Multi-Flexible-Body Dynamic Analysis of

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底盘衬套对整车平顺性影响灵敏度分析

收稿日期：2018－09－19基金项目：湖南省科技发展计划（专项）资金（2016WK2042）；长沙市2015科技人才创新创业专项资金（kc1701017）作者简介：王彬（1979—），男，硕士，研究方向为汽车整车性能集成开发。

E-mail ：wang_bingle@ 。

DOI ：10.19466/ki.1674－1986.2019.02.004底盘衬套对整车平顺性影响灵敏度分析王彬（湖南湖大艾盛汽车技术开发有限公司，湖南长沙410205）摘要：应用ADAMS 软件建立包含柔性体车身的刚柔耦合整车多体动力学模型，结合仿真分析和试验测试来研究底盘衬套对平顺性的影响。

选取底盘衬套Z 向刚度作为试验因素，对整车进行随机不平路面下的低频振动测试，并根据试验结果进行极差分析，得出各底盘衬套对整车平顺性的灵敏度结果。

关键词：刚柔耦合；平顺性；灵敏度中图分类号：U463.1文献标志码：B文章编号：1674－1986（2019）02－014－05Sensitivity Analysis of the Effect of Chassis Bushing on Vehicle Ｒide ComfortWANG Bin（Hunan Aisn Auto Ｒ＆D Co．，Ltd．，Changsha Hunan 410205，China ）Abstract ：The Multi-body dynamic model of rigid-flexible coupling vehicle with flexible body was established by using ADAMS software ，and the influence of chassis bushing on ride comfort was studied with test and simulation analysis．By selecting the Z -direction stiffness of the chassis bushing as the test factor ，the low frequency vibration test of the whole vehicle was carried out on the random uneven pavement．The range analysis was carried out according to the test results ，and the sensitivity results of each chassis bushing on the vehicle ride comfort were obtained．Keywords ：Ｒigid-flex coupling ；Ｒide comfort ；Sensitivity0引言平顺性是指汽车在行驶过程中产生的振动和冲击环境对乘员舒适性的影响保持在一定界限之内的能力［1］。

adams知识点总结

adams知识点总结Adams is a multi-body dynamics simulation software used to analyze the motion and behavior of mechanical systems. It is widely used in the automotive, aerospace, and industrial machinery industries to test and validate designs before physical prototypes are built. Adams is known for its ability to accurately predict the performance of complex systems and its user-friendly interface.Key features of Adams include advanced modeling, flexible analysis, and robust post-processing capabilities. The software allows users to create detailed models of mechanical systems, define complex interactions between components, and simulate various operating conditions to predict the system's behavior. In this summary, we will explore the key knowledge points of Adams and how they are used in engineering design and analysis.1. ModelingOne of the key knowledge points in Adams is modeling, which refers to the creation of a digital representation of a mechanical system. Adams offers a wide range of modeling tools to help users build accurate and detailed models of their systems. These tools include parametric modeling, flexible bodies, and contact modeling.Parametric modeling allows users to define their systems using mathematical equations and parameters, making it easy to create complex and customizable models. Flexible bodies enable users to model the deformations and dynamic behavior of components, such as gears, springs, and rubber mounts. Contact modeling allows users to simulate the interactions between bodies in a system, such as collisions, friction, and wear.By using these modeling tools, engineers can create highly realistic digital models of their systems, which can be used to predict the behavior of the physical system under various conditions.2. AnalysisAnother key knowledge point in Adams is analysis, which refers to the process of simulating the behavior of a mechanical system using the digital model. Adams offers a wide range of analysis tools to help users simulate and analyze complex mechanical systems. These tools include dynamic analysis, kinematic analysis, and optimization.Dynamic analysis allows users to simulate the motion and behavior of a mechanical system under various operating conditions, such as acceleration, braking, and cornering. This type of analysis is essential for predicting the performance and safety of systems, such as vehicle suspensions, steering systems, and drivetrains. Kinematic analysis allows users to study the motion and interactions between components in a system, without considering forces and torques. This type of analysis is often used to study mechanisms, such as linkages, cams, and gears.Optimization allows users to find the best design parameters for a given system, such as the shape of a component, the material properties, or the operating conditions. This type of analysis is used to improve the performance, efficiency, and reliability of mechanical systems, such as gears, bearings, and structural components.By using these analysis tools, engineers can gain valuable insights into the behavior of their systems, which can be used to optimize designs and improve the performance and reliability of mechanical systems.3. Post-processingThe final key knowledge point in Adams is post-processing, which refers to the visualization and interpretation of the results from the simulation. Adams offers a wide range of post-processing tools to help users visualize and interpret the behavior of their systems. These tools include animation, plotting, and reporting.Animation allows users to visualize the motion and behavior of their systems in a dynamic and interactive way. This type of post-processing is essential for understanding the kinematics and dynamics of systems, such as vehicle suspensions, engine systems, and gearboxes. Plotting allows users to generate graphs and charts to visualize and interpret the results from the simulation, such as the motion, forces, and torques of components. Reporting allows users to generate detailed reports of the results from the simulation, such as the performance, safety, and reliability of the system. This type of post-processing is essential for communicating the results of the analysis to other stakeholders, such as managers, engineers, and customers.By using these post-processing tools, engineers can gain valuable insights into the behavior of their systems, which can be used to make informed decisions about design changes and improvements.In conclusion, Adams is a powerful multi-body dynamics simulation software used to analyze the motion and behavior of mechanical systems. It offers advanced modeling, flexible analysis, and robust post-processing capabilities to help engineers create detailed models, simulate the behavior, and interpret the results of complex systems. By using these knowledge points, engineers can optimize designs, improve the performance, and ensure the reliability of mechanical systems in various industries.。

基于ADAMSCar的汽车悬架系统_动力学建模与仿真分析毕业设计

毕业设计（论文）题目：基于ADAMS/Car的汽车悬架系统动力学建模与仿真分析毕业设计（论文）原创性声明和使用授权说明原创性声明本人郑重承诺：所呈交的毕业设计（论文），是我个人在指导教师的指导下进行的研究工作及取得的成果。

尽我所知，除文中特别加以标注和致谢的地方外，不包含其他人或组织已经发表或公布过的研究成果，也不包含我为获得及其它教育机构的学位或学历而使用过的材料。

对本研究提供过帮助和做出过贡献的个人或集体，均已在文中作了明确的说明并表示了谢意。

作者签名：日期：指导教师签名：日期：使用授权说明本人完全了解大学关于收集、保存、使用毕业设计（论文）的规定，即：按照学校要求提交毕业设计（论文）的印刷本和电子版本；学校有权保存毕业设计（论文）的印刷本和电子版，并提供目录检索与阅览服务；学校可以采用影印、缩印、数字化或其它复制手段保存论文；在不以赢利为目的前提下，学校可以公布论文的部分或全部内容。

作者签名：日期：学位论文原创性声明本人郑重声明：所呈交的论文是本人在导师的指导下独立进行研究所取得的研究成果。

除了文中特别加以标注引用的内容外，本论文不包含任何其他个人或集体已经发表或撰写的成果作品。

对本文的研究做出重要贡献的个人和集体，均已在文中以明确方式标明。

本人完全意识到本声明的法律后果由本人承担。

作者签名：日期：年月日学位论文版权使用授权书本学位论文作者完全了解学校有关保留、使用学位论文的规定，同意学校保留并向国家有关部门或机构送交论文的复印件和电子版，允许论文被查阅和借阅。

本人授权大学可以将本学位论文的全部或部分内容编入有关数据库进行检索，可以采用影印、缩印或扫描等复制手段保存和汇编本学位论文。

涉密论文按学校规定处理。

作者签名：日期：年月日导师签名：日期：年月日指导教师评价：一、撰写（设计）过程1、学生在论文（设计）过程中的治学态度、工作精神□优□良□中□及格□不及格2、学生掌握专业知识、技能的扎实程度□优□良□中□及格□不及格3、学生综合运用所学知识和专业技能分析和解决问题的能力□优□良□中□及格□不及格4、研究方法的科学性；技术线路的可行性；设计方案的合理性□优□良□中□及格□不及格5、完成毕业论文（设计）期间的出勤情况□优□良□中□及格□不及格二、论文（设计）质量1、论文（设计）的整体结构是否符合撰写规范？□优□良□中□及格□不及格2、是否完成指定的论文（设计）任务（包括装订及附件）？□优□良□中□及格□不及格三、论文（设计）水平1、论文（设计）的理论意义或对解决实际问题的指导意义□优□良□中□及格□不及格2、论文的观念是否有新意？设计是否有创意？□优□良□中□及格□不及格3、论文（设计说明书）所体现的整体水平□优□良□中□及格□不及格建议成绩：□优□良□中□及格□不及格（在所选等级前的□内画“√”）指导教师：（签名）单位：（盖章）年月日评阅教师评价：一、论文（设计）质量1、论文（设计）的整体结构是否符合撰写规范？□优□良□中□及格□不及格2、是否完成指定的论文（设计）任务（包括装订及附件）？□优□良□中□及格□不及格二、论文（设计）水平1、论文（设计）的理论意义或对解决实际问题的指导意义□优□良□中□及格□不及格2、论文的观念是否有新意？设计是否有创意？□优□良□中□及格□不及格3、论文（设计说明书）所体现的整体水平□优□良□中□及格□不及格建议成绩：□优□良□中□及格□不及格（在所选等级前的□内画“√”）评阅教师：（签名）单位：（盖章）年月日教研室（或答辩小组）及教学系意见教研室（或答辩小组）评价：一、答辩过程1、毕业论文（设计）的基本要点和见解的叙述情况□优□良□中□及格□不及格2、对答辩问题的反应、理解、表达情况□优□良□中□及格□不及格3、学生答辩过程中的精神状态□优□良□中□及格□不及格二、论文（设计）质量1、论文（设计）的整体结构是否符合撰写规范？□优□良□中□及格□不及格2、是否完成指定的论文（设计）任务（包括装订及附件）？□优□良□中□及格□不及格三、论文（设计）水平1、论文（设计）的理论意义或对解决实际问题的指导意义□优□良□中□及格□不及格2、论文的观念是否有新意？设计是否有创意？□优□良□中□及格□不及格3、论文（设计说明书）所体现的整体水平□优□良□中□及格□不及格评定成绩：□优□良□中□及格□不及格（在所选等级前的□内画“√”）教研室主任（或答辩小组组长）：（签名）年月日教学系意见：系主任：（签名）年月日********大学毕业设计（论文）任务书姓名：院（系）：专业：班号：任务起至日期：毕业设计（论文）题目：基于ADAMS/Car汽车悬架系统动力学建模与仿真分析立题的目的和意义：汽车悬架是车架（或车身）与车轴（或车轮）之间的弹性联结装置的统称。

多体动力学模型英文

多体动力学模型英文英文回答：Multi-body dynamics (MBD) modeling is a powerful tool used to analyze the behavior of complex mechanical systems consisting of multiple rigid or flexible bodies connected by joints and constraints. It employs advanced numerical techniques to simulate the dynamic interactions between these bodies, considering factors such as gravity, external forces, and contact forces.MBD models are commonly utilized in various engineering disciplines, including automotive, aerospace, robotics, and biomedical engineering. Engineers leverage MBD software to design, analyze, and optimize systems ranging from vehicles to industrial machinery and human bodies.The primary advantages of MBD modeling include:Accurate representation of complex systems: MBD modelscapture the intricate interactions and behaviors of multi-body systems, which can be challenging to analyze using traditional methods.Insight into system dynamics: MBD simulations provide valuable insights into the dynamic behavior of a system, allowing engineers to assess its stability, performance,and safety.Optimization of system design: By analyzing MBD models, engineers can identify potential design improvements, optimize component interactions, and enhance overall system performance.Virtual prototyping: MBD models enable virtual prototyping, reducing the need for physical prototypes and accelerating the product development process.Collaboration and communication: MBD models facilitate collaboration among engineers from different disciplines, providing a shared platform for design analysis and optimization.The process of creating an MBD model typically involves the following steps:1. Modeling the geometry: The physical geometry of the system is defined using CAD software or other modeling tools.2. Defining joints and constraints: The connections and constraints between bodies are specified, defining the permissible motions and interactions.3. Applying loads and boundary conditions: External forces, gravity, and other boundary conditions are applied to the model.4. Solving the equations of motion: Numerical integration methods are employed to solve the equations of motion, simulating the dynamic behavior of the system.5. Analyzing the results: The simulation outputs are analyzed to extract insights about system dynamics,performance, and potential design improvements.中文回答：多体动力学模型。

汽车盘式制动分析毕业设计论文

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制动器刚体模型分析........................................................................................................15 3.1 多刚体系统动力学................................................................................................. 15 3.1.1 3.1.2 3.1.3 3.1.4 3.2 多刚体系统的坐标系...................................................................................15 多刚体系统组成成分...................................................................................15 多刚体系统的自由度...................................................................................16 多刚体系统的动力学方程...........................................................................16
关键词：盘式制动器；虚拟样机；振动；多柔体模型
I
沈阳理工大学学士学位论文
Abstract
With the development of the economy,the vehicles have been one of the best means of transportation in modern time.Because the brakes play an important part in the vehicles’Safety and Comfort,how to reduce the cars’brake vibration and noise has become an important research topic. First the paper introduced the history of brakes.the research status of brake vibration,then introduced a multi-body dynamic model of the basic theory and self-excited vibration theoretical of the disc brake vibration.All these theories provide a feasible means for further develop.Next,introduced how to build the flexible multi-body of the brake system using the FEA technology and the multi-body dynamic technology.Including hhow to get the model neutral file(MNF)of the brake disc and brake pad by utilizing the FEA technology.In the process of building the MNF,the free model analysis of the brake disc and pads were studied.Introduced the process of the multi-body dynamics modeling:import flexible bodies and rigid bodies,in order to calculate accurately,should gave the rigid bodies a certain material properties,add the constraints between the disc and brake pads were achieved by the contact command. The brake angular velocity and acceleration curves can be carried out by dynamical simulation and analysis.The flexible multi-body model not only concerned the flexibility deformation of the components of the brake system,but also concerned the influence of moment of inertia of the rotating components of the automobile,so the simulation was more reasonable.The method of building the flexible multi-body model is universal and it can be useful for future disk brake noise analysis and structural optimization design.

Recurdyn介绍

新一代的系统级多体动力学分析软件—虚拟产品设计开发工具RecurDyn (Recursive Dynamic)是由韩国FunctionBay公司基于其划时代算法——递归算法开发出的新一代多体系统动力学仿真软件。

它采用相对坐标系运动方程理论和完全递归算法，非常适合于求解大规模及复杂接触的多体系统动力学问题。

传统的动力学分析软件对于机构中普遍存在的接触碰撞问题解决得远远不够完善，这其中包括过多的简化、求解效率低下、求解稳定性差等问题，难以满足工程应用的需要。

基于此，韩国FunctionBay 公司充分利用最新的多体动力学理论，基于相对坐标系建模和递归求解，开发出RecurDyn软件。

该软件具有令人震撼的求解速度与稳定性，成功地解决了机构接触碰撞中上述问题，极大地拓展了多体动力学软件的应用范围。

RecurDyn不但可以解决传统的运动学与动力学问题，同时是解决工程中机构接触碰撞问题的专家。

RecurDyn 借助于其特有的MFBD(Multi Flexible Body Dynamics)多柔体动力学分析技术，可以更加真实地分析出机构运动中的部件的变形，应力，应变。

RecurDyn 中的MFBD技术用于分析柔性体的大变形非线性问题，以及柔性体之间的接触，柔性体和刚性体相互之间的接触问题。

传统的多体动力学分析软件只可以考虑柔性体的线型变形，对于大变形，非线性，以及柔性体之间的相互接触就无能为力了。

RecurDyn 中为用户提供了完整的解决方案，包含控制，电子，液压以及CFD，为用户的产品开发提供了完整的产品虚拟仿真、开发平台。

RecurDyn 的专业模块还包括，送纸机构模块，齿轮元件模块，链条分析模块，皮带分析模块，高速运动履带分析模块，低速运动履带分析模块，轮胎模块，发动机开发设计模块。

鉴于RecurDyn的强大功能，软件广泛应用航空、航天、军事车辆、军事装备、工程机械、电器设备、娱乐设备、汽车卡车、铁道、船舶机械及其它通用机械等行业。

英语力学词汇英汉对译

力学词汇英汉对译通类名词力学 mechanics牛顿力学 Newtonian mechanics经典力学 classical mechanics静力学 statics运动学 kinematics动力学 dynamics动理学 kinetics宏观力学 macroscopic mechanics,macromechanics细观力学 mesomechanics微观力学 microscopic mechanics,micromechanics一般力学 general mechanics固体力学 solid mechanics流体力学 fluid mechanics理论力学 theoretical mechanics应用力学 applied mechanics工程力学 engineering mechanics实验力学 experimental mechanics计算力学 computational mechanics理性力学 rational mechanics物理力学 physical mechanics地球动力学 geodynamics力 force作用点 point of action作用线 line of action力系 system of forces力系的简化 reduction of force system等效力系 equivalent force system刚体 rigid body力的可传性 transmissibility of force平行四边形定则 parallelogram rule力三角形 force triangle力多边形 force polygon零力系 null-force system平衡 equilibrium力的平衡 equilibrium of forces平衡条件 equilibrium condition平衡位置 equilibrium position平衡态 equilibrium state分析力学 analytical mechanics拉格朗日乘子 Lagrange multiplier拉格朗日[量] Lagrangian拉格朗日括号 Lagrange bracket循环坐标 cyclic coordinate循环积分 cyclic integral哈密顿[量] Hamiltonian哈密顿函数 Hamiltonian function正则方程 canonical equation正则摄动 canonical perturbation正则变换 canonical transformation正则变量 canonical variable哈密顿原理 Hamilton principle作用量积分 action integral哈密顿--雅可比方程 Hamilton-Jacobi equation作用--角度变量 action-angle variables 阿佩尔方程 Appell equation劳斯方程 Routh equation拉格朗日函数 Lagrangian function诺特定理 Noether theorem泊松括号 poisson bracket边界积分法 boundary integral method 并矢 dyad运动稳定性 stability of motion轨道稳定性 orbital stability李雅普诺夫函数 Lyapunov function渐近稳定性 asymptotic stability结构稳定性 structural stability久期不稳定性 secular instability弗洛凯定理 Floquet theorem倾覆力矩 capsizing moment自由振动 free vibration固有振动 natural vibration暂态 transient state环境振动 ambient vibration反共振 anti-resonance衰减 attenuation库仑阻尼 Coulomb damping同相分量 in-phase component非同相分量 out-of -phase component超调量 overshoot参量[激励]振动 parametric vibration 模糊振动 fuzzy vibration临界转速 critical speed of rotation阻尼器 damper半峰宽度 half-peak width集总参量系统 lumped parameter system相平面法 phase plane method相轨迹 phase trajectory等倾线法 isocline method跳跃现象 jump phenomenon负阻尼 negative damping达芬方程 Duffing equation希尔方程 Hill equationKBM方法 KBM method, Krylov-Bogoliu-bov-Mitropol'skii method 马蒂厄方程 Mathieu equation平均法 averaging method组合音调 combination tone解谐 detuning耗散函数 dissipative function硬激励 hard excitation硬弹簧 hard spring, hardening spring谐波平衡法 harmonic balance method久期项 secular term自激振动 self-excited vibration分界线 separatrix亚谐波 subharmonic软弹簧 soft spring ,softening spring软激励 soft excitation邓克利公式 Dunkerley formula瑞利定理 Rayleigh theorem分布参量系统 distributed parameter system优势频率 dominant frequency模态分析 modal analysis固有模态 natural mode of vibration同步 synchronization超谐波 ultraharmonic范德波尔方程 van der pol equation频谱 frequency spectrum基频 fundamental frequencyWKB方法 WKB method, Wentzel-Kramers-Brillouin method 缓冲器 buffer风激振动 aeolian vibration嗡鸣 buzz倒谱 cepstrum颤动 chatter蛇行 hunting阻抗匹配 impedance matching机械导纳 mechanical admittance机械效率 mechanical efficiency机械阻抗 mechanical impedance随机振动 stochastic vibration, random vibration隔振 vibration isolation减振 vibration reduction应力过冲 stress overshoot喘振 surge摆振 shimmy起伏运动 phugoid motion起伏振荡 phugoid oscillation驰振 galloping陀螺动力学 gyrodynamics陀螺摆 gyropendulum陀螺平台 gyroplatform.陀螺力矩 gyroscoopic torque陀螺稳定器 gyrostabilizer陀螺体 gyrostat惯性导航 inertial guidance姿态角 attitude angle方位角 azimuthal angle舒勒周期 Schuler period机器人动力学 robot dynamics多体系统 multibody system多刚体系统 multi-rigid-body system机动性 maneuverability凯恩方法 Kane method转子[系统]动力学 rotor dynamics转子[一支承一基础]系统 rotor-support-foundation system 静平衡 static balancing动平衡 dynamic balancing静不平衡 static unbalance动不平衡 dynamic unbalance现场平衡 field balancing不平衡 unbalance不平衡量 unbalance互耦力 cross force挠性转子 flexible rotor分频进动 fractional frequency precession半频进动 half frequency precession油膜振荡 oil whip转子临界转速 rotor critical speed自动定心 self-alignment亚临界转速 subcritical speed涡动 whirl固体力学弹性力学 elasticity弹性理论 theory of elasticity均匀应力状态 homogeneous state of stress应力不变量 stress invariant应变不变量 strain invariant应变椭球 strain ellipsoid均匀应变状态 homogeneous state of strain应变协调方程 equation of strain compatibility拉梅常量 Lame constants各向同性弹性 isotropic elasticity旋转圆盘 rotating circular disk楔 wedge开尔文问题 Kelvin problem布西内斯克问题 Boussinesq problem艾里应力函数 Airy stress function克罗索夫--穆斯赫利什维利法 Kolosoff-Muskhelishvili method 基尔霍夫假设 Kirchhoff hypothesis板 Plate矩形板 Rectangular plate圆板 Circular plate环板 Annular plate波纹板 Corrugated plate加劲板 Stiffened plate,reinforced Plate 中厚板 Plate of moderate thickness弯[曲]应力函数 Stress function of bending 壳 Shell扁壳 Shallow shell旋转壳 Revolutionary shell球壳 Spherical shell[圆]柱壳 Cylindrical shell锥壳 Conical shell环壳 Toroidal shell封闭壳 Closed shell波纹壳 Corrugated shell扭[转]应力函数 Stress function of torsion 翘曲函数 Warping function半逆解法 semi-inverse method瑞利--里茨法 Rayleigh-Ritz method松弛法 Relaxation method莱维法 Levy method松弛 Relaxation量纲分析 Dimensional analysis自相似[性] self-similarity影响面 Influence surface接触应力 Contact stress赫兹理论 Hertz theory协调接触 Conforming contact滑动接触 Sliding contact滚动接触 Rolling contact压入 Indentation各向异性弹性 Anisotropic elasticity颗粒材料 Granular material散体力学 Mechanics of granular media热弹性 Thermoelasticity超弹性 Hyperelasticity粘弹性 Viscoelasticity对应原理 Correspondence principle褶皱 Wrinkle塑性全量理论 Total theory of plasticity 滑动 Sliding微滑 Microslip粗糙度 Roughness非线性弹性 Nonlinear elasticity大挠度 Large deflection突弹跳变 snap-through有限变形 Finite deformation格林应变 Green strain阿尔曼西应变 Almansi strain弹性动力学 Dynamic elasticity运动方程 Equation of motion准静态的 Quasi-static气动弹性 Aeroelasticity水弹性 Hydroelasticity颤振 Flutter弹性波 Elastic wave简单波 Simple wave柱面波 Cylindrical wave水平剪切波 Horizontal shear wave竖直剪切波 Vertical shear wave体波 body wave无旋波 Irrotational wave畸变波 Distortion wave膨胀波 Dilatation wave瑞利波 Rayleigh wave等容波 Equivoluminal wave勒夫波 Love wave界面波 Interfacial wave边缘效应 edge effect塑性力学 Plasticity可成形性 Formability金属成形 Metal forming耐撞性 Crashworthiness结构抗撞毁性 Structural crashworthiness 拉拔 Drawing破坏机构 Collapse mechanism回弹 Springback挤压 Extrusion冲压 Stamping穿透 Perforation层裂 Spalling塑性理论 Theory of plasticity安定[性]理论 Shake-down theory运动安定定理 kinematic shake-down theorem 静力安定定理 Static shake-down theorem率相关理论 rate dependent theorem载荷因子 load factor加载准则 Loading criterion加载函数 Loading function加载面 Loading surface塑性加载 Plastic loading塑性加载波 Plastic loading wave简单加载 Simple loading比例加载 Proportional loading卸载 Unloading卸载波 Unloading wave冲击载荷 Impulsive load阶跃载荷 step load脉冲载荷 pulse load极限载荷 limit load中性变载 nentral loading拉抻失稳 instability in tension加速度波 acceleration wave本构方程 constitutive equation完全解 complete solution名义应力 nominal stress过应力 over-stress真应力 true stress等效应力 equivalent stress流动应力 flow stress应力间断 stress discontinuity应力空间 stress space主应力空间 principal stress space静水应力状态 hydrostatic state of stress对数应变 logarithmic strain工程应变 engineering strain等效应变 equivalent strain应变局部化 strain localization应变率 strain rate应变率敏感性 strain rate sensitivity应变空间 strain space有限应变 finite strain塑性应变增量 plastic strain increment累积塑性应变 accumulated plastic strain永久变形 permanent deformation内变量 internal variable应变软化 strain-softening理想刚塑性材料 rigid-perfectly plastic Material 刚塑性材料 rigid-plastic material理想塑性材料 perfectl plastic material材料稳定性 stability of material应变偏张量 deviatoric tensor of strain应力偏张量 deviatori tensor of stress应变球张量 spherical tensor of strain应力球张量 spherical tensor of stress路径相关性 path-dependency线性强化 linear strain-hardening应变强化 strain-hardening随动强化 kinematic hardening各向同性强化 isotropic hardening强化模量 strain-hardening modulus幂强化 power hardening塑性极限弯矩 plastic limit bending Moment塑性极限扭矩 plastic limit torque弹塑性弯曲 elastic-plastic bending弹塑性交界面 elastic-plastic interface弹塑性扭转 elastic-plastic torsion粘塑性 Viscoplasticity非弹性 Inelasticity理想弹塑性材料 elastic-perfectly plastic Material 极限分析 limit analysis极限设计 limit design极限面 limit surface上限定理 upper bound theorem上屈服点 upper yield point下限定理 lower bound theorem下屈服点 lower yield point界限定理 bound theorem初始屈服面 initial yield surface后继屈服面 subsequent yield surface屈服面[的]外凸性 convexity of yield surface截面形状因子 shape factor of cross-section沙堆比拟 sand heap analogy屈服 Yield屈服条件 yield condition屈服准则 yield criterion屈服函数 yield function屈服面 yield surface塑性势 plastic potential能量吸收装置 energy absorbing device能量耗散率 energy absorbing device塑性动力学 dynamic plasticity塑性动力屈曲 dynamic plastic buckling塑性动力响应 dynamic plastic response塑性波 plastic wave运动容许场 kinematically admissible Field静力容许场 statically admissible Field流动法则 flow rule速度间断 velocity discontinuity滑移线 slip-lines滑移线场 slip-lines field移行塑性铰 travelling plastic hinge塑性增量理论 incremental theory of Plasticity米泽斯屈服准则 Mises yield criterion普朗特--罗伊斯关系 prandtl- Reuss relation特雷斯卡屈服准则 Tresca yield criterion洛德应力参数 Lode stress parameter莱维--米泽斯关系 Levy-Mises relation亨基应力方程 Hencky stress equation赫艾--韦斯特加德应力空间 Haigh-Westergaard stress space 洛德应变参数 Lode strain parameter德鲁克公设 Drucker postulate盖林格速度方程 Geiringer velocity Equation结构力学 structural mechanics结构分析 structural analysis结构动力学 structural dynamics拱 Arch三铰拱 three-hinged arch抛物线拱 parabolic arch圆拱 circular arch穹顶 Dome空间结构 space structure空间桁架 space truss雪载[荷] snow load风载[荷] wind load土压力 earth pressure地震载荷 earthquake loading弹簧支座 spring support支座位移 support displacement支座沉降 support settlement超静定次数 degree of indeterminacy机动分析 kinematic analysis结点法 method of joints截面法 method of sections结点力 joint forces共轭位移 conjugate displacement影响线 influence line三弯矩方程 three-moment equation单位虚力 unit virtual force刚度系数 stiffness coefficient柔度系数 flexibility coefficient力矩分配 moment distribution力矩分配法 moment distribution method 力矩再分配 moment redistribution分配系数 distribution factor矩阵位移法 matri displacement method单元刚度矩阵 element stiffness matrix单元应变矩阵 element strain matrix总体坐标 global coordinates贝蒂定理 Betti theorem高斯--若尔当消去法 Gauss-Jordan elimination Method 屈曲模态 buckling mode复合材料力学 mechanics of composites复合材料 composite material纤维复合材料 fibrous composite单向复合材料 unidirectional composite泡沫复合材料 foamed composite颗粒复合材料 particulate composite层板 Laminate夹层板 sandwich panel正交层板 cross-ply laminate斜交层板 angle-ply laminate层片 Ply多胞固体 cellular solid膨胀 Expansion压实 Debulk劣化 Degradation脱层 Delamination脱粘 Debond纤维应力 fiber stress层应力 ply stress层应变 ply strain层间应力 interlaminar stress比强度 specific strength强度折减系数 strength reduction factor强度应力比 strength -stress ratio横向剪切模量 transverse shear modulus横观各向同性 transverse isotropy正交各向异 Orthotropy剪滞分析 shear lag analysis短纤维 chopped fiber长纤维 continuous fiber纤维方向 fiber direction纤维断裂 fiber break纤维拔脱 fiber pull-out纤维增强 fiber reinforcement致密化 Densification最小重量设计 optimum weight design网格分析法 netting analysis混合律 rule of mixture失效准则 failure criterion蔡--吴失效准则 Tsai-W u failure criterion达格代尔模型 Dugdale model断裂力学 fracture mechanics概率断裂力学 probabilistic fracture Mechanics格里菲思理论 Griffith theory线弹性断裂力学 linear elastic fracture mechanics, LEFM 弹塑性断裂力学 elastic-plastic fracture mecha-nics, EPFM 断裂 Fracture脆性断裂 brittle fracture解理断裂 cleavage fracture蠕变断裂 creep fracture延性断裂 ductile fracture晶间断裂 inter-granular fracture准解理断裂 quasi-cleavage fracture穿晶断裂 trans-granular fracture裂纹 Crack裂缝 Flaw缺陷 Defect割缝 Slit微裂纹 Microcrack折裂 Kink椭圆裂纹 elliptical crack深埋裂纹 embedded crack[钱]币状裂纹 penny-shape crack预制裂纹 Precrack短裂纹 short crack表面裂纹 surface crack裂纹钝化 crack blunting裂纹分叉 crack branching裂纹闭合 crack closure裂纹前缘 crack front裂纹嘴 crack mouth裂纹张开角 crack opening angle,COA裂纹张开位移 crack opening displacement, COD裂纹阻力 crack resistance裂纹面 crack surface裂纹尖端 crack tip裂尖张角 crack tip opening angle, CTOA裂尖张开位移 crack tip opening displacement, CTOD裂尖奇异场 crack tip singularity Field 裂纹扩展速率 crack growth rate稳定裂纹扩展 stable crack growth定常裂纹扩展 steady crack growth亚临界裂纹扩展 subcritical crack growth 裂纹[扩展]减速 crack retardation止裂 crack arrest止裂韧度 arrest toughness断裂类型 fracture mode滑开型 sliding mode张开型 opening mode撕开型 tearing mode复合型 mixed mode撕裂 Tearing撕裂模量 tearing modulus断裂准则 fracture criterionJ积分 J-integralJ阻力曲线 J-resistance curve断裂韧度 fracture toughness应力强度因子 stress intensity factor HRR场 Hutchinson-Rice-Rosengren Field 守恒积分 conservation integral有效应力张量 effective stress tensor应变能密度 strain energy density能量释放率 energy release rate内聚区 cohesive zone塑性区 plastic zone张拉区 stretched zone热影响区 heat affected zone, HAZ延脆转变温度 brittle-ductile transition temperature剪切带 shear band剪切唇 shear lip无损检测 non-destructive inspection双边缺口试件 double edge notched specimen, DEN specimen单边缺口试件 single edge notched specimen, SEN specimen三点弯曲试件 three point bending specimen, TPB specimen中心裂纹拉伸试件 center cracked tension specimen, CCT specimen 中心裂纹板试件 center cracked panel specimen, CCP specimen紧凑拉伸试件 compact tension specimen, CT specimen大范围屈服 large scale yielding小范围攻屈服 small scale yielding韦布尔分布 Weibull distribution帕里斯公式 paris formula空穴化 Cavitation应力腐蚀 stress corrosion概率风险判定 probabilistic risk assessment, PRA损伤力学 damage mechanics损伤 Damage连续介质损伤力学 continuum damage mechanics细观损伤力学 microscopic damage mechanics累积损伤 accumulated damage脆性损伤 brittle damage延性损伤 ductile damage宏观损伤 macroscopic damage细观损伤 microscopic damage微观损伤 microscopic damage损伤准则 damage criterion损伤演化方程 damage evolution equation 损伤软化 damage softening损伤强化 damage strengthening损伤张量 damage tensor损伤阈值 damage threshold损伤变量 damage variable损伤矢量 damage vector损伤区 damage zone疲劳 Fatigue低周疲劳 low cycle fatigue应力疲劳 stress fatigue随机疲劳 random fatigue蠕变疲劳 creep fatigue腐蚀疲劳 corrosion fatigue疲劳损伤 fatigue damage疲劳失效 fatigue failure疲劳断裂 fatigue fracture疲劳裂纹 fatigue crack疲劳寿命 fatigue life疲劳破坏 fatigue rupture疲劳强度 fatigue strength疲劳辉纹 fatigue striations疲劳阈值 fatigue threshold交变载荷 alternating load交变应力 alternating stress应力幅值 stress amplitude应变疲劳 strain fatigue应力循环 stress cycle应力比 stress ratio安全寿命 safe life过载效应 overloading effect循环硬化 cyclic hardening循环软化 cyclic softening环境效应 environmental effect裂纹片 crack gage裂纹扩展 crack growth, crack Propagation 裂纹萌生 crack initiation循环比 cycle ratio实验应力分析 experimental stress Analysis 工作[应变]片 active[strain] gage基底材料 backing material应力计 stress gage零[点]飘移 zero shift, zero drift应变测量 strain measurement应变计 strain gage应变指示器 strain indicator应变花 strain rosette应变灵敏度 strain sensitivity机械式应变仪 mechanical strain gage直角应变花 rectangular rosette引伸仪 Extensometer应变遥测 telemetering of strain横向灵敏系数 transverse gage factor横向灵敏度 transverse sensitivity焊接式应变计 weldable strain gage平衡电桥 balanced bridge粘贴式应变计 bonded strain gage粘贴箔式应变计 bonded foiled gage粘贴丝式应变计 bonded wire gage桥路平衡 bridge balancing电容应变计 capacitance strain gage补偿片 compensation technique补偿技术 compensation technique基准电桥 reference bridge电阻应变计 resistance strain gage温度自补偿应变计 self-temperature compensating gage 半导体应变计 semiconductor strain Gage集流器 slip ring应变放大镜 strain amplifier疲劳寿命计 fatigue life gage电感应变计 inductance [strain] gage光[测]力学 Photomechanics光弹性 Photoelasticity光塑性 Photoplasticity杨氏条纹 Young fringe双折射效应 birefrigent effect等位移线 contour of equal Displacement暗条纹 dark fringe条纹倍增 fringe multiplication干涉条纹 interference fringe等差线 Isochromatic等倾线 Isoclinic等和线 isopachic应力光学定律 stress- optic law主应力迹线 Isostatic亮条纹 light fringe光程差 optical path difference热光弹性 photo-thermo -elasticity光弹性贴片法 photoelastic coating Method光弹性夹片法 photoelastic sandwich Method动态光弹性 dynamic photo-elasticity空间滤波 spatial filtering空间频率 spatial frequency起偏镜 Polarizer反射式光弹性仪 reflection polariscope残余双折射效应 residual birefringent Effect应变条纹值 strain fringe value应变光学灵敏度 strain-optic sensitivity应力冻结效应 stress freezing effect应力条纹值 stress fringe value应力光图 stress-optic pattern暂时双折射效应 temporary birefringent Effect脉冲全息法 pulsed holography透射式光弹性仪 transmission polariscope实时全息干涉法 real-time holographic interferometry 网格法 grid method全息光弹性法 holo-photoelasticity全息图 Hologram全息照相 Holograph全息干涉法 holographic interferometry全息云纹法 holographic moire technique全息术 Holography全场分析法 whole-field analysis散斑干涉法 speckle interferometry散斑 Speckle错位散斑干涉法 speckle-shearing interferometry, shearography 散斑图 Specklegram白光散斑法 white-light speckle method云纹干涉法 moire interferometry[叠栅]云纹 moire fringe[叠栅]云纹法 moire method云纹图 moire pattern离面云纹法 off-plane moire method参考栅 reference grating试件栅 specimen grating分析栅 analyzer grating面内云纹法 in-plane moire method脆性涂层法 brittle-coating method条带法 strip coating method坐标变换 transformation of Coordinates计算结构力学 computational structural mechanics加权残量法 weighted residual method有限差分法 finite difference method有限[单]元法 finite element method配点法 point collocation里茨法 Ritz method广义变分原理 generalized variational Principle最小二乘法 least square method胡[海昌]一鹫津原理 Hu-Washizu principle赫林格-赖斯纳原理 Hellinger-Reissner Principle 修正变分原理 modified variational Principle约束变分原理 constrained variational Principle 混合法 mixed method杂交法 hybrid method边界解法 boundary solution method有限条法 finite strip method半解析法 semi-analytical method协调元 conforming element非协调元 non-conforming element混合元 mixed element杂交元 hybrid element边界元 boundary element强迫边界条件 forced boundary condition自然边界条件 natural boundary condition离散化 Discretization离散系统 discrete system连续问题 continuous problem广义位移 generalized displacement广义载荷 generalized load广义应变 generalized strain广义应力 generalized stress界面变量 interface variable节点 node, nodal point[单]元 Element角节点 corner node边节点 mid-side node内节点 internal node无节点变量 nodeless variable杆元 bar element桁架杆元 truss element梁元 beam element二维元 two-dimensional element一维元 one-dimensional element三维元 three-dimensional element轴对称元 axisymmetric element板元 plate element壳元 shell element厚板元 thick plate element三角形元 triangular element四边形元 quadrilateral element四面体元 tetrahedral element曲线元 curved element二次元 quadratic element线性元 linear element三次元 cubic element四次元 quartic element等参[数]元 isoparametric element超参数元 super-parametric element亚参数元 sub-parametric element节点数可变元 variable-number-node element 拉格朗日元 Lagrange element拉格朗日族 Lagrange family巧凑边点元 serendipity element巧凑边点族 serendipity family无限元 infinite element单元分析 element analysis单元特性 element characteristics刚度矩阵 stiffness matrix几何矩阵 geometric matrix等效节点力 equivalent nodal force节点位移 nodal displacement节点载荷 nodal load位移矢量 displacement vector载荷矢量 load vector质量矩阵 mass matrix集总质量矩阵 lumped mass matrix相容质量矩阵 consistent mass matrix阻尼矩阵 damping matrix瑞利阻尼 Rayleigh damping刚度矩阵的组集 assembly of stiffness Matrices 载荷矢量的组集 consistent mass matrix质量矩阵的组集 assembly of mass matrices单元的组集 assembly of elements局部坐标系 local coordinate system局部坐标 local coordinate面积坐标 area coordinates体积坐标 volume coordinates曲线坐标 curvilinear coordinates静凝聚 static condensation合同变换 contragradient transformation形状函数 shape function试探函数 trial function检验函数 test function权函数 weight function样条函数 spline function代用函数 substitute function降阶积分 reduced integration零能模式 zero-energy modeP收敛 p-convergenceH收敛 h-convergence掺混插值 blended interpolation等参数映射 isoparametric mapping双线性插值 bilinear interpolation小块检验 patch test非协调模式 incompatible mode节点号 node number单元号 element number带宽 band width带状矩阵 banded matrix变带状矩阵 profile matrix带宽最小化 minimization of band width 波前法 frontal method子空间迭代法 subspace iteration method 行列式搜索法 determinant search method 逐步法 step-by-step method纽马克法 Newmark威尔逊法 Wilson拟牛顿法 quasi-Newton method牛顿-拉弗森法 Newton-Raphson method增量法 incremental method初应变 initial strain初应力 initial stress切线刚度矩阵 tangent stiffness matrix割线刚度矩阵 secant stiffness matrix模态叠加法 mode superposition method平衡迭代 equilibrium iteration子结构 Substructure子结构法 substructure technique超单元 super-element网格生成 mesh generation结构分析程序 structural analysis program前处理 pre-processing后处理 post-processing网格细化 mesh refinement应力光顺 stress smoothing组合结构 composite structure流体力学流体动力学 fluid dynamics连续介质力学 mechanics of continuous media 介质 medium流体质点 fluid particle无粘性流体 nonviscous fluid, inviscid fluid 连续介质假设 continuous medium hypothesis 流体运动学 fluid kinematics水静力学 hydrostatics液体静力学 hydrostatics支配方程 governing equation伯努利方程 Bernoulli equation伯努利定理 Bernonlli theorem毕奥-萨伐尔定律 Biot-Savart law欧拉方程 Euler equation亥姆霍兹定理 Helmholtz theorem开尔文定理 Kelvin theorem涡片 vortex sheet库塔-茹可夫斯基条件 Kutta-Zhoukowski condition 布拉休斯解 Blasius solution达朗贝尔佯廖 d'Alembert paradox雷诺数 Reynolds number施特鲁哈尔数 Strouhal number随体导数 material derivative不可压缩流体 incompressible fluid质量守恒 conservation of mass动量守恒 conservation of momentum能量守恒 conservation of energy动量方程 momentum equation能量方程 energy equation控制体积 control volume液体静压 hydrostatic pressure涡量拟能 enstrophy压差 differential pressure流[动] flow流线 stream line流面 stream surface流管 stream tube迹线 path, path line流场 flow field流态 flow regime流动参量 flow parameter流量 flow rate, flow discharge 涡旋 vortex涡量 vorticity涡丝 vortex filament涡线 vortex line涡面 vortex surface涡层 vortex layer涡环 vortex ring涡对 vortex pair涡管 vortex tube涡街 vortex street卡门涡街 Karman vortex street 马蹄涡 horseshoe vortex对流涡胞 convective cell卷筒涡胞 roll cell涡 eddy涡粘性 eddy viscosity环流 circulation环量 circulation速度环量 velocity circulation 偶极子 doublet, dipole驻点 stagnation point总压[力] total pressure总压头 total head静压头 static head总焓 total enthalpy能量输运 energy transport速度剖面 velocity profile库埃特流 Couette flow单相流 single phase flow单组份流 single-component flow均匀流 uniform. flow非均匀流 nonuniform. flow二维流 two-dimensional flow三维流 three-dimensional flow准定常流 quasi-steady flow非定常流 unsteady flow, non-steady flow 暂态流 transient flow周期流 periodic flow振荡流 oscillatory flow分层流 stratified flow无旋流 irrotational flow有旋流 rotational flow轴对称流 axisymmetric flow不可压缩性 incompressibility不可压缩流[动] incompressible flow浮体 floating body定倾中心 metacenter阻力 drag, resistance减阻 drag reduction表面力 surface force表面张力 surface tension毛细[管]作用 capillarity来流 incoming flow自由流 free stream自由流线 free stream line外流 external flow进口 entrance, inlet出口 exit, outlet扰动 disturbance, perturbation分布 distribution传播 propagation色散 dispersion弥散 dispersion附加质量 added mass ,associated mass 收缩 contraction镜象法 image method无量纲参数 dimensionless parameter 几何相似 geometric similarity运动相似 kinematic similarity动力相似[性] dynamic similarity平面流 plane flow势 potential势流 potential flow速度势 velocity potential复势 complex potential复速度 complex velocity流函数 stream function源 source汇 sink速度[水]头 velocity head拐角流 corner flow空泡流 cavity flow超空泡 supercavity超空泡流 supercavity flow空气动力学 aerodynamics低速空气动力学 low-speed aerodynamics 高速空气动力学 high-speed aerodynamics 气动热力学 aerothermodynamics亚声速流[动] subsonic flow跨声速流[动] transonic flow超声速流[动] supersonic flow锥形流 conical flow楔流 wedge flow叶栅流 cascade flow非平衡流[动] non-equilibrium flow细长体 slender body细长度 slenderness钝头体 bluff body钝体 blunt body翼型 airfoil翼弦 chord薄翼理论 thin-airfoil theory构型 configuration后缘 trailing edge迎角 angle of attack失速 stall脱体激波 detached shock wave波阻 wave drag诱导阻力 induced drag诱导速度 induced velocity临界雷诺数 critical Reynolds number前缘涡 leading edge vortex附着涡 bound vortex约束涡 confined vortex综合类：广义连续统力学 generalized continuum mechanics简单物质 simple material纯力学物质 purely mechanical material微分型物质 material of differential type积分型物质 material of integral type混合物组份 constituents of a mixture非协调理论 incompatibility theory微极理论 micropolar theory决定性原理 principle of determinism等存在原理 principle of equipresence局部作用原理 principle of objectivity客观性原理 principle of objectivity电磁连续统理论 theory of electromagnetic continuum 内时理论 endochronic theory非局部理论 nonlocal theory混合物理论 theory of mixtures里夫林-矣里克森张量 Rivlin-Ericksen tensor声张量 acoustic tensor半向同性张量 hemitropic tensor各向同性张量 isotropic tensor应变张量 strain tensor伸缩张量 stretch tensor连续旋错 continuous dislination连续位错 continuous dislocation动量矩平衡 angular momentum balance余本构关系 complementary constitutive relations共旋导数 co-rotational derivative, Jaumann derivative 非完整分量 anholonomic component爬升效应 climbing effect协调条件 compatibility condition错综度 complexity当时构形 current configuration能量平衡 energy balance变形梯度 deformation gradient有限弹性 finite elasticity熵增 entropy production标架无差异性 frame. indifference弹性势 elastic potential熵不等式 entropy inequality极分解 polar decomposition低弹性 hypoelasticity参考构形 reference configuration响应泛函 response functional动量平衡 momentum balance奇异面 singular surface贮能函数 stored-energy function内部约束 internal constraint物理分量 physical components本原元 primitive element普适变形 universal deformation速度梯度 velocity gradient测粘流动 viscometric flow当地导数 local derivative岩石力学 rock mechanics原始岩体应力 virgin rock stress构造应力 tectonic stress三轴压缩试验 three-axial compression test 三轴拉伸试验 three-axial tensile test三轴试验 triaxial test岩层静态应力 lithostatic stress吕荣 lugeon地压强 geostatic pressure水力劈裂 hydraulic fracture咬合[作用] interlocking内禀抗剪强度 intrinsic shear strength循环抗剪强度 cyclic shear strength残余抗剪强度 residual shear strength土力学 soil mechanics孔隙比 void ratio内磨擦角 angle of internal friction休止角 angle of repose孔隙率 porosity围压 ambient pressure渗透系数 coefficient of permeability [抗]剪切角 angle of shear resistance渗流力 seepage force表观粘聚力 apparent cohesion粘聚力 cohesion稠度 consistency固结 consolidation主固结 primary consolidation次固结 secondary consolidation固结仪 consolidometer浮升力 uplift扩容 dilatancy有效应力 effective stress絮凝[作用] flocculation主动土压力 active earth pressure 被动土压力 passive earth pressure 土动力学 soil dynamics应力解除 stress relief次时间效应 secondary time effect 贯入阻力 penetration resistance 沙土液化 liquefaction of sand泥流 mud flow多相流 multiphase flow马格努斯效应 Magnus effect韦伯数 Weber number环状流 annular flow泡状流 bubble flow层状流 stratified flow平衡流 equilibrium flow二组份流 two-component flow冻结流 frozen flow均质流 homogeneous flow二相流 two-phase flow。

在非惯性系中研究动力刚化问题

在非惯性系中研究动力刚化问题梁立孚;王鹏;宋海燕【摘要】Correct understanding of the dynamic stiffening problem is signality for further researching spacecraft dynamics and establishing a rational numerical model of flexible body dynamics. The dynamic stiffening problem was studied using the theory of a mechanical problem in a non-inertial coordinate system. Two kinds of numerical models for the dynamic stiffening problem were established. The physical meaning of the dynamic stiffening problem was clarified. The approach of correct zero-order modeling was explored. There is a substantive difference between the research of this paper and the research of other scholars.%正确认识动力刚化问题,对深入研究航天器动力学和合理建立柔体动力学的数值计算模型意义重大.应用非惯性坐标系中的力学问题的理论来研究动力刚化问题,给出两类研究动力刚化问题的计算模型,明确了动力刚化问题的物理意义,探索了正确处理零次建模的途径.这样处理动力刚化问题,表现出与其他学者的研究有实质性的差异.【期刊名称】《哈尔滨工程大学学报》【年(卷),期】2012(033)008【总页数】5页(P1052-1056)【关键词】动力刚化;非惯性坐标系;柔体;刚体;航天器动力学【作者】梁立孚;王鹏;宋海燕【作者单位】哈尔滨工程大学力学一级学科博士点,黑龙江哈尔滨150001;上海大学应用数学与力学研究所,上海200444;哈尔滨工程大学力学一级学科博士点,黑龙江哈尔滨150001【正文语种】中文【中图分类】O313文献［1］指出，1987 年 Kane［2］对大范围刚体运动槽型弹性梁进行了研究，指出在大范围刚体运动作高速旋转时，零次耦合建模方法得到弹性梁的变形将无限增大的结果，与实际情况相反.为此，Kane对弹性梁的变形作了比较精确的描述(包括了弯曲变形、剪切变形和扭曲变形)，首次提出动力刚化(dynamic stiffening)的概念.这一问题的提出，引起了各国学者的普遍关注.1989年，Banerjee和Kane［3］又对作大范围刚体运动的弹性薄板进行了研究.Haering［4］，Padilla ［5］采用类似方法对弹性梁动力学性质进行了分析.所得到的结果表明，人们在关于柔性多体系统动力学耦合机理的认识上有待深入，对所描述对象数学模型的准确性有待进一步研究.为了适应我国航天事业发展的需要，我国学者也对这一问题进行了广泛的、深入的研究［6-12］.以上研究，多数是数值的、定量的分析方法，少数学者进行解析的分析讨论.正确的进行解析分析对于深刻把握动力刚化的力学实质、建立正确的数值计算模型是有利的.因此，有必要继续研究下去.在文献［1，12］中，通过一个典型的实例进行研究，本文在其基础上，应用非惯性坐标系中的力学问题的理论来研究动力刚化问题，给出两类研究动力刚化问题的计算模型，得到具有明确物理意义的研究结果.从物理和数学方面说明了产生零级耦合建模的不合理现象的原因，并且建议了合理的处理方法，以便避免零级耦合建模中可能发生不合理现象.这样处理动力刚化问题，表现出与其他学者的研究有实质性的差异.1 在非惯性系中典型实例研究设有如图1所示的力学系统，2根无质量杆AB和BC在B点用铰链连接，在铰链处有一个刚度系数为k的扭簧.长度为R的杆AB的另一端固定在铰链A上，并且绕A点以角速度ω(t)在平面中转动.长度为L的杆BC的另一端固定着质量块m.杆AB和BC之间的相对转角为θ(t)，并且在系统的运动过程中，θ(t)可以为有限量，也可以为小量，其初始值为0.图1 非惯性坐标系Fig.1 Non-inertial coordinate system建立固连于杆AB的连体坐标系Bb1b2(如图1)，由于杆的转动，使得该坐标系成为非惯性坐标系.在这个非惯性坐标系中，如前所述θ(t)可以为有限量，也可以为小量.通过运动分析，可得系统的动能为作用在系统上的力矩，除了弹性力矩kθ外，还有惯性力矩.在转角θ(t)为有限量假设的情况下，离心惯性力fcf为引起的力矩为切向惯性力ft为引起的力矩为其外力势能为在建立动能和势能的表达式时，应当注意:以角速度ω转动的转动中心是A点，该点与质量m的距离为，以角速度转动的转动中心是B点，该点与质量m的距离为L.根据广义协变原理，在非惯性坐标系中，只要合理引入惯性力，就可以将相关力学定律表示为与在惯性系中类似的形式［13-15］，因此Lagrange方程可以表示为将动能的表达式和势能的表达式代入Lagrange方程的各项，并且推导如下:将推导结果代入Lagrange方程，可得整理可得这里顺便指出，方程式(13)是以角位移θ为基本变量的动力学方程.mL2为动力学项，kθ为扭簧引起的力矩，mω2RLsin θ为离心惯性力引起的力矩，m(Rcosθ+L)L为切向惯性力引起的力矩.2 进一步典型实例研究建立固连于杆AB的连体坐标系Bb1b2(图1)，由于杆的转动，使得该坐标系成为非惯性坐标系.在这个非惯性坐标系中，假设θ(t)始终为小角，使得sin θ≈θ，cos θ≈1.通过运动分析，可得系统的动能为作用在系统上的力矩，除了弹性力矩kθ外，还有惯性力矩.在θ(t)始终为小角假设的情况下，离心惯性力的计算公式为引起的力矩为切向惯性力的计算公式为引起的力矩为其外力势能为在建立动能和势能的表达式时，应当注意:以角速度ω转动的转动中心是A点，该点与质量m的距离为(R+L)，以角速度转动的转动中心是B点，该点与质量m的距离为L.根据广义协变原理，在非惯性坐标系中，只要合理引入惯性力，就可以将相关力学定律表示为与在惯性系中类似的形式［13-15］，因此Lagrange方程可以表示为将动能的表达式和势能的表达式代入Lagrange方程的各项，并且推导如下:将推导结果代入Lagrange方程，可得进而可得动力刚度项式(26)明确显示，在这个典型实例中，引起动力刚化的原因是离心惯性力的影响.这里顺便指出，方程式(25)是以角位移为基本变量的动力学方程.mL2为动力学项，kθ为扭簧引起的力矩，mω2RLθ为离心惯性力引起的力矩，m(R+L)L为切向惯性力引起的力矩.本节处理问题的过程，与一般文献中所提及的零级耦合建模相似，只是这里是在非惯性坐标系中研究问题的，而一般文献中多数是在惯性坐标系中.以上论述表明，在非惯性系中合理的处理问题，所谓的零次建模也是可行的.这一点也可说明在非惯性坐标系中研究动力刚化问题的优越性.3 典型实例的另一类计算模型研究建立固连于杆AB的连体坐标系Bb1b2(图2)，由于杆的转动，使得该坐标系成为非惯性坐标系.在这个非惯性坐标系中，假设θ(t)始终为小角，使得sin θ≈θ，cos θ≈1 .通过运动分析，可以得系统的动能为图2 θ(t)始终为小角Fig.2 θ(t)always small angle作用在系统上的力矩，除了弹性力矩kθ外，还有惯性力矩.在θ(t)始终为小角假设的情况下，离心惯性力的计算公式为引起的力矩为将离心惯性力作为主动力引起的附加势能为这一结果与文献［12］给出的结果相同.切向惯性力的计算公式为引起的力矩为将切向惯性力作为主动力引起的附加势能为系统的总外力势能为在建立动能和势能的表达式时，应当注意:以角速度ω转动的转动中心是A点，该点与质量m的距离为(R+L)，以角速度转动的转动中心是B点，该点与质量m的距离为L.根据广义协变原理，在非惯性坐标系中，只要合理引入惯性力，就可以将相关力学定律表示为与在惯性系中类似的形式，因此Lagrange方程可表示为将动能的表达式和势能的表达式代入Lagrange方程的各项，并且推导如下:将推导结果代入Lagrange方程，可得进而可得动力刚度项为式(42)明确显示，在这个典型实例中，引起动力刚化的原因是离心惯性力的影响.这里顺便指出，方程式(41)是以角位移为基本变量的动力学方程.mL2为动力学项，kθ为扭簧引起的力矩，mω2(R+L)Lθ为离心惯性力引起的力矩，m(R+L)L为切向惯性力引起的力矩.4 讨论零级建模如果在应用Lagrange方程之前，对势能函数应用泰勒展开并且取一级近似，可得可见，将使得离心惯性力引起的外力势能消失.这从物理方面说明了所谓零级建模不可行的原因.正弦函数和余弦函数的泰勒展开为如果在应用Lagrange方程之前，对势能函数应用泰勒展开.以往的简化是将正弦函数和余弦函数的泰勒展开都取一级近似.考虑到正弦函数的泰勒级数收敛较快，余弦函数的泰勒级数的收敛较慢，因而取正弦函数的泰勒展开的一级近似，取余弦函数的泰勒展开的二次近似，可得势能的表达式:可见，式(46)与式(18)相同，这也可以从一个侧面说明这样处理问题的正确性.将势能的表达式代入Lagrange方程的有关势能的项，并且推导如下:动能的表达式及其相关推导同前.将推导结果代入Lagrange方程，可得整理可得可见，在应用Lagrange方程之前简化，只要合理进行近似计算，也可以得到合理的建模.具体问题具体分析对于科技工作者来说是至关重要的.研究表明，考虑动力刚化的柔体动力学的建模问题，内容丰富，可以分门别类的进行研究.5 结束语本文是在非惯性坐标系中研究动力刚化问题.首先，给出在非惯性坐标系中研究动力刚化典型实例的一类力学模型，应用有限位移理论研究动力刚化问题的典型实例，得到具有明确物理意义的结果.将这类研究退化到小位移理论，表明所谓零次耦合建模方法也是可行的.然后，给出在非惯性坐标系中研究动力刚化典型实例的另一类力学模型.最后，进一步讨论了如何正确地进行所谓零次耦合建模的问题.参考文献:【相关文献】［1］洪嘉振，蒋丽忠.动力刚化与多体系统刚-柔耦合动力学［J］.计算力学学报，1999，16(3):295-301.HONG Jiazhen，JIANG Lizhong.Dynamic stiffening and multibody dynamics with coupled rigid and deformation motions［J］.Chinese Journal of Computational Mechanics，1999，16(3):295-301.［2］KANE T R，RYAN R R，BANER J A K，Dynamics of a cantilever beam attached to a moving base［J］.Journal of Guidance Control and Dynamics，1987，10(2):139-151.［3］BANERJEE A K，KANE T R.Multi-flexible body dynamics capturing movtion-induced stiffnes［J］.Journal of Applied Mechanics，1989，56:887-892.［4］HAERING W J，RYAN R R，SCOTT A.New formulation for flexible beams undergoing large overall plane motion［J］.Journal of Guidance，Control and Dynamics，1994，17(1):76-83.［5］PADILLA C E，VON FLOTOW A H.Nonlinear strain displacement relations and flexible multibody dynamics［J］.Journal of 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Presented at the ASME Wind Energy Symp., Reno, January and Stol11 considers coupling of ﬂapping motion of blades, teetering motion of hub, and yawing motion of tower, based on rigid body dynamic analysis using Symdyn, a symbolic dynamic rigid-body dynamic analysis code similar to YawDyn. The result of this study identiﬁes instability may occur in the teetering mode of hub. This signiﬁcant result indicates that more accurate and meaningful dynamic analysis of HAWT’s demands new methodology to consider both the coupling of the subsystems including teeter degree of freedom of hub and the ﬂexibility of tower and blades. The goal of the present work is to develop a tool for aeroelastic modeling of horizontal-axis wind turbines that, when applied to simpliﬁed analytical models, can be used in control design. As a ﬁrst step, a consistent structural analysis is presented which models the dynamic characteristics of the wind turbine consisting of connected ﬂexible bodies in a vacuum. An aerodynamic model will be added later to construct a complete analysis tool.
∗ Post Doctoral Fellow, School of Aerospace Engineering. Member, AIAA. Presently, Assistant Professor (Research), Duke University, Durham, North Carolina. † Graduate Research Assistant, School of Aerospace Engineering. Student Member, AIAA. ‡ Professor, School of Aerospace Engineering. Fellow, AIAA.
INTRODUCTION
Accurate modeling and analysis of wind turbines is quite useful and has the potential of increasing the economic eﬃciency of wind-energy generation. Firstly, it helps in understanding the dynamic response of the wind turbine to disturbances at various levels of wind loading. Such insight into the behavior helps in better design of the wind turbines not only to improve eﬃciency of energy conversion, but also to improve the life of the structure. Secondly, an accurate model will help in designing eﬃcient controllers leading to better performance and extended working life. There are various research eﬀorts throughout the world aimed at
Copyright c 2001 by Mayuresh J. Patil, Donghoon Lee, and Dewey H. Hodges. Published by the American Institute of Aeronautics and Astronautics, Inc. with permission.
AIAA 2001–0064
Multi-Flexible-Body Dynamic Analysis of Horizontal-Axis Wind Turbines
Mayuresh J. Patil,∗ Donghoon Lee,† and Dewey H. Hodges‡ Georgia Institute of Technology, Atlanta, Georgia 30332-0150 ABSTRACT
A dynamic stability analysis is presented for a horizontal-axis wind turbine modeled as a multi-body system with both rigid- and ﬂexible-body subsystems. The rigid-body subsystems are modeled as an interconnected set of rigid bodies using Kane’s method, which can lead to equations of motion that are more compact than they would be using other methods. The ﬂexible-body subsystems are modeled using nonlinear beam ﬁnite elements, derived from a mixed variational formulation for the dynamics of moving beams. The equations for the rigid and ﬂexible subsystems are coupled to obtain a uniﬁed framework that models the dynamic behavior of the complete system. Linearization of the dynamic equations about the steady-state solution yields system equations with periodic coeﬃcients that must be solved by Floquet theory to extract the dynamic characteristics. Numerical studies are presented to investigate the natural frequencies and mode shapes for a wind turbine with ﬂexible blades. The presented results demonstrate the performance of the present methodology to aid in understanding of the dynamic characteristics of the wind turbine. better understanding of the wind-turbine. These research eﬀorts encompass various technical disciplines, including, atmospheric modeling, wind-turbine structural and aerodynamic modeling, energy conversion system, power distribution technology. The present eﬀort is directed towards better understanding of the structural dynamic characteristics of the wind turbines. The previous research on the structural dynamics of HAWT’s can be generally classiﬁed into three groups. The ﬁrst group of studies analyzed isolated blades and were mainly conducted in 1970’s. Ormiston1 considered the basic ﬂapping response of a wind turbine blade using elementary analytical techniques and a simple rigid, centrally hinged, spring restrained blade model. Kaza and Hammond2 considered the ﬂap-lag stability of wind turbine rotors in the presence of velocity gradients, using a single centrally-hinged model for the blade. Kottapalli3 included ﬂap, lead-lag, torsion degrees of freedom along with gravity loads. The coupled ﬂap-lag-torsion dynamics of an isolated wind turbine blade was also treated by Chopra and Dugundji4 with an emphasis on nonlinear eﬀects associated with moderate blade deﬂection. The studies on rotor/tower or rotor/yaw coupling problem form the second group. Mathematical modeling of coupled rotor/tower dynamical system was ﬁrst presented by Warmbrodt and Friedmann.5 The coupled rotor/tower dynamics of wind turbine was treated by Garrad and Quarton6 using symbolic computing. Experimental study by Olorunsola7 indicated that the torque associated with rotor stall is an important factor in the yaw motion of HAWT. A concentrated study on the yaw motion of the rotor of HAWT’s was done by Hansen8 along with the development of the YawDyn code. Bir and Butterﬁeld9 studied the eﬀect of tower ﬂexibility on the system modes using ADAMS. The third group of studies consider the complete system dynamics of HAWT’s. Molenaarx and Dijkstra10 presented the development of the complete system dynamics model of a wind turbine using “superelement” modeling method used to divide the structure into a number of superelements consisting of four rigid bodies connected by torsional springs and dampers. A recent study of the structural modeling of HAWT’s