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。     

转子—轴承—基础系统的动力分析计算程序;DAROF程序简介

采用模态综合法可以将转子——轴承——基础系统简化成一个只有很少自由度但又有较高近似程度的数学模型,从而对整系统进行各种动力分析。本文介绍了根据[1]的计算方法而编制的计算机程序——DAROF (Dynamic Analysis of Rotor—Oilfilm—Foundation)。作为实例,计算了国产30万千瓦核汽轮发电机组(1:10)几何相似模型的临界转速,并与实测值进行了比较。结果表明,不仅计算值与实测值接近,而且实验中所观察到的主要现象也能由计算结果给以解释。     

外弹性支承滑动轴承—刚性转子系统非线性动力稳定性的研究

研究外弹性支承滑动轴承－刚性转子系统的动力稳定性问题。建立了弹性支承圆瓦轴承－Jeffcot转子系统的力学模型,针对滑动轴承水平转子,在油膜力非线性的情况下,采用Newmark方法计算其响应。对于一个具体的算例,通过改变其参数,确定其稳定区,并与滑膜力线性化时理论分析的结果进行了比较。     

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。     

弹性支撑圆柱绕流稳定性分析

基于CFD 技术,采用系统辨识方法,建立了亚临界雷诺数(Re < 47) 下绕圆柱流动的非定常气动力模型(reduced order model, ROM). 耦合结构运动方程和降阶气动力模型,建立了弹性支撑圆柱绕流的稳定性分析模型. 算例分析了亚临界雷诺数下,结构固有频率、质量比等参数以及支撑方式对弹性系统稳定性的影响. 对于单自由度横向支撑圆柱,当结构固有频率趋近流动最不稳定模态频率时,弹性系统会在一定频率范围内失稳,这种现象最低可在Re~20 时出现. 旋转自由度的释放能够进一步降低系统的稳定性,可将临界雷诺数进一步降低至18 左右. ROM 方法不仅具有很高的效率,而且清晰地指出了弹性系统失稳的根本原因:流动模态和结构模态耦合作用导致结构模态失稳所致. 因此,失稳状态下系统振荡频率锁定于结构固有频率. 基于ROM 技术预测的失稳边界与直接CFD/CSD 仿真结果吻合,证明了该方法的正确性和精度.      

大型汽轮发电机组短路时轴系扭振动力响应计算与分析

大型汽轮发电机组在短路时的轴系扭振动力响应，对于机组的安全可靠运行甚为关键。本文以国产某２００ＭＷ机组为例，建立了轴系的连续质量计算模型，利用传递矩阵法求得其扭振固有频率及主振型，用振型查加法计算轴系在两相短路情况下的动力响应，计算中考虑了叶片叶轮系统与轴系扭振的耦合作用。本文对计算结果进行了分析，讨论了该机组的轴系扭振安全性，为机组的安全运行提供了理论依据。     

弹性连接旋转柔性梁动力学分析

采用Chebyshev 谱方法对考虑根部连接弹性的平面内旋转柔性梁动力学特性进行研究. 基于Gauss-Lobatto 节点与Chebyshev 多项式方法对柔性梁变形场进行离散,通过投影矩阵法施加固定及弹性连接边界条件. 利用Chebyshev 谱方法获得了系统固有频率和模态振型数值解,通过与有限元方法及加权残余法的比较,验证了方法的有效性. 分析了弹性连接刚度、角速度比率、系统径长比及梁的长细比等参数对系统固有频率及模态振型的影响. 研究发现:由于系统弯曲模态、拉伸模态的频率随各参数的变化规律不一致,将出现频率转向与振型转换现象;随着弹性连接刚度、角速度比率及系统径长比的增大,低阶弯曲模态频率增大并超过高阶拉伸模态频率,随着梁的长细比的增大,低阶拉伸模态频率增大并超过高阶弯曲模态频率.      

关于国际模态分析会议

在航空航天器、车辆、船舶、海洋工程、机床、动力机械、土建工程等结构系统的发展中,振动问题在分析、设计、使用过程中日益重要,结构动力特性的确定成为动态设计的核心环节。所谓模态分析就是用分析或试验的方法来确定结构系统的固有频率、阻尼系数和振型等模态参数的过程。广义的模态分析还包括试验与分析方法的结合。结构动力学修改,结构系统数学模型的建立,并用于分析系统的动力响应、稳定性以及振动控制。     

滚动轴承-偏置转子系统动力特性数值分析与实验研究

应用有限元法建立偏置转子的计算模型,采用考虑轴承Hertzian接触力和内间隙等非线性因素的二自由度滚动轴承模型,建立了滚动轴承-偏置转子系统的非线性动力学模型.通过数值仿真和实验研究分析了转子系统的非线性动力特性.实验数据和有限元模型计算结果是一致的,证实了所建立滚动轴承-转子系统非线性模型的合理性.发现由于滚动轴承非线性因素的影响,当转速达到系统共振转速的两倍附近时,激起了系统亚谐共振.     

不同约束条件对深海采矿输送管道动力学的影响

针对深海采矿系统长距离垂直输送管道顶端不同约束条件对复杂流固耦合振动特性的影响,采用基于双向流固耦合的模态分析方法,重点研究了铰接约束和弹性约束对管道固有频率及振型的影响;结合模态分析结果以及管道外壁所受应力和变形情况,对弹性约束管道进行谐响应分析,并根据分析结果对结构进行了优化设计。研究表明：对比两种约束条件模态分析结果,弹性约束管道固有频率最大、振幅最小,且振型最为简单,实际工程中管道顶端选用弹性约束最合适;当激励频率处于第7阶固有频率附近时,管道的振动响应最为激烈;通过增焊强环圈的方法对输送管道进行优化,对比优化前后模态分析结果,证明了优化的可行性。     

弹性地基上含孔隙功能梯度材料板的自由振动和动力响应

为研究弹性地基上含孔隙的材料特性沿厚度呈Sigmoid函数变化的功能梯度材料(S-FGM)板的振动特性,本文基于改进的Voigt模型,分别建立了孔隙为均匀分布和非均匀分布两种类型的功能梯度材料的物性参数模型。根据复合材料薄板理论导出了弹性地基上含孔隙的功能梯度材料板的运动方程,用伽辽金法寻求四边简支边界条件下板自由振动和动力响应的解析解;讨论了孔隙、弹性地基参数、材料组分指数等因素对S-FGM板自由振动和动力响应的影响。结果表明:孔隙对板自振频率的影响比较复杂,不仅与孔隙率的大小和分布形式有关,还与弹性地基参数有关;当有弹性地基作用时,板的量纲归一化基频随着孔隙率的增大而提高,并且孔隙均匀分布的S-FGM板与孔隙非均匀分布的情况相比,其量纲归一化基频更高;孔隙增大了板的动力响应,其中孔隙为均匀分布的板的动力响应对孔隙率的变化更为敏感。     

Dynamic behaviour modelling of a flexible gear system by the elastic foundation theory in presence of defects

In this paper a novel approach for modelling a spur gear system using finite element method combined with elastic foundation theory is developed. The pinion is modelled by shaft finite element and the wheel by a three-dimensional finite element. Elastic foundation is utilized to model the gearmesh. The modal analysis showed the presence of lower natural frequency for thin rimmed gear cases susceptible to be excited by the operating running condition. The transmission error is affected by the wheel shape and by the presence of lower natural frequencies. Eccentricity error and tooth crack are also modelled to observe their influence on the dynamics behaviour of the system. It was found that they are responsible of the apparition of an amplitude modulation.     

The validity range of CPT and Mindlin plate theory in comparison with 3-D vibrational analysis of circular plates on the elastic foundation

The validity and the range of applicability of the classical plate theory (CPT) and the first-order shear deformation plate theory, also called Mindlin plate theory (MPT), in comparison with three-dimensional (3-D) p-Ritz solution are presented for freely vibrating circular plates on the elastic foundation with different boundary conditions. In order to achieve this purpose, a study of the 3-D elasticity solution is carried out to determine the free vibration frequencies of clamped, simply supported and free circular plates resting on an elastic foundation. The Pasternak model with adding a shear layer to the Winkler model is used for describing the elastic foundation. In addition to being employed the p-Ritz algorithm, the analysis is based on the linear, small strain and 3-D elasticity theory. In this analysis method, a set of orthogonal polynomial series in a cylindrical polar coordinate system is used to arrive eigenvalue equation yielding the natural frequencies for the circular plates. The accuracy of these results is verified by appropriate convergence studies and checked with the available literature and the MPT. Furthermore, the effect of the foundation stiffness parameters, thickness-radius ratio, and different boundary conditions on the ill-conditioning of the mass matrix as well as on the vibration behavior of the circular plates is investigated. Afterwards, the validity and the range of applicability of the results obtained on the basis of the CPT and MPT for a thin and moderately thick circular plate with different values of the foundation stiffness parameters are graphically presented through comparing them with those obtained by the present 3-D p-Ritz solution. Finally, the phenomenon of mode shape switching is investigated in graphical forms for a wide range of the Winkler foundation stiffness parameters.     

Surface and thermal effects on vibration of embedded alumina nanobeams based on novel Timoshenko beam model

This paper deals with the free vibration analysis of circular alumina （Al2O3） nanobeams in the presence of surface and thermal effects resting on a Pasternak foun- dation. The system of motion equations is derived using Hamilton＇s principle under the assumptions of the classical Timoshenko beam theory. The effects of the transverse shear deformation and rotary inertia are also considered within the framework of the mentioned theory. The separation of variables approach is employed to discretize the governing equa- tions which are then solved by an analytical method to obtain the natural frequencies of the alumina nanobeams. The results show that the surface effects lead to an increase in the natural frequency of nanobeams as compared with the classical Timoshenko beam model. In addition, for nanobeams with large diameters, the surface effects may increase the natural frequencies by increasing the thermal effects. Moreover, with regard to the Pasternak elastic foundation, the natural frequencies are increased slightly. The results of the present model are compared with the literature, showing that the present model can capture correctly the surface effects in thermal vibration of nanobeams.     

Vertical vibrations of elastic foundation resting on saturated half-space

This paper is mainly concerned with the dynamic response of an elastic foun- dation of finite height bounded to the surface of a saturated half-space.The foundation is subjected to time-harmonic vertical loadings.First,the transform solutions for the governing equations of the saturated media are obtained.Then,based on the assumption that the contact between the foundation and the half-space is fully relaxed and the half- space is completely pervious or impervious,this dynamic mixed boundary-value problem can lead to dual integral equations,which can be further reduced to the Fredholm integral equations of the second kind and solved by numerical procedures.In the numerical exam- ples,the dynamic compliances,displacements and pore pressure are developed for a wide range of frequencies and material/geometrical properties of the saturated soil-foundation system.In most of the cases,the dynamic behavior of an elastic foundation resting on the saturated media significantly differs from that of a rigid disc on the saturated half-space. The solutions obtained can be used to study a variety of wave propagation problems and dynamic soil-structure interactions.     

On discrete supports and continued support of structures

There have been several papers dealing with elastic discrete supports of structures. And we are interested in what relation there is between elastic discrete supports and continued support and what difference would result in for dynamic properties of structures under the two kinds of support. Through the present analysis, it is pointed out that natural frequencies reflect a certain proportion of kinetic and potential energies in total energy of a system, and the frequencies can be guaranteed to be invariable in transforming between elastic discrete and continued supports by means of a proper energy equivalence. And the theoretical formulation of beams and numerical results of shells of revolution are presented in this paper.     

弹性地基上转动FGM梁自由振动的DTM分析

基于Euler-Bernoulli梁理论,利用广义Hamilton原理推导得到弹性地基上转动功能梯度材料(FGM)梁横向自由振动的运动控制微分方程并进行无量纲化,采用微分变换法(DTM)对无量纲控制微分方程及其边界条件进行变换,计算了弹性地基上转动FGM梁在夹紧-夹紧、夹紧-简支和夹紧-自由三种边界条件下横向自由振动的无量纲固有频率,再将控制微分方程退化到无转动和地基时的FGM梁,计算其不同梯度指数时第一阶无量纲固有频率值,并和已有文献的FEM和Lagrange乘子法计算结果进行比较,数值完全吻合。计算结果表明,三种边界条件下FGM梁的无量纲固有频率随无量纲转速和无量纲弹性地基模量的增大而增大;在一定无量纲转速和无量纲弹性地基模量下,FGM梁的无量纲固有频率随着FGM梯度指数的增大而减小;但在夹紧-简支和夹紧-自由边界条件下,一阶无量纲固有频率几乎不变。     

Non-local free and forced vibrations of graded nanobeams resting on a non-linear elastic foundation

We consider in this paper the free and forced vibration response of simply-supported functionally graded (FG) nanobeams resting on a non-linear elastic foundation. The two-constituent Functionally Graded Material (FGM) is assumed to follow a power-law distribution through the beam thickness. Eringen׳s non-local elasticity model with material length scales is used in conjunction with the Euler–Bernoulli beam theory with von Kármán geometric non-linearity that accounts for moderate rotations. Non-linear natural frequencies of non-local FG nanobeams are obtained using He׳s Variational Iteration Method (VIM) and the direct and discretized Method of Multiple Scales (MMS), while the primary resonance analysis of an externally forced non-local FG nanobeam is performed only using the MMS. The effects of the non-local parameter, power-law index, and the parameters of the non-linear elastic foundation on the non-linear frequency-response are investigated.     

粘弹性地基上含孔隙的石墨烯增强功能梯度板的振动

为分析粘弹性地基上含孔隙的石墨烯增强功能梯度板的自由和强迫振动特性，基于三参数粘弹性地基模型及复合材料薄板理论，建立了粘弹性地基上含孔隙石墨烯增强功能梯度板的运动方程，用伽辽金法求解其固有频率和动力响应，并通过数值算例分析了粘弹性地基参数、孔隙率、孔隙类型及石墨烯纳米片分布模式、含量等因素对自由振动和动力响应的影响．结果表明，固有频率随着孔隙率的增大非单调变化，孔隙率对固有频率的影响随着地基参数、孔隙类型的不同而不同．另外，在三种孔隙类型中，上下表面层含有最少孔隙数量的板的动挠度最小，且其动挠度随着孔隙率的增大而微弱提高．     

混凝土空心板动力损伤诊断研究

利用4块预应力混凝土空心板的动力测试数据,对板的支承条件和损伤参数进行了识别。识别板的支承条件时,引入弹性支座－质量体系,利用实测的前四阶固有频率作为已知信息,直接采用牛顿法求解,根据板的损伤特征,以线弹性断裂力学为基础,推导了混凝土构件裂缝截面转动刚度表达式。然后利用特征值灵敏度分析和实测的固有频率变化率对单条裂缝的位置及裂缝程度进行了识别。