车-桥耦合系统动力学建模与响应分析

车辆行驶过桥时,车与桥之间存在相互耦合作用.本文根据车的三种简化模型,分别建立了车与桥结构相互耦合作用的动力学模型,并给出桥结构在两轴车载荷作用下的动响应计算方法,该方法很容易推广到更一般的多轴车载荷作用的情况.文中通过数值算例计算了基于车的三种简化模型桥梁的响应,将三种计算结果与实验数据比较,证明二自由度的车简化模型为最优,此时桥梁的弯矩响应与实验结果能较好地吻合.     

带弹簧-质量系统的车-桥耦合演变随机振动

提取悬挂有弹簧-质量系统桥梁的模态函数,将车辆简化为一个两自由度的移动系统,以桥面不平度功率谱密度为输入,建立车辆与带弹簧-质量系统的桥梁的耦合系统力学模型. 结合状态空间理论和演变随机过程的一般理论,研究车-桥耦合演变随机振动的弹簧-质量系统控制. 通过数值算例可知:弹簧-质量系统对车辆的随机响应没有影响,而可以降低桥梁的随机响应. 最后,探讨了弹簧-质量系统与桥梁质量比、弹簧--质量系统个数对桥梁随机响应的影响.     

城市高架桥车-桥-墩系统竖向振动分析

假设城市高架桥为两端简支的欧拉-伯努利梁模型以及桥墩为底部固结的柱,考虑两自由度车辆移动系统与桥面结构表面接触处不平整产生的随机激励以,建立了多个移动车辆系统-桥-墩的耦合力学模型,并且给出了耦合振动方程详细的求解步骤.数值分析采用Wilson-θ法求解.通过仿真分析,讨论了在不同路面等级、不同车辆移动速度下桥梁跨中位移响应和桥墩轴力的变化规律.最后根据车-桥-墩耦合力学模型和车-桥耦合力学模型,比较了两种分析模型对桥墩底部轴力和桥梁跨中截面位移的影响.分析结果表明桥墩对桥梁跨中截面位移的影响可以忽略不计,但是对桥墩本身所受轴力的影响则非常显著.     

基于二阶系统解耦的精细积分格式下动载荷时域识别

基于模态分析法的载荷识别方法利用模态矩阵获得系统的非耦合形式,推导单自由度系统的载荷识别公式,但要求系统为比例阻尼。在模态模型基础上,对一般系统建立基于二阶系统解耦的动载荷时域识别模型。首先,利用基于Lancaster结构的二阶系统解耦方法推导出系统的非耦合形式;然后,采用精细逐步积分方法,在载荷为阶跃力的假设下,推导出载荷识别数学公式;最后,由系统实时响应反求结构载荷的时间历程。数值算例验证了本文方法针对比例阻尼系统较模态模型具有更高的精度,而且对非比例阻尼系统也有效可行。     

基于改进萤火虫算法的移动车辆参数识

提出了一种基于萤火虫优化算法的移动车辆参数直接识别方法.采用四自由度双轴十二参数车辆模型和欧拉梁有限元模型建立了车桥耦合系统的动力方程,并利用Newmark直接积分法求解了系统的动力响应.通过引入一种局部搜索策略和末位淘汰机制改进了萤火虫优化算法的收敛速率,并提高了识别结果的精度.本文方法仅利用车辆振动的竖向加速度响应测量就能进行移动车辆参数的识别.数值算例表明,改进的萤火虫优化算法可以准确地识别出车辆的质量、悬挂刚度和阻尼等参数,并且对测量噪声不敏感.     

基于移动车载响应的连续梁损伤识别

应用有限元法将连续桥梁结构离散为两跨耦合欧拉-伯努利梁模型.利用Newmark直接积分法求出在移动车载作用下桥梁的动态响应,并进一步推导出动态响应桥梁对物理参数(如杨氏模量)的时域灵敏度.在反问题中利用基于响应灵敏度的有限元模型修正法识别出桥梁的局部损伤,并讨论了人工测量噪声对损伤识别结果的影响.算例表明本文方法能够快速有效地识别出耦合梁系统的局部损伤,并具有精度高、对测量噪声不敏感等特点.     

车辆-桥梁耦合作用分析

文章通过拉氏方程，在时变动力学的基础上，建立车-桥耦合振动的系统方程。重点探讨了车的质量、车速、刚度、阻尼比、桥跨、桥的阻尼比，桥面粗糙程度等参数在车．桥耦合振动中的作用。其中车速、车的刚度、桥的形式、桥的阻尼起着重要作用。文中还比较了把车辆分别模拟为移动力、移动刚体、移动的弹性体时车．桥互相作用力的差别，得出有必要将车辆模拟为移动的弹性体，以减小分析高速车辆所引起的互相作用力的误差。并考虑了车-桥耦合振动中行驶车辆的转动效应，虽然它的影响是很小的；还尝试性的讨论了桥上行车舒适度的问题，车的阻尼起着很重要的作用。     

基于对称性的三维车辆轨道耦合系统随机振动虚拟激励方法

基于结构的对称性提出了用于三维车辆轨道耦合系统高效随机动力响应分析的虚拟激励方法.车辆采用刚体动力学模型,轨道结构利用三维轨道广义单元建模,车辆与轨道通过线性轮轨关系耦合.采用虚拟激励法将高低、方向和水平三类轨道不平顺转化为一系列筒谐的虚拟不平顺;考虑车辆及轨道结构的对称性,分别推导了耦合系统的对称和反对称凝聚矩阵,提出了用于车辆轨道耦合系统动力响应计算的自由度凝聚方法,将耦合系统的自由度缩减至原来的一半以下,并在此基础上实现了耦合系统随机振动的高效分析.数值算例将本文方法与传统有限元方法进行对比,验证了本文方法的正确性和有效性.     

基于移动载荷响应的多跨连续桥梁损伤检测

应用有限元法将连续桥梁结构离散为两跨弱耦合欧拉-伯努利梁模型,研究了该弱耦合梁系统由于局部损伤而引起的振动模态局部化现象.利用Newmark直接积分法求出在移动车载作用下桥梁的动态响应,并进一步推导出动态响应桥梁对物理参数(如杨氏模量)的时域灵敏度.在反问题中利用基于响应灵敏度的有限元模型修正法识别出桥梁的局部损伤,并讨论了人工测量噪声对损伤识别结果的影响.算例表明该方法能够快速有效地检测具有相重频率的弱耦合系统的局部损伤,并具有精度高、对测量噪声不敏感等特点.     

基于改进萤火虫算法的移动车辆参数识别

提出了一种基于萤火虫优化算法的移动车辆参数直接识别方法。采用四自由度双轴十二参数车辆模型和欧拉梁有限元模型建立了车桥耦合系统的动力方程,并利用Newmark直接积分法求解了系统的动力响应。通过引入一种局部搜索策略和末位淘汰机制改进了萤火虫优化算法的收敛速率,并提高了识别结果的精度。本文方法仅利用车辆振动的竖向加速度响应测量就能进行移动车辆参数的识别。数值算例表明,改进的萤火虫优化算法可以准确地识别出车辆的质量、悬挂刚度和阻尼等参数,并且对测量噪声不敏感。     

基于荷载形函数的大跨桥梁结构移动荷载识别

大跨桥梁结构中的移动荷载识别是结构健康监测的重要组成部分之一,其作为动力学中的反问题,存在唯一性及稳定性等病态问题。本文首先推导出移动荷载作用下结构响应的卷积形式的离散公式,然后利用有限元理论中的形函数拟合移动荷载,推导出基于荷载形函数的移动荷载识别表达式。将移动荷载的识别转化为荷载形函数拟合系数的识别,降低了需要识别的未知量,减小了逆运算的计算量,消除或减弱逆问题病态性,并提高了计算效率。利用某大跨刚构-连续预应力混凝土桥梁修正后的有限元模型进行数值仿真,考虑路面粗糙度,由模态叠加法计算移动荷载作用下的响应;然后采用荷载形函数方法识别移动荷载,证明该方法在5%以下的噪声时能快速并精确识别复杂桥梁结构的移动荷载。     

Experimental Testing of a Moving Force Identification Bridge Weigh-in-Motion Algorithm

Bridge weigh-in-motion systems are based on the measurement of strain on a bridge and the use of the measurements to estimate the static weights of passing traffic loads. Traditionally, commercial systems employ a static algorithm and use the bridge influence line to infer static axle weights. This paper describes the experimental testing of an algorithm based on moving force identification theory. In this approach the bridge is dynamically modeled using the finite element method and an eigenvalue reduction technique is employed to reduce the dimension of the system. The inverse problem of finding the applied forces from measured responses is then formulated as a least squares problem with Tikhonov regularization. The optimal regularization parameter is solved using the L-curve method. Finally, the static axle loads, impact factors and truck frequencies are obtained from a complete time history of the identified moving forces.     

A new method for detecting non-linear damping and restoring forces in non-linear oscillation systems from transient data

The purpose of this study is to recover the functional form of both non-linear damping and non-linear restoring forces in the non-linear oscillatory motions of an autonomous system. Using two sets of measured motion response data of the system, an inverse problem is formulated for recovering (or identification): the differential equation of motion is transformed into an equivalent integral equation of motion. The identification, which is non-linear, is shown to be one-to-one. However, the inverse problem formulated herein is concerned with the Volterra-type of non-linear integral equation of the first kind. This leads to numerical instability: solutions of the inverse problem lack stability properties. In order to overcome the difficulty, a regularization method is applied to the identification process. In addition, an L-curve criterion, combined with regularization, is introduced to find an optimal choice for the regularization parameter (i.e., the number of iterations), in the presence of noisy data. The workability of the identification is investigated for simultaneously recovering the functional form of the non-linear damping and the non-linear restoring forces through a numerical experiment.     

Motion of a cylinder in a viscous electroconductive medium with a magnetic field

The method of force sources is used to consider the planar problem of the motion of a circular cylinder in a viscous electroconductive medium with a magnetic field. The conventional and magnetic Reynolds numbers are assumed to be small. Expressions are obtained for the hydrodynamic reaction forces of the medium, acting on the moving cylinder. It is shown that as a result of the flow anisotropy in the medium, caused by the magnetic field, in addition to the resistance forces on bodies moving at an angle to the field, there are deflecting forces perpendicular to the velocity vector. The velocity field disturbances at great distances from the moving cylinder are determined.The problems of viscous electroconductive flow about solid bodies in the presence of a magnetic field constitute one of the divisions of magnetohydrodynamics. Motion of an electroconductive medium in a magnetic field gives rise to inductive electromagnetic fields and currents which interact with the velocity and pressure hydrodynamic fields in the medium [1, 2]. Under conditions of sufficiently strong interaction, the number of independent flow similarity parameters in MHD is considerably greater than in conventional hydrodynamics. This circumstance complicates the theoretical analysis of MHD flow about bodies, and therefore we must limit ourselves to consideration of individual particular flow cases.Here we consider the linear problem of the motion of an infinite circular cylinder in a viscous incompressible medium with finite electroconductivity located in a uniform magnetic field.There are many studies devoted to the flow of a viscous electroconductive medium with a magnetic field about solid bodies (see, for example, [3–5]). Because of this, some of the results obtained here include previously known results, which will be indicated below. In contrast to the cited studies, the examination is made by the method of force sources, suggested in [6]. This method permits obtaining integral equations for the distribution of the forces acting on the surface of the moving body. Their solution is obtained for small Reynolds and Hartmann numbers. Then the nature of the velocity disturbances at great distances from the body are determined. These results are compared with conventional viscous flow about a cylinder in the Oseen approximation.     

CONTINUUM TOPOLOGY OPTIMIZATION FOR MONOLITHIC COMPLIANT MECHANISMS OF MICRO-ACTUATORS

A multi-objective scheme for structural topology optimization of distributed compliant mechanisms of micro-actuators in MEMS condition is presented in this work, in which mechanical flexibility and structural stiffness are both considered as objective functions. The compliant micro-mechanism developed in this way can not only provide sufficient output work but also have sufficient rigidity to resist reaction forces and maintain its shape when holding the work-piece. A density filtering approach is also proposed to eliminate numerical instabilities such as checkerboards, mesh-dependency and one-node connected hinges occurring in resulting mechanisms. SIMP is used as the interpolation scheme to indicate the dependence of material modulus on element-regularized densities. The sequential convex programming method, such as the method of moving asymptotes (MMA), is used to solve the optimization problem. The validation of the presented methodologies is demonstrated by a typical numerical example.     

The computer simulation of drill column dragging in inclined bore-holes with geometrical imperfections

The problem about identification of resistance forces acting on a drill column moving in an inclined bore-hole is stated. It is supposed that the well trajectories can have geometrical imperfections in the shape of cylindrical spiral or plane cosinusoidal curves. The system of ordinary differential equations is derived on the basis of the theory of curvilinear flexible elastic rods. It permits one to describe static effects of the drill column bending accompanying the processes of its raising, lowering and rotating inside the bore-hole. Through the use of this system the direct and inverse problems of the drill column deforming are formulated for calculation of internal and external resistance forces acting on the drill column tube. The methods for numerical solution of the constructed equations are elaborated. With their use the phenomena of the drill columns motion and their frictional seizure inside the bore-holes are simulated for different geometrical imperfections and relations between the velocities and directions of their rotation and axial motion.     

Interaction of two spherical particles in a steady flow of viscous fluid when the Reynolds number is not small

The problem of the interaction of two or more particles moving in a viscous incompressible fluid at small Reynolds numbers (Re 1) has been well studied. The linearity of the Stokes equations makes it possible to develop effective methods of solution of the problem for two and many particles [1]. If the Reynolds number is not small, the inertia forces in the Navier-Stokes equations cannot be ignored, and the problem becomes nonlinear, i.e., much more complicated. The present note is devoted to the problem of the interaction of two spherical particles in a steady uniform flow of a viscous incompressible fluid when the Reynolds number is not small. Asymptotic expressions are obtained for the interaction forces between the particles when the distances between them are large compared with their radius.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 3, pp. 142–144, May–June, 1983.     

轴向运动导电薄板磁弹性耦合动力学理论模型

针对磁场环境中轴向运动导电薄板的动力学理论建模问题进行研究,得到较为完备的磁弹性耦合振动基本方程及相应的补充关系式。在考虑几何非线性效应下,给出薄板运动的动能、应变能以及外力虚功的表达式。应用哈密顿变分原理,推得磁场中轴向运动薄板的非线性磁弹性耦合振动方程,并得到力和位移满足的边界条件。基于麦克斯威尔电磁场方程,并考虑相应的电磁本构关系和电磁边界条件,推得任意磁场环境中轴向运动导电薄板满足的电动力学方程和所受电磁力表达式。分别针对纵向磁场环境、横向磁场环境、条形板等具体情形,给出了振动方程、电动力学方程和电磁力的简化形式。所得结果,可为此类问题的进一步求解和分析提供理论参考。