PERFECTLY PLASTIC STRESS FIELD AT A MIXED-MODE CRACK TIP UNDER PLANE AND ANTI-PLANE STRAIN

Under the condition that any Perfectly plastic stress component at a crack tip isnothing but the function of θ only. making use of equilibrium equations, stress-strain-rate relations, compatibility equations and yield condition. in this paper. we derive thegeneral analytical expressions of the perfectly plastic stress field at a Mixed-Mode cracktip under plane and anti-plane strain. Applying this general analytical expressions to theMixed-Mode cracks. we can obtain the analytical expressions of perfectly plastic stressfields at the tips of Mixed-ModeⅠ-Ⅲ.Ⅱ-Ⅲ andⅠ-Ⅱ-Ⅲ cracks.     

Studies on nonlinear stability of three-dimensional H-type disturbance

The three-dimensional H-type nonlinear evolution process for the problem of boundary layer stability is studied by using a newly developed method called parabolic stability equations (PSE). The key initial conditions for sub-harmonic disturbances are obtained by means of the secondaryinstability theory. The initial solutions of two-dimensional harmonic waves are expressed in Landau expansions. The numerical techniques developed in this paper, including the higher order spectrum method and the more effective algebraic mapping for dealing with the problem of an infinite region, increase the numerical accuracy and the rate of convergence greatly. With the predictor-corrector approach in the marching procedure, the normalization, which is very important for PSE method, is satisfied and the stability of the numerical calculation can be assured. The effects of different pressure gradients, including the favorable and adverse pressure gradients of the basic flow, on the “H-type“ evolution are studied in detail. The results of the three-dimensional nonlinear “H-type“ evolution are given accurately and show good agreement with the data of the experiment and the results of the DNS from the curves of the amplitude variation, disturbance velocity profile and the evolution of velocity.     

A study of the construction of lyapunov function for a class of fourth order nonlinear systems

ＡＳＴＵＤＹＯＦＴＨＥＣＯＮＳＴＲＵＣＴＩＯＮＯＦＬＹＡＰＵＮＯＶＦＵＮＣＴＩＯＮＦＯＲＡＣＬＡＳＳＯＦＦＯＵＲＴＨＯＲＤＥＲＮＯＮＬＩＮＥＡＲＳＹＳＴＥＭＳＬｉａｎｇＺａｉ－ｚｈｏｎｇ（梁在中）（ＤｅｐａｒｔｍｅｎｔｏｆＡｐｐｌｉｅｄＭａｔｈｅｍａ...     

Almost sure stability condition of weakly coupled linear nonautonomous random systems

In this study, the sufficient condition of almost sure stability of twodimensional oscillating systems under parametric excitations is investigated. The systems considered are assumed to be composed of two weakly coupled subsystems. The driving actions are considered to be stationary stochastic processes satisfying ergodic properties. The properties of quadratic forms are used in conjunction with the bounds for the eigenvalues to obtain, in a closed form, the sufficient condition for the almost sure stability of the systems.     

基于扰动方程的超音速轴对称射流马赫波辐射研究

超音速不稳定波是导致剪切流失稳和转捩的主要不稳定模态,这种模态以马赫波的形式辐射到远场,从而产生强烈的声场。采用线性稳定性理论和非线性扰动方程(NLDE)分析,计算超音速轴对称射流不稳定波的扰动演化(Ma=2.1),对马赫波辐射进行研究,包括马赫波辐射方向、辐射源位置,以及随斯特劳哈尔数的变化情况。研究结果表明,在超音速轴对称射流中,马赫波沿固定方向辐射向远方,不稳定波相位沿另一方向传播,这两个方向相互正交;马赫波辐射源位置位于不稳定波压力幅值最大处;斯特劳哈尔数St越大,马赫波辐射的能力越强,辐射区域越集中。     

SINGULAR ANALYSIS OF BIFURCATION OF NONLINEAR NORMAL MODES FOR A CLASS OF SYSTEMS WITH DUAL INTERNAL RESONANCES

ＩｎｔｒｏｄｕｃｔｉｏｎＡｎｉｎｔｅｒｅｓｔｉｎｇｆｅａｔｕｒｅｉｎｔｈｅｆｒｅｅｖｉｂｒａｔｉｏｎｏｆａｎｏｎｌｉｎｅａｒｓｙｓｔｅｍｉｓｔｈｅｆａｃｔｔｈａｔｔｈｅｎｕｍｂｅｒｏｆｅｘｉｓｔｉｎｇｎｏｒｍａｌｍｏｄｅｓｍａｙｅｘｃｅｅｄｔｈｅｎｕｍｂｅｒｏｆｄｅｇｒｅｅｓｏｆｆｒｅｅｄｏｍ ,ａｐｈｅｎｏｍｅｎｏｎｎｏｔｅｎｃｏｕｎｔｅｒｅｄｉｎａｌｉｎｅａｒｓｙｓｔｅｍａｎｄｃａｕｓｅｄｂｙｍｏｄｅｂｉｆｕｒｃａｔｉｏｎ .Ｔｈｅｒｅｆｏｒｅｍｕｃｈｗｏｒｋｈａｓｂｅｅｎｄｏｎｅｏｎｔｈｅｓｔ…     

ADAPTIVE H-INFINITY CONTROL OF A CLASS OF UNCERTAIN NONLINEAR SYSTEMS

It is concerned with the problem of disturbance attenuation with stability for uncertain nonlinear systems by adaptive output feedback. By a partial-state observer and Backstepping technique, an adaptive output feedback controller was constructed, which can solve the standard gain disturbance attenuation problem with internal stability.     

Dynamic controller design for a class of nonlinear uncertain systems subjected to time-varying disturbance

Inheriting advantages of both proportional-integral-derivative controller and standard sliding mode control theory, a synthetic controller design for a class of nonlinear system is presented. Regarding the architecture of the developed controller, it does not include model-based nominal control term so that the method eliminates complicated processes for system parameters identification and design of extra compensators. With simple gain tuning rules, the proposed control algorithm provides global asymptotical stability and is capable of alleviating discontinuous control switching considerably. A self-sustained oscillations phenomenon caused by the proposed control configuration is also further addressed. Simulations and experiments are conducted to verify the feasibility and applicability of the proposed approach.     

Instability of solution for a class of the third order nonlinear differential equation

ＩＮＳＴＡＢＩＬＩＴＹＯＦＳＯＬＵＴＩＯＮＦＯＲＡＣＬＡＳＳＯＦＴＨＥＴＨＩＲＤＯＲＤＥＲＮＯＮＬＩＮＥＡＲＤＩＦＦＥＲＥＮＴＩＡＬＥＱＵＡＴＩＯＮＬｕＤｅｙｕａｎ卢德渊（ＲｅｃｅｉｖｅｄＮｏｖ１０１９９４ＣｏｍｍｕｎｉｃａｔｅｄｂｙＺｈａｎｇＳｈｉ...     

Sufficient practical-stability conditions for nonlinear impulsive systems

A new approach to solving the practical-stability problem for nonlinear impulsive systems is described.Translated from Prikladnaya Mekhanika, Vol. 40, No. 10, pp. 131–134, October 2004.     

一类非线性发展方程的交替分段显隐并行数值方法

给出了一类非线性发展方程的交替分段显隐并行数值方法 ,得到了方法的无条件稳定性和并行性兼顾的结果。数值例子说明理论分析的正确性和格式的有效性     

RESEARCH OF THE PERIODIC SOLUTION FOR A CLASS OF NONLINEAR DIFFERENTIAL EQUATIONS

ＲＥＳＥＡＲＣＨＯＦＴＨＥＰＥＲＩＯＤＩＣＳＯＬＵＴＩＯＮＦＯＲＡＣＬＡＳＳＯＦ　ＮＯＮＬＩＮＥＡＲＤＩＦＦＥＲＥＮＴＩＡＬＥＱＵＡＴＩＯＮＳＲＥＳＥＡＲＣＨＯＦＴＨＥＰＥＲＩＯＤＩＣＳＯＬＵＴＩＯＮＦＯＲＡＣＬＡＳＳＯＦＮＯＮＬＩＮＥＡＲＤＩＦＦＥ...     

Composite fuzzy control of a class of uncertain nonlinear systems with disturbance observer

Nonlinear Dynamics - In this paper, a novel composite control, using fuzzy logic system (FLS) and disturbance observer, is proposed for a class of uncertain nonlinear systems with actuator...     

一类非线性发展方程的交替分组的并行数值算法

给出了一类非线性发展方程的交替分组4点格式,并得到该方法的无条件稳定性及具有并行本性兼顾的结果。能够适合在并行计算系统上使用。文中还进行了并行计算的数值实验。     

旋转机械系统多自由度非线性动力学数值分析

首先将转子系统的动力响应问题归结为2n维未知向量v的一阶非线性动力学方程dv／dt=Hv＋f（v,t）,并给出了求解这一方程的一次近似式法和三次多项式迫近法。在非稳态、非线性油膜力等作用下,以刚性Jeffcott转子与112个自由度的汽轮发电机组低压转子系统为例,用上述求解方法分析了它们的动力响应及非线性动力学特性;其问,还将计算结果与Runge—Kutta法、Newmark法的相应结果进行了比较,并深入讨论了数值稳定性问题。汽轮发电机组的算例表明对一些具有较复杂的非线性右端项,、同时规模又较大的问题,如果采用四阶Runge—Kutta法,才算几步就因数值骤然增大而失控;但若用同样步长的一次近似式,由于它是一种显式的无条件稳定算式,则计算过程迅速且结果合理可靠。     

二自由度耦合非线性随机系统的最大Lyapunov指数和稳定性

利用摄动方法讨论了一类耦合二自由度非线性系统，在小强度白噪声参数激励下系统运动模态的稳定性，获得了系统扩散过程的稳态概率密度的渐近表达式，由此获得了系统运动模态几乎必然稳定的充分必要条件。     

On the asymptotical behaviour of solutions of a class of nonlinear control systems

Ｃｏｎｓｉｄｅｒｔｈｅｆｏｌｌｏｗｉｎｇｎｏｎｌｉｎｅａｒｃｏｎｔｒｏｌｓｙｓｔｅｍ：·ｘ＝Ａｘ＋Ｂ（σ）,σ＝ＣＴｘ,（１）ｗｈｅｒｅｘ＝（ｘ１,ｘ２,…,ｘｎ）Ｔ∈Ｒｎ,ｔｈｅｎｏｔｅＴｅｘｐｒｅｓｓｅｓｔｈｅｔｒａｎｓｐｏｓｅｏｆｍａｔｒｉｘａｎｄｖｅｃｔｏｒ,Ａ,ＢａｎｄＣａｒｅｎ×ｎ,ｎ×ｍａｎｄｎ×ｍｃｏｎｓｔａｎｔｍａｔｒｉｃｅｓｒｅｓｐｅｃｔｉｖｅｌｙ,σ＝（σ１,σ２,…,σｍ）Ｔ∈Ｒｍａｎｄ（σ）＝（１（σ１）,２（σ２）,…,ｍ（σｍ））Ｔ：Ｒｍ→Ｒｍｉｓｃｏｎｔ…     

Conditional and unconditional nonlinear stability for convection induced by absorption of radiation in a porous medium

Convection induced by the selective absorption of radiation is investigated, for the case of an internal heat source that is modelled quadratically with respect to concentration. The growth rate for the linearised system is shown to be real, and a linear instability analysis is performed. To establish conditional and unconditional nonlinear stability results, both the Darcy and Forchheimer models are employed to describe fluid flow. Due to the presence of significant regions of potential subcritical instabilities, the results indicate that linear theory may only be accurate enough to predict the onset of convective motion when the model for the internal heat source is predominantly linear.Received: 6 May 2003, Accepted: 9 August 2003, Published online: 12 December 2003     

GLOBAL ATTRACTIVITY FOR A CLASS OF NONLINEARDELAY DIFFERENCE EQUATIONS

ＩｎｔｒｏｄｕｃｔｉｏｎＣｏｎｓｉｄｅｒｔｈｅｇｌｏｂａｌａｔｔｒａｃｔｉｖｉｔｙｏｆｔｈｅｎｏｎｌｉｎｅａｒｄｅｌａｙｄｉｆｆｅｒｅｎｃｅｅｑｕａｔｉｏｎΔｘｎ+ａｎｘｎ+ｆ(ｎ ,∑0ｓ=-ｋ ｑｓ,ｎｘｓ+ｎ) =0　 (ｎ=0 ,1 ,2 ,… ) . ( 1 )ＴｈｅｉｎｉｔｉａｌｖａｌｕｅｏｆＥｑ .( 1 )ｉｓｘｓ =φｓ　 (ｓ=-ｋ ,-ｋ+ 1 ,… ,-1 ,0 ) . ( 2 )Ｉｎｔｈｅｓｅｑｕｅｌ,ｗｅａｌｗａｙｓｓｕｐｐｏｓｅｔｈａｔＤ1) ａｎ ｉｓａｎｏｎｎｅｇａｔｉｖｅｒｅａｌｓｅｑｕｅｎｃｅ ,0 ≤ａｎ <1ａｎｄｋｉｓａｐｏｓｉｔｉｖｅ…