence of counterstream forced motion the flow stability increases sharply.__________Translated from Izvestiya Rossiiskoi Academii Nauk, Mekhanika Zhidkosti i Gaza, No. 2, 2005, pp. 14–17.Original Russian Text Copyright © 2005 by Lobov.     

旋转三角形绳系卫星编队系统动态稳定性分析

本文研究了平动点附近的旋转三角形绳系卫星编队系统的动态稳定性问题.为了便于分析,假设系绳始终保持张紧状态,且不计系绳的质量.为了建立更加符合实际的数学模型,考虑了姿态运动和轨道运动的相互影响,即姿轨耦合,并在此基础上推导出了考虑姿轨耦合的非线性动力学方程.最后用数值方法模拟了在不同的旋转速度情况下系统的动态稳定性,模拟结果表明旋转速率越大系统稳定性越好.     

Water Redistribution in Irrigated Soil Profiles: Invariant Solutions of the Governing Equation

Exact solutions for a class of nonlinear partial differential equations modelling soil water infiltration and redistribution in irrigation systems are studied. These solutions are invariant under two-parameter symmetry groups obtained by the group classification of the governing equation. A general procedure for constructing invariant solutions is presented in a way convenient for investigating numerous new exact solutions.     

The Dynamics of Stretchable Rods in the Inertial Case

Nonlinear amplitude equations for the near-threshold behavior of twisted extensible elastic rods under tension with inertial and dissipative dynamics are derived. In the inertial case localized solutions to the amplitude equations are derived and a linear stability criterion for the pulse solutions is obtained using the Hamiltonian formulation of the problem.     

The deformation of the front of a 3D interface crack propagating quasistatically in a medium with random fracture properties

One studies the evolution in time of the deformation of the front of a semi-infinite 3D interface crack propagating quasistatically in an infinite heterogeneous elastic body. The fracture properties are assumed to be lower on the interface than in the materials so that crack propagation is channelled along the interface, and to vary randomly within the crack plane. The work is based on earlier formulae which provide the first-order change of the stress intensity factors along the front of a semi-infinite interface crack arising from some small but otherwise arbitrary in-plane perturbation of this front. The main object of study is the long-time behavior of various statistical measures of the deformation of the crack front. Special attention is paid to the influences of the mismatch of elastic properties, the type of propagation law (fatigue or brittle fracture) and the stable or unstable character of 2D crack propagation (depending on the loading) upon the development of this deformation.     

Phase transitions induced by extension in a slender SMA cylinder: Analytical solutions for the hysteresis loop based on a quasi-3D continuum model

In this paper, we propose a quasi-3D continuum model to study the rate-independent hysteresis phenomenon in phase transitions of a slender shape memory alloy (SMA) cylinder subject to the uniaxial tension. Based on the three-dimensional field equations and the traction-free boundary conditions, by using a coupled series-asymptotic expansion method, we manage to express the total elastic potential energy of the cylinder in terms of the leading order term of the axial strain. We further consider the rate-independent dissipation effect in a purely one-dimensional setting. The mechanical dissipation functions are also expressed in terms of the axial strain. The equilibrium configuration of the cylinder is then determined by using the principle of maximizing the total energy dissipation. An illustrative example with some special chosen material constants is further considered. Free end boundary conditions are proposed at the two ends of the cylinder. By conducting a phase plane analysis and through some calculations, we obtain the analytical solutions of the equilibrium equation. We find that the engineering stress–strain curves corresponding to the obtained solutions can capture some important features of the experimental results. It appears that the analytical results obtained in this paper reveal the multiple solutions nature of the problem and shed certain light on the instability phenomena during the phase transition process.     

A numerical study of an unsteady laminar flow in a doubly constricted 3D vessel

Unsteady flow dynamics in doubly constricted 3D vessels have been investigated under pulsatile flow conditions for a full cycle of period T. The coupled non‐linear partial differential equations governing the mass and momentum of a viscous incompressible fluid has been numerically analyzed by a time accurate Finite Volume Scheme in an implicit Euler time marching setting. Roe's flux difference splitting of non‐linear terms and the pseudo‐compressibility technique employed in the current numerical scheme makes it robust both in space and time. Computational experiments are carried out to assess the influence of Reynolds' number and the spacing between two mild constrictions on the pressure drop across the constrictions. The study reveals that the pressure drop across a series of mild constrictions can get physiologically critical and is also found to be sensitive both to the spacing between the constrictions and the oscillatory nature of the inflow profile. The flow separation zone on the downstream constriction is seen to detach from the diverging wall of the constriction leading to vortex shedding with 3D features earlier than that on the wall in the spacing between the two constrictions. Copyright © 2002 John Wiley & Sons, Ltd.     

Nonlinear Vibrations of a Simply Supported Rectangular Metallic Plate Subjected to Transverse Harmonic Excitation in the Presence of a One-to-One Internal Resonance

The nonlinear response of rectangular and square metallic plates subjectto transverse harmonic excitations is studied. The nonlinearitiesoriginate from the use of Von Kármán strains. The method of multiplescales is used to solve the system of differential equationsapproximately. Frequency response curves are presented for both squareand rectangular plates for primary resonance of either mode in thepresence of a one-to-one internal resonance. Stability of steady statesolutions is investigated. Bifurcation points and their types arediscussed.     

Regularity criteria for the 3D MHD equations in terms of the pressure

In this paper we consider the regularity criteria for weak solutions to the 3D MHD equations. It is proved that under the condition b being in the Serrin's regularity class, if the pressure p belongs to L^α,γ with or the gradient field of pressure p belongs to L^α,γ with on [0,T], then the solution remains smooth on [0,T].     

Traction discontinuity problem in 3D BEM of the transversely isotropic material

The so-called edge problem, i.e., the traction discontinuity at edges or corners of the domain, is solved for the case of the transversely isotropic material being introduced into 3D BEM. The auxiliary relationship equations for the additional traction components are derived and the arbitrary inclination of the isotropic plane of the material is taken into account in the mean time. An example is given, and the comparison of the numerical result of the example with the theoritical solution is also illustrated.     

用刚体元方法求空间极限平衡问题的上限解

刚体元方法是研究块体系的变形和运动的一种数值方法,可以用它来研究弹塑性物体的极限平衡问题,文中用通用的二维刚体元程序计算了正方形柱体顶面中心区域作用方形基础载荷情况的上限解,结果表明,这种方法较好的精度和广泛的适用性。