裂纹转子分岔、混沌行为研究

分析非线性涡动中裂纹转子在裂纹存在和裂纹扩展两种情形下的典型非线性动力学行为－－混沌和分岔现象。在2／3倍临界转速区，裂纹深度浅于R／2的裂纹转子有分岔和拟周期响应出现；深度超过R／2的裂纹转子会出现分岔及混沌现象。裂纹角β对这些非线性动力学行为有很大影响。     

裂纹转子振动特性分析

以具有刚性支承的水平Jefcott裂纹转子为研究对象,考虑涡动的影响,建立了裂纹转轴在固定坐标系中的刚度矩阵,推导了裂纹转子振动的运动方程,并通过数值方法分析了其动态特性。数值分析表明：裂纹转子振动响应中出现1X、2X、3X……分量,且当Ω=1/2,1/3…时,2X,3X…分量分别达到最大值;转子的中心轨迹形状随Ω变化而变化,当β=0-π逐渐增大时,响应中1X分量显著减小。考虑弯扭耦合振动时,振动响应中出现一些新的频率成分。同步激励的情况下,当ω＝ωN／n(n=2,3,4,…）时,扭转振动响应中nX分量也达到最大值。     

一类非线性离散人口模型的稳定性和振动性

本文讨论了非线性差分方程ｘｎ＋１＝ｘｎ／１－ａ－ｂｘｎ－ｋ＋ｃｘ＾２ｎ－ｋ平衡点的稳定性，并获得了此方程在条件ａ∈（１，∞），ｂ∈（－∞，＋∞）＝Ｒ，ｃ∈（０，∞）下其正解的渐近性质及其关于正平衡点振动的充分条件，且当Ｋ＝０时建立了正平衡点渐近稳定的充分必要性准则。’     

对饱和多孔介质波动问题中本构关系的探讨

依据连续介质力学的混合物理论，讨论了饱和多孔介质的波动一般方程。其中考虑了质量耦合、初始压力及其浮力效应等。对于澄清这一研究课题中的某些基本概念，以及完善其理论体系具有重要意义。）其中ｖ￣（２）为速度涨落，于是单位体积内流相的动能为：因此将流相动能的涨落Ｋ￣（２）归于自由能更自然些。又因为当：ｖ￣（２＊）≡ｖ￣１时，即Δｖ＝ｖ￣１－ｖ￣２＝０时ｖ￣（２）＝０，此时Ｋ￣（２）＝０而且显然Ｋ￣（２）随着Δｖ·Δｖ的增大而增大，一个简单的近似是令Ｋ￣（２）＝ρ·Δｖ＿ｋ·Δｖ＿ｋ并且是常数。由此可导出表现质量力。由自由能的非负性质知，所以有．由（４．１３ａ）很容易推出质量密度矩阵的对称性和正定性。参考文献     

非稳态非线性油膜力作用下柔性轴裂纹转子的动力特性分析

分析了在动载轴承非稳态非线性油膜力作用下，具有横向裂纹柔性轴Jeffcott转子在非线性涡动影响下的动力特性。通过数值计算表明，在油膜失稳转速前，随着裂纹轴刚度变化比的增大，系统在低转速区域内具有丰富的非线性动力行为，出现倍周期分叉及混沌现象，涡动振幅随转速升高而减小，直到非稳态非线性油膜失稳，在无裂纹转子油膜临界失稳点处发现了类Hopf分叉现象，系统运动由平衡变为拟周期运动；裂纹转子在油膜临界失稳时的系统运动亦为拟周期运动，裂纹转子轴刚度变化对油膜失稳点及油膜失稳之后转子的运动影响不大，转子系统作拟周期运动。     

对饱和多孔介质波动问题中本构关系的探讨

依据连续介质力学的混合物理论，讨论了饱和多孔介质的波动一般方程。其中考虑了质量耦合、初始压力及其浮力效应等。对于澄清这一研究课题中的某些基本概念，以及完善其理论体系具有重要意义。）其中ｖ￣（２）为速度涨落，于是单位体积内流相的动能为：因此将流相动能的涨落Ｋ￣（２）归于自由能更自然些。又因为当：ｖ￣（２＊）≡ｖ￣１时，即Δｖ＝ｖ￣１－ｖ￣２＝０时ｖ￣（２）＝０，此时Ｋ￣（２）＝０而且显然Ｋ￣（２）随着Δｖ·Δｖ的增大而增大，一个简单的近似是令Ｋ￣（２）＝ρ·Δｖ＿ｋ·Δｖ＿ｋ并且是常数。由此可导出表现质量力。由自由能的非负性质知，所以有．由（４．１３ａ）很容易推出质量密度矩阵的对称性和正定性。参考文献     

LY12复合型断裂的实验研究

应用有限元方法和断裂实验对铝合金ＬＹ１２在Ｉ＋Ⅱ型复合载荷作用下的弹塑性断裂行为进行了研究，给出了复合型弹塑性断裂的Ｊ积分准则，结果表明：（１）不同复合型下启裂Ｊ积分值满足ＪＩｉ／ＪＩｃ＋ＪⅡｉ／ＪⅡｃ＝１，ＪＭＣ＝ＪＩｉ＋ＪⅡｉ的关系，随Ⅱ型分量增加，启裂的Ｊ积分值ＪＭＣ增加ＪＩＣ为ＪＩＣ的两部；（２）ＪＭＣ值与复合比满足ＪＭＣ＝Ｋ＾２Ｉ．ＪＩＣ／（Ｋ＾２１＋αＫ＾２ＩＩ）＋αＫ＾２Ｉ．ＪＩＣ／     

用于断裂可靠性设计的P-Km-da/dN-ΔK曲面

本文提出了疲劳裂纹扩展Ｋｍ－ｄａ／ｄＮ－ΔＫ曲面，并给出了Ｐ－Ｋｍ－ｄａ／ｄＮ－ΔＫ曲面实验数据处理及参数估计公式；利用该曲面可进行断裂损伤折算及随机载荷谱作用下构件裂纹扩展寿命估算。最后给出了一实例。     

双晶体的取向因子

本文通过对双晶体应力分析，提出了双晶体的取向因子ΩＢ，与其组元单晶体Ｇ１，Ｇ２的Ｓｃｈｍｉｄ因子Ω１及Ω２的关系为ΩＢ＝ＶＧ１Ω１＋ＶＧ２Ω２－１．并借助于双晶体的取向因子ΩＢ来比较单晶体与双晶体塑性变形行为的差别，以确定晶界对滑移带开动的晶界阻力．     

一种光弹性法确定应力强度因子的简便方法

在考虑远场非奇异应力σａｘ影响的基础上,建立了Ⅰ－Ⅱ混合型裂纹问题应力强度因子Ｋ１、ＫⅡ与等差线条纹图上点的极坐标间的非线性方程,为确定ＫⅠ、ＫⅡ及σａ,本文将θ＝０及θ＝π／２两级轴与两级不同条纹交点的坐标代入方程,从而得到了一种光强弹性法确定Ⅰ－Ⅱ混合型裂纹问题应力强度因子的简便方法。作为实例,本文一了环树脂及聚碳酸脂材料在不同载荷、不同裂纹条件下的应力强度因子,并将所得结果与相应的理论计算值     

Experimental Observation of Chaotic Motion in a Rotor with Rubbing

This paper presents an application for chaotic motion identification in a measured signal obtained in an experiment. The method of state space reconstruction with delay co-ordinates with the dynamic evolution described by a map is used. Poincaré diagrams, correlation dimensions and Lyapunov exponents are obtained as tools for deciding about the existence of chaotic behaviour. The method is applied to measurements of the lateral displacement of a vertical rotor experiencing rubbing and in some signals chaos is observed. The work concludes that the possibility of chaotic motion is well determined with the observation of Poincaré diagrams and computation of Lyapunov exponents. Correlation dimensions computations, strongly influenced by noise, are not convenient tools for investigation of chaotic behaviour in signals generated by mechanical systems.     

The Analysis for the Airflow Exciting-Vibration Force of Control Stage of Steam Turbine

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Static and dynamic behaviour of a rigid rotor on journal bearings

This experimental investigation concerns the static and dynamic behaviour of a rigid balanced rotor on journal bearings. Running conditions were chosen in order to obtain relatively high eccentricity ratios near the instability threshold speeds.The results, compared also with the theoretical predictions of some authors, have substantially shown the importance of examining the static behaviour near the instability threshold speed to allow a correct interpretation of some aspects of the dynamic behaviour.In order to clarify the discrepancies between the observed and the theoretically predicted dynamic behaviour, some further tests have been carried out.

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Sommario E' stato esaminato sperimentalmente sia il comportamento statico che quello dinamico di un rotore rigido e bilanciato sostenuto da cuscinetti cilindrici lubrificati.Le condizioni di funzionamento sono state scelte in modo tale che, in prossimità della soglia di instabilità, il valore del rapporto di eccentricità risultasse relativamente grande.I risultati, confrontati anche con le indicazioni teoriche di altri autori, hanno sostanzialmente evidenziato l'importanza dell'esame del comportamento statico in prossimità della soglia di instabilità al fine di interpretare correttamente alcuni aspetti del fenomeno dell'instabilità.Sono state inoltre effettuate una serie di ulteriori indagini con lo scopo di chiarire le discordanze fra il comportamento dinamico osservato e quello previsto dalla teoria.

     

转子系统非线性动力学DEM建模研究

将DEM方法引入转子系统非线性动力学的分析计算,对其建模过程和有关本构关系,作了比较详尽的介绍。该模型可用于碰摩、弯曲振动和扭转振动等转子系统的大部分动力学和运动学问题分析计算,不仅适用于单跨转子系统,也适用于多跨转子系统,尤其是在碰摩计算时,可考虑其摩擦特性随时间历程而变的特点,从而使分析计算更加接近实际情况。     

Discussion on “Rectangular Plates with Free Edges on Elastic Foundations”

This paper points out the former work does not fulfill the boundary conditions that the concentrated force at the four corner points should not exist. Therefore, Ritz method adopted by the author concerned in the illustrative example will not be convergent in the best way. Moreover, Garlerkin method which is illustrated in this paper may carry out incorrect results if we apply its formulae. We have proved that the boundary conditions which govern the concentrated force equal to zero at the four corner points are indispensable if the problem is properly set.     

Analysis of unsteady wave processes in a rotating channel

The impact of passage rotation on the gasdynamic wave processes is analyzed through a numerical simulation of ideal shock-tube flow in a closed rotating-channel containing a gas in an initial state of homentropic solid-body rotation. Relevant parameters of the problem such as wheel Mach number, hub-to-tip radius ratio, length-to-tip radius ratio, diaphragm temperature ratio, and diaphragm pressure ratio are varied. It is shown that for a fixed geometry and initial conditions, the contact interface acquires a distorted three-dimensional time-dependent orientation at non-zero wheel Mach numbers. At a fixed wheel Mach number, the level of distortion depends primarily on the density ratio across the interface and also the hub-to-tip radius ratio. The nature of the rarefaction and shock wave propagation is one-dimensional, although the acoustic waves are diffracted due to the radially varying propagation speed. Under conditions of initially homentropic solid-body rotation, a degree of similarity exists between rotating and stationary shock-tube flows. This similarity is exploited to arrive at an approximate analytical solution to the Riemann problem in a rotating shock-tube.     

小阻尼转子系统动力学的本征解

本文把小阻尼转子系统的动力学方程化为一种新形式，用摄动法展开该方程，导致一个反对称矩阵的广义本征值问题，因此获得了高精度的本征解。文中给出了一个简例。     

大型转子-基础-地基系统的非线性动力分析

针对实际工程中的大型机组，在线性理论分析基础上，引入转子系统的非线性油膜力项，采用子结构模态综合法，形成一个比较接近实际大型汽轮发电机组的包括陀螺转子-非稳态非线性油膜转承-弹性基础-地基系统的非线性系统计算模型。通过对系统方程进行分块直接积分求解，得到了不同位置的轴承在不同转速和不同转子偏心量下引起的系统非线性动力学现象，为大机组的非线性分析和改进提供较完善的理论分析和计算的基础。     

求非线性转子－轴承系统周期响应的一种计算方法

本文把求非线性转子－轴承系统瞬态响应的分块Ｎｅｗｍａｒｋ方法与打靶法结合求系统的周期解，该方法利用了分块Ｎｅｗｍａｒｋ方法求解速度快的优点和Ｊａｃｏｂｉ矩阵求解时每步不需迭代的特点。本文首先给出周期解的求解公式，然后用一个算例，讨论了周期解的稳定性及失稳后的分岔行为。     

用机电耦合模型研究转子系统的非平稳过程

建立恰当的转子系统模型,对非平稳过程进行正确完备的描述是进行转子系统设计、实施状态监测和故障诊断的关键。通过考虑驱动电机的影响,建立了异步电机-受驱转子系统的机电耦合数学模型,并利用该模型对机电转子系统由串联补偿电容和负载波动引起的两种机电耦合非平稳过程进行了数值研究。研究结果表明：建立的机电耦合模型可以多方位地研究转子系统在非平衡过程中的机电耦合动力学规律。