陀螺转子动力学系统的时间有限元内点法

将保辛的时间有限元法(FEM)应用于陀螺转子动力学系统,给出了陀螺转子动力学系统时间有限元法的时间单元刚度阵列式和非齐次外力的表达式,以及辛时间传递矩阵。在此基础上,提出了精度更高的时间有限元内点法(IDTFEA),该方法既继承了时间有限元保辛的优良特性,又大大提高了数值计算精度,具有非常明显的优越性。算例给出了该方法和Newmark方法的比较结果,表明该方法的优越性。     

计及陀螺效应的翼吊式机翼-发动机系统结构动力学特性研究

针对翼吊式发动机机翼系统的特点,运用Hamilton原理建立了计及发动机陀螺效应的Bernoulli-Euler悬臂梁振动方程;从陀螺力矩理论出发,分析了转子对结构的耦合作用机理,研究了不同转子转速和结构参数条件下,转子陀螺效应对悬臂梁结构固有特性的影响,从而为进一步研究计及转子陀螺效应的大型客机机翼发动机系统动力学特性及气动弹性特性奠定了一定的理论基础。     

微陀螺动力学建模与非线性分析

建立了微陀螺的动力学模型,采用多尺度方法对微陀螺的非线性模型进行求解,探讨了驱动微弹性梁和检测微弹性梁的非线性刚度对微陀螺输出的影响规律,研究了微陀螺的带宽在非线性刚度作用下的设计原则,结果表明:微陀螺振动系统的检测灵敏度和带宽呈反比关系;微弹性梁的非线性刚度会使得输入角速度与检测输出呈非线性关系。因此,从微弹性梁的设计角度出发,可根据较大的输出或者较小的非线性要求选取合适的驱动微弹性梁;而检测微弹性梁则需要选取较小的非线性刚度。     

陀螺系统的受迫振动及其时滞反馈控制

对简谐激励下陀螺系统的受迫振动及其在含时滞的位移和速度反馈控制下的动力学行为进行研究。利用拉格朗日方程,建立了两自由度陀螺系统的运动微分方程。考虑主共振和1:1内共振的情况,采用平均法得到了平均方程。通过对平均方程进行化简,得到了关于系统振幅的分岔方程,分别讨论了各个参数对系统振幅的影响。根据奇异性理论,分析了参数变化对系统分岔行为的影响。对受迫陀螺系统施加含时滞的位移和速度反馈控制,讨论了反馈增益和时滞对系统振幅的影响。     

谱分解理论及在时滞反馈控制中应用

运用矩阵多项式的GLR理论系统地给出阻尼陀螺系统、粘性阻尼系统及无阻尼陀螺系统的谱分解定理。以粘性阻尼系统为例，应用谱分解定理的正交性结果求解时滞状态反馈下部分极点配置问题，构造性出多输入情况下解的参数表示。     

新型机枪枪架及其动态特性分析

以某型重机枪为研究对象,在不改动枪身的前提下设计了一种新型弹性三角枪架。通过建立机枪有限元模型,分析计算了其固有特性;建立基于刚柔耦合多体系统动力学的机枪虚拟样机模型,求解出其在连发状态下的动力响应。所得结果与原有三脚架进行了分析比较,证明了新型三脚架的优越性。     

参数激励驱动微陀螺系统的非线性振动特性研究

对于一类典型的切向梳齿驱动型微陀螺,建立两自由度、具有刚度立方非线性和参数激励驱动的微陀螺系统动力学模型。考虑主参数共振和1∶1内共振的情况,利用多尺度法获得周期解的解析形式,并利用分岔理论,得到Hopf分岔条件,结合数值模拟系统的动力学响应,揭示系统参数对驱动和检测模态振幅和分岔行为的影响机制。研究结果表明,在1∶1内共振和较大的载体角速度下,激励频率的变化容易引起微陀螺振动系统的多稳态解、振幅跳跃现象和概周期响应等复杂动力学行为。     

时滞位移反馈作用下多自由度微陀螺的刚度非线性及控制研究

为揭示多自由度微陀螺非线性系统中位移反馈项对系统动力学特性的影响规律,探索对非线性的控制方法,以一类四自由度静电驱动微机械陀螺为研究对象,采用多尺度法对微陀螺受控系统在频域和时域中的动力学特性进行了分析。研究发现:时滞量为整周期或半周期时反馈增益可有效的对系统共振频率进行调节;时滞量为四分之一或四分之三周期时,反馈增益主要影响幅值大小,共振频率基本保持不变;反馈控制参数选取得当可消除非线性引起的多稳态解,增加陀螺的灵敏度稳定性,选取不当会导致系统出现复杂的概周期运动使灵敏度稳定性遭到破坏。     

基于混合模型的转子临界转速计算

采用集总参数和分布质量混合建模的方法,建立了转子-支承系统的力学模型,应用改进的Riccati传递矩阵法,综合考虑陀螺力矩、支承刚度、剪切变形等因素的影响,推导出了混合模型传递矩阵表达式,并在VB平台上编制了界面友好、操作简单、拓展性强的通用的转子临界转速计算程序。通过算例对程序的验证计算结果表明,混合建模方法计算结果精度高,算法正确,程序运行可靠。     

预估校正Galerkin方法及其在大型转子-轴承系统中的应用

根据非线性Galerkin方法和后处理Galerkin方法的思路,提出了用于大型非线性动力系统降阶的预估校正Galerkin方法。在模态坐标下,将大型非线性动力学系统分成‘主子系统’,‘从属子系统’和‘可忽略子系统’。略去‘可忽略子系统’的影响,发展一种新颖的预估校正算法综合处理‘主子系统’和‘从属子系统’,以达到降维和节省计算时间的目的。以某200MW汽轮机组低压转子的有限元模型作为分析对象,通过比较系统的动力学特性验证新方法的精度和效果。结果表明:新方法可在不影响精度的前提下,大幅缩减计算时间。     

轴向变速运动弯曲梁的固有频率分析

基于动力刚度矩阵法对轴向变速运动弯曲梁的固有频率进行分析,根据Hamilton原理,推导轴向变速运动弯曲梁的时域控制方程和边界条件,通过傅里叶变换得到频域控制方程和边界条件,求解频域控制方程,并结合位移边界条件和载荷边界条件,建立轴向变速运动弯曲梁的动力刚度矩阵模型;引入Hermite形式的形函数,建立了轴向变速运动弯曲梁的有限元模型。算例中,通过对比现有文献中的结果、有限元模型结果和动力刚度矩阵法模型结果,验证了该文所建立的力学模型,动力刚度矩阵法比有限元法具有更高的精度和效率,分析了轴向变速运动弯曲梁固有频率随着弯曲梁轴向运动速度、加速度、轴向受力、边界条件的变化规律。     

Transient analysis of three-dimensional dynamic interaction between multilayered soil and rigid foundation

The study of dynamic soil-structure interaction is significant to civil engineering applications, such as machine foundation vibration, traffic-induced vibration, and seismic dynamic response. The scaled boundary finite element method (SBFEM) is a semi-analytical algorithm, which is used to solve the dynamic response of a three-dimensional infinite soil. It can automatically satisfy the radiation boundary condition at infinity. Based on the dynamic stiffness matrix equation obtained by the modified SBFEM, a continued fraction algorithm is proposed to solve the dynamic stiffness matrix of layered soil in the frequency-domain. Then, the SBFEM was coupled with the finite element method (FEM) at the interface to solve the dynamic stiffness matrices of the rigid surface/buried foundation. Finally, the mixed-variable algorithm was used to solve the three-dimensional transient dynamic response of the foundation in the time domain. Numerical examples were performed to verify the accuracy of the proposed algorithm in solving the dynamic stiffness matrix of the infinite domain in the frequency domain and the dynamic transient displacement response of the foundation in the time domain. Compared with the previous numerical integration technique, the dynamic stiffness matrix in the frequency domain calculated by using the proposed algorithm has higher accuracy and higher efficiency.     

A coupled symmetric BE–FE method for acoustic fluid–structure interaction

A coupled symmetric BE–FE method for the calculation of linear acoustic fluid–structure interaction in time and frequency domain is presented. In the coupling formulation a newly developed hybrid boundary element method (HBEM) will be used to describe the behaviour of the compressible fluid. The HBEM is based on Hamilton's principle formulated with the velocity potential. The state variables are separated into boundary variables which are approximated by piecewise polynomial functions and domain variables which are approximated by a superposition of static fundamental solutions. The domain integrals are eliminated, respectively, replaced by boundary integrals and a boundary element formulation with a symmetric mass and stiffness matrix is obtained as result. The structure is discretized by FEM. The coupling conditions fulfil C¹-continuity on the interface. The coupled formulation can also be used for eigenfrequency analyses by transforming it from time domain into frequency domain.     

光滑有限元的声学研究：时域和频域分析

摘　要：在使用有限元进行声场的数值模拟中,存在着两个主要误差,一个是数值方法中常规的插值误差,另外一个是计算声学中所特有的耗散误差(dispersion error),后者则是影响声学模拟仿真置信度的最重要因素。产生耗散误差的本质原因是由于有限元的数值模型刚度“偏硬”造成的。为了控制耗散误差,最重要的是使数值模型更好的反映真实模型。本文采用了一种基于边光滑的有限元方法(ES-FEM)来对声场的时域和频域进行数值模拟研究。该方法只采用对复杂问题域适应性很强的三角形网格,通过引进基于边的广义梯度光滑技术,能够使得有限元系统得到适当的“软化”。关于时域和频域的算例表明了在使用同样网格的情况下,本方法在声学模拟中的精度都要比有限元模型的高。     

粘弹性分数阶导数模型的有限元法

本文给出了粘弹性分数阶导数模型的有限元格式,并用模态分析的方法进行了运动方程解耦。用Laplace变换及其反变换,解析地计算了解耦后单自由度系统的时域和频域响应。时域响应被分为极点部分和截断部分,它们分别代表短期内的衰减振动和长时间内的缓慢恢复效应。以一维杆件为例,对有限元算法和解析解做了对比,分析了响应精度与单元个数的关系。结果表明用有限元法计算的位移接近解析解,而要得到准确的高频加速度响应,则需要划分许多单元格。     

谱元法与透射边界的配合使用及其稳定性研究

在无限域波动模拟中引入透射边界条件时,目前多将边界上的透射公式与内域的有限元法结合使用,其计算精度由有限元方法决定,而谱元法因结合有限元和频谱法的优势则比有限元空间域积分具有更高的计算精度。该文基于谱元法非等距网格划分特性,研究了内域的谱元法与边界上的透射公式结合的理论方法,给出了相应的透射公式使用方法,并基于建立的谱元法波动数值模型探讨了透射公式的稳定性问题。研究表明:空间域插值系数需控制在一个合理范围内,空间域插值方法相对于时间域插值方法更为稳定,高频失稳出现可能性相对较小;Gamma算子的使用可提高模拟的精度,采用Gamma算子后对于高阶透射公式仍可出现低频漂移现象,可结合降阶消漂的方式实现稳定精度高的透射边界应用。     

Acoustic modelling by BEM–FEM coupling procedures taking into account explicit and implicit multi‐domain decomposition techniques

The numerical modelling of interacting acoustic media by boundary element method–finite element method (BEM–FEM) coupling procedures is discussed here, taking into account time‐domain approaches. In this study, the global model is divided into different sub‐domains and each sub‐domain is analysed independently (considering BEM or FEM discretizations): the interaction between the different sub‐domains of the global model is accomplished by interface procedures. Numerical formulations based on FEM explicit and implicit time‐marching schemes are discussed, resulting in direct and optimized iterative BEM–FEM coupling techniques. A multi‐level time‐step algorithm is considered in order to improve the flexibility, accuracy and stability (especially when conditionally stable time‐marching procedures are employed) of the coupled analysis. At the end of the paper, numerical examples are presented, illustrating the potentialities and robustness of the proposed methodologies. Copyright © 2008 John Wiley & Sons, Ltd.     

3D mass-redistributed finite element method in structural–acoustic interaction problems

A 2D mass-redistributed finite element method (MR-FEM) for pure acoustic problems was recently proposed to reduce the dispersion error. In this paper, the 3D MR-FEM is further developed to solve more complicated structural–acoustic interaction problems. The smoothed Galerkin weak form is adopted to formulate the discretized equations for the structure, and MR-FEM is applied in acoustic domain. The global equations of structural–acoustic interaction problems are then established by coupling the MR-FEM for the acoustic domain and the edge-based smoothed finite element method for the structure. The perfect balance between the mass matrix and stiffness matrix is able to improve the accuracy of the acoustic domain significantly. The gradient smoothing technique used in the structural domain can provide a proper softening effect to the “overly-stiff” FEM model. A number of numerical examples have demonstrated the effectiveness of the mass-redistributed method with smoothed strain.     

A face‐based smoothed finite element method (FS‐FEM) for 3D linear and geometrically non‐linear solid mechanics problems using 4‐node tetrahedral elements

This paper presents a novel face‐based smoothed finite element method (FS‐FEM) to improve the accuracy of the finite element method (FEM) for three‐dimensional (3D) problems. The FS‐FEM uses 4‐node tetrahedral elements that can be generated automatically for complicated domains. In the FS‐FEM, the system stiffness matrix is computed using strains smoothed over the smoothing domains associated with the faces of the tetrahedral elements. The results demonstrated that the FS‐FEM is significantly more accurate than the FEM using tetrahedral elements for both linear and geometrically non‐linear solid mechanics problems. In addition, a novel domain‐based selective scheme is proposed leading to a combined FS/NS‐FEM model that is immune from volumetric locking and hence works well for nearly incompressible materials. The implementation of the FS‐FEM is straightforward and no penalty parameters or additional degrees of freedom are used. The computational efficiency of the FS‐FEM is found better than that of the FEM. Copyright © 2008 John Wiley & Sons, Ltd.