Nonlinear Absolute Nodal Coordinate Formulation of a Flexible Beam Considering Shear Effect

IntroductionIn the previous hybrid-coordinate formulationof an elastic beam, with the assumption of smalldeformation, the relation between the strain anddeformations is approximated to one order. Suchlinear approximated formulation fails to explain thestiffening effect for a high-speed rotating elasticbeam[1,2]. Some authors developed the systemequations of motion of flexible multibody systemsthat include stress stiffening effects[3]. A furtherimprovement in the formulation can be achieved bye…     

跨座式单轨交通系统耦合振动特性

将列车的每节车厢简化为15自由度的动力系统,由拉格朗日方程导出其振动微分方程,将轨道梁简化为欧拉梁,基于能量法和车辆与轨道梁位移协调条件,建立了车辆和轨道梁耦合运动控制方程,研究了跨座式单轨交通轨道梁的动力特性。计算了列车以不同车速通过时轨道梁的动力响应,并比较了计算结果与实测结果。比较结果表明:理论计算结果与实测结果基本吻合,车速对轨道梁挠度的影响较小,但对加速度影响较大,加速度随车速增大而增大,在40~50 km.h-1处出现最大值,之后随车速增大反而减小;轮胎模型与轨道表面不平度功率谱密度函数对轨道梁横向响应计算结果影响较大,使计算误差增大。     

质量加速度矩定理探讨

本文提出质点和质点系 (绝对运动和相对运动 )质量加速度矩定理。由牛顿定律直接导出此定理 ,并给出此定理用于刚体平面运动的各种动力学方程 :矩心为定轴、质心、加速度瞬心、特殊速度瞬心、以及任意动点。这些方程最简明地给定了物体转动运动量与物体所受力系主矩之间的关系。此定理可以理解工科理论力学中儿乎所有用动量矩定理和用动静法力矩方程解的问题 ,而且比它们更直接 ,简明、方便     

Study on launch dynamics of the tank marching fire

As an army main battle equipment, it is required that the tank should have high firing accuracy and high first round hit probability during marching. The initial disturbance of the projectile is the premier factor that takes effect on the marching fire accuracy of the tank. And the marching fire accuracy of the tank depends on the launch dynamics behaviors of the tank. In this paper, the launch dynamics theory of a tank marching fire is studied, and its launch dynamics model is established. Based on the transfer matrix method for multibody system(MSTMM) and the automatic deduction theorem of overall transfer equations, the overall transfer equation and the overall transfer matrix of a tank multibody system are deduced; the launch dynamics equations of the tank marching fire are deduced, and the dynamic response of the tank system, the motion of projectile in barrel, the initial disturbance of the projectile and the vertical target dispersion are exactly simulated; meanwhile, the results of simulation are verified by tests. This work provides both theoretical foundation and simulation approaches for improving the marching fire accuracy of the tank.     

Dynamic investigation on composite flexible multi-body system considering thermal effect

The dynamic performance of composite flexible multi-body system under the simultaneous action of thermal fields and driving constraint is analyzed. Based on strain-displacement relation of the Mindlin plate theory which includes transverse shear deformation, and considering thermal effect, variation equations of laminated plate are derived by the principle of virtual work. The finite element method is used for discretization. According to kinematics constraint relation, dynamic equations for spatial slider-crank system are established. Simulation results show that spatial deformation (torsion deformation) appears in the multi-layered composite slider-crank mechanism which is simulated with planar motions. Furthermore, the influence of coupling between thermal expansion and flexible deformations of non-symmetrical composite plates on the large overall motion under the uniform temperature field is investigated. Finally, significant change in constraint force due to the spatial deformation is shown.     

基于桥梁动力响应的车-桥接触力识别方法

将桥梁划分为欧拉梁单元建立桥梁的振动方程,基于拉格拉日原理建立汽车的振动方程,根据接触点处的接触力将汽车和桥梁系统耦合在一起。求解汽车-桥梁系统耦合方程得到桥梁节点动力响应,由广义正交函数和模态叠加原理确定模态响应及其导数,用正则化方法得到稳定的识别结果。数值模拟结果表明,该方法用于识别车桥接触力是有效的、可行的。     

跨座式列车与预应力混凝土轨道梁动力特性分析

为研究跨座式单轨列车与预应力混凝土轨道梁的动力特性,建立了列车-轨道梁空间耦合振动模型.车辆运动微分方程由拉格朗日方程导出,轨道梁用模态综合法建立其运动微分方程.计算了不同车速下车辆和轨道梁的动力响应.结果表明:车速对轨道梁挠度的影响较小,但对加速度影响较大;在计算车速下,轨道梁具有良好的动力特性,列车能安全舒适地通过此轨道梁.     

连续梁桥车桥耦合振动分析的数值解法

将连续梁桥简化为二维的平面梁单元模型,车辆简化为五自由度二分之一车模型,分别建立车辆与桥梁振动方程;该方法以车轮接触处位移协调条件与相互作用力的平衡关系相联系,建立车辆与桥梁耦合振动方程,利用模态综合叠加法并结合Newmark-β积分格式进行迭代求解.通过本文数值解与解析方程的Runge-kutta法解进行对比,证明该方法确实有效可行.由于桥梁振动响应主要由若干低阶振动模态起控制作用,对于大跨度复杂桥梁,这就大大降低了矩阵的维数,提高了计算速度,且该方法对于不同类型桥梁具有很强的通用性.     

高速弓网耦合系统动态仿真研究

采用欧拉-伯努利梁结构的接触网和受电弓的二质量块模型建立了弓网垂直耦合动力学模型,通过拉格朗日方程推导出弓网系统运动微分方程组,并利用Newmark法编写数值仿真程序,在给定的条件下,讨论不同速度下弓网耦合系统的动态性能。采用MATLAB对高速受电弓与接触网的相互作用进行仿真并对结果进行分析,为研究不同速度下受电弓与接触网参数的优化奠定基础。     

Coupled Vibration of Long-Span Railway Curved Girder Bridges and Vehicles

The structure of a long curved girder bridge is represented with a three-dimensional curved finite element model. Each 4-axle vehicle is modeled by a dynamic system of 35 degrees of freedom. The random irregularities of the track are generated from a power spectral density function under the given track condition. The dynamic interaction between the bridge and train is realized through the contact forces between the wheels and track. Then based on these models, the coupled equations of motion are solved by applying the time-integration and iteration techniques to the coupled system. The proposed formulation and the associated computer program are then applied to a real curved girder bridge. The dynamic responses of the bridge-vehicle system and the derailments and offload factors related to the riding and running safeties of vehicles are computed. The results show that the formulation presented in this paper can well predict dynamic behaviors of both bridge and train with reasonable computation efforts.     

晃荡冲击影响下的潜艇运动实用稳定性分析

液舱内自由液面的晃荡会影响船舶的稳定性。通过引入实用稳定性的概念,研究了在晃荡影响下的潜艇运动实用稳定性。利用计算流体力学软件对潜艇横摇过程中液舱的液面晃荡进行了模拟计算,根据仿真结果,分析了液舱晃荡对潜艇稳定性的影响,建立了液舱晃荡和潜艇横摇运动的耦合作用模型。通过数值仿真,验证了在液舱晃荡影响下的潜艇横摇运动系统的实用稳定性,从而证明了该方法的可行性。     

板式轨道动力响应分析方法

为了计算在高速车辆移动荷载作用下板式轨道的动力响应,将轨道板视为线性粘弹性连续支承梁,将钢轨视为线性粘弹性点支承梁,将钢轨和轨道板统一划分为有限单元,基于车辆-轨道耦合动力学理论,利用弹性系统动力学总势能不变值原理,建立了高速列车-板式轨道的垂向耦合动力学方程,计算了车辆通过板式轨道钢轨焊接区短波不平顺时的轮轨动力学响应。仿真结果表明:与其他成熟仿真方法相比较,响应变化趋势与幅值基本一致,表明该方法可行。     

箱梁的空间振动分析探讨

本文采用三角形板单元对箱梁分段建立运动微分方程,解出模态,对整体结构动态综合时进行了缩阶,求出结构的低频模态。在Zienkiewicz处理单元刚度矩阵奇异问题方法的基础上,提出采用假设板单元面内转动质量系数的方法处理质量矩阵的奇异问题。本文还用坐标总集推导了总装方程,结果表明,所作近似与各分段模态间之正交性等价。算例表明:对板单元刚度、质量矩阵奇异性问题在不计结点之面内转动自由度时之处理方法将是可行的。有限元法与动态子结构法结合(简称FEDS)对箱梁进行动态分析是有效的。     

The Coupling Effect of Spatial Reticulated Shell Structure with Cables

The spatial reticulated shell structure with cables (RSC) is a kind of coupling working system, which consists of flexible cables, reticulated shell structure (RS) and tower columns. The dynamic analysis of RSC based on the coupling model was carried out. Three kinds of elements such as the spatial bar element, cable element and beam element were introduced to analyze the reticulated shell, cable and tower column respectively. Furthermore,such parameter influences as structural boundary conditions, grid configuration, the span-to-depth ratio and the arrangement of cable system upon structural dynamics were analyzed. The structural vibration modes can be divided into four groups based on some numerical examples. And the frequencies in the same group are very close while the frequencies in different groups are different from each other obviously. It is clear that the sequence of the appearance of the each mode group heavily depends on the comparative stiffness of the tower column system, RS and cables.     

变温环境下粘弹性梁的混沌运动

根据Kelvin粘弹性材料本构关系、梁的运动方程及变形几何方程建立了同时具有温度扰动和横向分布力扰动的粘弹性梁非线性动力学模型.用Galerkin方法将系统简化为参数激励和强迫激励耦合的单模态Duffing振子,得到了系统的不动点和同宿轨道.用Melnikov函数法推导出系统混沌运动的临界条件,分析了系统通向混沌的途径.研究表明,非线性粘弹性梁在周期性横向激励及周期性温度联合作用下可能进入混沌运动,并且在发生Smale马蹄意义下的混沌前,将经历多次的次谐分岔.     

Free-Surface Wave Interaction with a Very Large Floating Structure

The free-surface wave interaction with a pontoon-type very large floating structure（VLFS） is analyzed by utilizing a modal expansion method. The modal expansion method consists of separating the hydrodynamic analysis and the dynamic response analysis of the structure. In the dynamic response analysis of the structure,the deflection of the structure with various edge conditions is decomposed into vibration modes that can be arbitrarily chosen. Free-free beam model, pinned-free beam model and fixed-free beam model are three different types of edge conditions considered in this study. For each of these beam models, the detailed mathematical formulations for calculating the corresponding eigenvalues and eigenmodes have been given, and the mathematical formulations corresponding to the beam models of pinned-free beam and fixed-free beam are novel. For the hydrodynamic analysis of the structure, the boundary value problem（BVP） equations in terms of plate modes have been established, and the BVP equations corresponding to the beam models of pinned-free beam and fixedfree beam are also novel. When these BVP equations are solved numerically, the structure deflections and the wave reflection and transmission coefficients can be obtained. These calculation results point out some findings valuable for engineering design.     

桥梁结构随机振动分析

桥梁结构的随机振动有别于其他结构。由于车辆在桥上的位置是不断变化的,因此,即使作为输入的随机激励是平稳随机过程,车桥的动力响应也超出平稳随机过程的范围,即质量在梁上不断的运动,使系统运动方程组成为一个时变系数的二阶微分方程组,一般只能采用逐步积分的数值方法,也可以用频域法,假定其频率响应函数在瞬间不随时间变化,近似的处理这种时变性问题。     

考虑畸变的起重机薄壁箱梁的自由振动分析

为了提高薄壁箱梁固有频率的计算精确度,基于广义坐标原理,对薄壁箱梁的动力特性进行了分析. 首先,通过虚功原理且考虑畸变形变的影响,获取了5种高度耦合模态（延伸、弯曲、扭转、翘曲和畸变）的自由振动微分方程组;其次,考虑转动惯性运动项的影响,建立了简支边界条件下的运动学模型,获得了薄壁箱形梁自由振动固有频率的四阶代数方程,进而求得固有频率的精确解;最后,通过算例将考虑畸变的固有频率精确解与Proki? 理论以及有限元分析方法的结果进行比较,验证了该方法的有效性和准确性. 结果表明:考虑畸变效应能够更准确地反映高阶状态下薄壁箱形梁的自由振动固有频率;对自由振动的4阶固有频率进行比较,当箱形梁长度为3 m时,本文理论的相对误差相较于Proki? 理论的0.42%下降至0.38%;当箱梁长度分别为4 m和5 m时,相对误差进一步下降至0.30% 和0.40%.      

轮对柔性对直线电机车辆动态响应的影响分析

直线电机地铁车辆有内置和外置两种轴箱布置方式,针对这两种轴箱布置的直线电机地铁车辆,分别建立了考虑轮对柔性的直线电机地铁车辆-轨道耦合动力学模型. 模型中轮轴采用欧拉梁模拟,考虑轮对柔性变形对一系悬挂作用力、电机吊杆力以及轮轨空间动态相互作用的影响,对比分析了在轮轨不平顺激扰作用下,轴箱内置和外置直线电机地铁车辆轮对柔性响应特性及其对系统动态响应的影响. 研究结果表明:相比于刚性轮对模型,两种直线电机地铁车辆柔性轮对模型求解所得轮轨垂向力响应均存在77 Hz的主振频率峰值,对应于轮对的一阶弯曲模态频率;当考虑轮对柔性效应时,相比于轴箱外置直线电机地铁车辆,轴箱内置直线电机地铁车辆的轮轨垂向力更大,气隙更小.