流固耦合系统动力响应的模态分析理论

本文建立了流固耦合系统动力响应的模态分析理论.首先,从系统的位移-速度势型有限元方程出发,导出了一对具有三个实对称矩阵的广义特征值问题以及两者的相互关系.然后,建立了模态矢量之间的广义正交关系,并通过模态展开,获得了系统对外界激励的响应的封闭解.作为示例,最后给出了两个具体问题的解答.     

管道及管路系统流固耦合振动问题的研究动态

对管道及管路系统流固耦合振动问题在近二十年来的进展作了综述。根据问题特点，将本课题分为三个分支，即从紊流到振动噪声源的研究，流－弹耦合振动的研究和声－弹耦合振动的研究。在分别总结这三个分支的研究成果的同时指出了尚需进一步研究的某些问题。     

ALE动网格法在流固耦合数值模拟中的应用

为了解决流固耦合问题中的物体大幅度运动带来的困难,采用ALE(Arbitrary Lagrange-Euler)动网格方法跟踪自由表面上浮体的运动.计算表明:浮体在无粘流体中的垂荡与弹簧-物体的振动模型理论解符合得较好;浮体在粘性流体中的自由横摇为阻尼运动,其横摇角度随时间的增加而减小,且在不同初始角度下运动系统的固有周期相当.在有外力力矩激励时,外力力矩的周期与系统的固有周期相当时浮体横摇运动趋于共振状态,运动幅度最大.计算结果验证了计算程序的可靠性与精度.本文方法为ALE方法应用于流体-多浮体耦合运动分析奠定了基础.     

流固耦合力学概述

本文简要介绍了流固耦合力学及其特点、研究分支、一些进展及进一步发展的趋势     

U型充液管道的流固耦合分析

基于流固耦合原理,在ADINA软件中建立了U型充液管道的有限元模型,对其进行了流固耦合模态分析,研究了壁厚对管道固有频率的影响;并对简支U型管道的充液过程进行了数值仿真,研究了充液加速度和壁厚对管道位移及应力的影响。结果表明:随着模态阶数的增加,管道的固有频率逐渐增大;在无耦合时计算的管道固有频率大于流固耦合状态时的结果,管道固有频率随壁厚的增加呈非线性增加;在充液过程中U型管道的最大应力出现在弯头处;在充液过程中管道的位移与应力随充液加速度的增大而增大,随壁厚的增大而减小;但无论充液加速度多大,充液后管道的最终位移基本相同。     

混凝土输送泵车臂架系统流固耦合振动分析

针对混凝土泵车的工作原理和结构特点,结合现有输送管流固耦合理论的研究成果,提出了基础有平动位移的悬臂输送管理论模型,并通过多体运动学理论和Hamilton变分原理,建立该模型的运动微分方程.采用有限单元理论建立混凝土泵车臂架系统的流固耦合运动微分方程.选取混凝土流速U=2.265m/s和不考虑混凝土流动进行对比仿真分析后发现:两者臂架振动响应均值相同;但稳态时两者振动幅值比值最大,接近2;而改变Rayleigh阻尼系数则对臂架振动响应影响不大,这说明混凝土的流动增加臂架振动阻尼效应显著.结合Matlab仿真分析与Ansys三维有限元模型,模拟计算出了臂架结构动应力,对比测点应力测试结果与模拟计算结果,两者应力历程变化趋势相似,应力值较接近,最大差异小于20MPa,验证了仿真模型的合理性.     

基于ALE有限元法的流固耦合强耦合数值模拟

针对不同流固耦合问题,提出一种基于任意拉格朗日--欧拉(ALE)有限元技术的分区强耦合算法. 运用半隐式特征线分裂算法求解ALE描述下的不可压缩黏性流体Navier-Stokes方程. 分别考虑一般平面运动刚体和几何非线性固体,采用复合隐式时间积分法推进结构运动方程,故可选用较大时间步长;进一步应用单元型光滑有限元法求解几何非线性固体大变形,获得更精确结构解且不影响计算效率. 运用子块移动技术结合正 交--半扭转弹簧近似法高效更新流体动网格;同时将一质量源项引入压力泊松方程满足几何守恒律,无需复杂构造网格速度差分格式. 采用简单高效的固定点法配合Aitken动态松弛技术实现各场耦合,可灵活选择先进单场求解技术,具备较好程序模块性. 运用本文算法分别模拟了H型桥梁截面颤振问题和均匀管道流内节气阀涡激振动问题. 研究表明,数值结果与已有文献数据吻合,计算精度和求解效率均令人满意.      

基于流固耦合的跨声速压气机叶片静气动弹性分析

采用时域推进的双向流固耦合方法对一级跨声速压气机叶片流场和固体域进行数值模拟,研究跨声速转子叶片静气动弹性变形及其对气动性能的影响,对比分析了100%转速下转子叶片的气动特性和固有频率的变化.结果表明:转子叶片在气动力和离心惯性力共同作用下的弹性变形以扭转变形为主,气动力对叶尖前缘变形量的影响可达总变形量的20%.转子叶片变形后通道流通能力增强,气动特性曲线向大流量方向偏移.     

海洋地震工程流固耦合问题统一计算框架

海底地震动的模拟以及海洋工程结构的地震反应分析中,涉及到海水、饱和海床、弹性基岩、结构之间的相互耦合.传统的方法分别采用声波方程描述理想流体、Biot方程描述饱和海床、弹性波方程描述基岩和结构,分别考虑相互之间的耦合,十分不便.本文基于理想流体、固体分别为饱和多孔介质的特殊情形(孔隙率分别为1和0),由饱和多孔介质的Biot方程可退化得到理想流体的声波方程和固体的弹性波方程.然后,以饱和多孔介质方程为基础,经集中质量有限元离散,考虑不同孔隙率的饱和多孔介质之间耦合的一般情形,建立了该耦合情形的求解方法.进一步论证了该一般情形的耦合计算方法可分别退化到流体与固体、流体与饱和多孔介质、固体与饱和多孔介质之间的耦合计算,从而将流体、固体、饱和多孔介质间的耦合问题纳入到统一计算框架,并编制了相应的三维并行分析程序.以P-SV波垂直入射时,半无限层状海水-饱和海床、海水-弹性基岩、海水-饱和海床-弹性基岩三种情形的动力分析为例,采用统一计算框架结合透射边界条件进行求解,并与传递矩阵方法得到的解进行对比,验证了该统一计算框架的有效性以及并行计算的可行性.      

管阵动力响应的模态分析

核反应堆堆心、热交换器之类的重要结构是由浸没在流体中的有着规则排列的大量管梁组成，流固耦合作用是影响管束动力响应的重要现象。很多研究者为提出一个可以预测管束全局行为的数学模型作为不少努力。本文基于张提出的三维耦合模型，在流体域采用流体速度势而非压力作为基本未知量，从而避免了采用压力格式而导致的系数矩阵非戏称性的弊端，得到了易于注解的陀螺系统，通过计算系统特征值，利用模态展开法，求得了地震激励下系统     

Advanced Proper Orthogonal Decomposition Tools: Using Reduced Order Models to Identify Normal Modes of Vibration and Slow Invariant Manifolds in the Dynamics of Planar Nonlinear Rods

Reduced order models for the dynamics of geometrically exact planar rods are derived by projecting the nonlinear equations of motion onto a subspace spanned by a set of proper orthogonal modes. These optimal modes are identified by a proper orthogonal decomposition processing of high-resolution finite element dynamics. A three-degree-of-freedom reduced system is derived to study distinct categories of motions dominated by a single POD mode. The modal analysis of the reduced system characterizes in a unique fashion for these motions, since its linear natural frequencies are near to the natural frequencies of the full-order system. For free motions characterized by a single POD mode, the eigen-vector matrix of the derived reduced system coincides with the principal POD-directions. This property reflects the existence of a normal mode of vibration, which appears to be close to a slow invariant manifold. Its shape is captured by that of the dominant POD mode. The modal analysis of the POD-based reduced order system provides a potentially valuable tool to characterize the spatio-temporal complexity of the dynamics in order to elucidate connections between proper orthogonal modes and nonlinear normal modes of vibration.     

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。     

均匀来流条件下并行排列旗帜耦合运动模式的实验

利用高速摄影技术在低速风洞中记录了不同间距并行排列的两个旗帜在不同来流速度中的耦合运动。利用自编的时间-空间演化图像处理软件分析总结了旗帜的耦合运动模式以及旗帜摆动振幅、频率和St数的变化规律。实验结果显示,随着排列间距和来流速度的变化,两旗帜可能以静止、同向摆动、反向摆动和过渡状态这四种不同的模态耦合运动。两旗帜同向摆动时摆动频率明显低于单个旗帜在相同来流中的值,反向摆动时情况相反。在过渡状态中两旗帜摆动的振幅交替增减并且运动中同时包含有两个频率,而同向和反向摆动都是单频率的运动。     

水中圆锥形柱腿的自振特性分析

水中圆锥形柱腿的抗弯刚度和分布质量沿柱高是变化的，液团交界面不是一个圆柱面，分析该系统的耦联振动有一定难度。本文基于线性自由液面条件和势流模型，采用干模态展开，深入研究了这类柱腿的弯曲自振特性。文中首先借助微分算子分解和变量代换求出相应的干模态，由于它是封闭解，从而给干模态展开研究湿模态问题带来极大的方便。然后再利用干模态的完备正交性，将求干模态空间里的主坐标变成一个低阶广义特征值问题。和有限元等数值方法相比，计算工作量小且精度高。     

车-桥系统耦合振动响应的简便计算

依据振动理论推导出了二自由度模型车辆与桥梁系统竖向耦合振动微分方程，采用模态分析的离散化方法，将复杂的偏微分方程问题转化为变系数常微分方程问题，并将微分方程数值积分的Runge-Kutta方法引入到该时变系统的振动响应计算中，使复杂的耦合响应问题得到简便的解决。通过算例验证了该方法的有效性和简便性。该方法只需要直接数值积分，具有公式简单，编程方便，计算速度快等优点，特别适合于工程实际问题的计算，并且不仅适用于匀速运动车辆，也适用于变速运动车辆。     

流固偶合运动的边界元法

本文给出了流固偶合运动(包括物体散射辐射及偶合运动)的边界元法理论和应用.对于散射问题,求出了物体引起的散射势及入射波作用于物体的载荷.对于辐射问题,求出了辐射势及物体在流体中运动的附加质量和附加阻尼.偶合问题包括求其中包含的散射势和辐射势以及作用于物体之上的散射力、物体的附加质量、附加阻尼、物体在入射波作用下的运动.在偶合运动问题中,本文采取了边界积分方程与物体在流体中的运动方程联立求解的方法,并将其运用到边界元法的数值过程中.所编制的程序有较高的精度.最后给出了数值计算结果与理论解的比较.     

A Trigger of Coupled Singularities

By using example of nonlinear dynamics of a pair of coupled gears, the phenomenon of appearance and disappearance of a trigger of coupled singularities and homoclinic orbits in the form of number eight in the phase portrait in the phase plane is investigated. That phenomenon is an accompanying phenomenon of loss of stability of the local unique equilibrium position. For a generalized case under certain conditions, a theorem of the appearance of a trigger of coupled singularities in a nonlinear dynamical conservative system, the first derivative of the system potential energy which is a product of two periodic functions with different periods, and one bifurcation parameter, which is the cause for the appearance of new roots of these two functions, is defined.     

A Trigger of Coupled Singularities

By using example of nonlinear dynamics of a pair of coupled gears, the phenomenon of appearance and disappearance of a trigger of coupled singularities and homoclinic orbits in the form of number eight in the phase portrait in the phase plane is investigated. That phenomenon is an accompanying phenomenon of loss of stability of the local unique equilibrium position. For a generalized case under certain conditions, a theorem of the appearance of a trigger of coupled singularities in a nonlinear dynamical conservative system, the first derivative of the system potential energy which is a product of two periodic functions with different periods, and one bifurcation parameter, which is the cause for the appearance of new roots of these two functions, is defined.     

Nonlinear Normal Modes and Their Bifurcations for an Inertially Coupled Nonlinear Conservative System

This work concerns the nonlinear normal modes (NNMs) of a 2 degree-of-freedom autonomous conservative spring–mass–pendulum system, a system that exhibits inertial coupling between the two generalized coordinates and quadratic (even) nonlinearities. Several general methods introduced in the literature to calculate the NNMs of conservative systems are reviewed, and then applied to the spring–mass–pendulum system. These include the invariant manifold method, the multiple scales method, the asymptotic perturbation method and the method of harmonic balance. Then, an efficient numerical methodology is developed to calculate the exact NNMs, and this method is further used to analyze and follow the bifurcations of the NNMs as a function of linear frequency ratio p and total energy h. The bifurcations in NNMs, when near 1:2 and 1:1 resonances arise in the two linear modes, is investigated by perturbation techniques and the results are compared with those predicted by the exact numerical solutions. By using the method of multiple time scales (MTS), not only the bifurcation diagrams but also the low energy global dynamics of the system is obtained. The numerical method gives reliable results for the high-energy case. These bifurcation analyses provide a significant glimpse into the complex dynamics of the system. It is shown that when the total energy is sufficiently high, varying p, the ratio of the spring and the pendulum linear frequencies, results in the system undergoing an order–chaos–order sequence. This phenomenon is also presented and discussed.     

A Degenerate Bifurcation Structure in the Dynamics of Coupled Oscillators with Essential Stiffness Nonlinearities

We study the degenerate bifurcations of the nonlinear normal modes(NNMs) of an unforced system consisting of a linear oscillator weaklycoupled to a nonlinear one that possesses essential stiffnessnonlinearity. By defining the small coupling parameter , we study thedynamics of this system at the limit 0. The degeneracy in the dynamics ismanifested by a 'bifurcation from infinity' where a bifurcation point isgenerated at high energies, as perturbation of a state of infiniteenergy. Another (nondegenerate) bifurcation point is generated close tothe point of exact 1:1 internal resonance between the linear andnonlinear oscillators. The degenerate bifurcation structure can bedirectly attributed to the high degeneracy of the uncoupled system inthe limit 0, whose linearized structure possesses a double zero, and aconjugate pair of purely imaginary eigenvalues. First we construct localanalytical approximations to the NNMs in the neighborhoods of thebifurcation points and at other energy ranges of the system. Then, we`connect' the local approximations by global approximants, and identifyglobal branches of NNMs where unstable and stable mode and inverse modelocalization between the linear and nonlinear oscillators take place fordecreasing energy.