变流速输液管的周期和混沌振动

研究了参数激励和外激励联合作用下输流管道的非线性振动问题．只考虑管道变形的几何非线性因素,利用Hamilton原理得到单侧受简谐均布载荷作用下输液管的非线性动力学方程,对系统运动偏微分方程综合运用多尺度法和Galerkin离散方法,得到了主参数共振-1／2亚谐共振和1：2内共振情况下的平均方程．数值模拟结果表明参数激励和外激励联合作用下的悬臂输液管呈现周期运动、多倍周期运动和混沌运动的变化规律．     

复模态分析超临界轴向运动梁横向非线性振动

近似解析研究了简支边界条件下超临界轴向运动梁横向非线性自由振动的固有频率和模态函数.采用复模态方法处理控制方程,一个积分偏微分方程.将Galerkin截断思想用于近似处理线性化方程,一个含空间依赖系数的常微分方程.给出了不同截断项数对固有频率的影响.基于8项截断,讨论了系统参数对模态函数的影响.     

粘弹性传动带的分岔特性和混沌振动分析

研究了粘弹性传动带横向振动的分岔特性和混沌动力学行为．将传动带视为沿轴向运动的抗弯刚度较 小的粘弹性梁模型,同时考虑变形的几何非线性和材料的非线性因素,运用弹性力学方法建立了其横向振动 的偏微分方程,利用 Galerkin 方法得到了时空坐标解耦的二阶非线性动力学方程,重点探讨了带速波动对系统 动态特性的影响．采用数值方法对系统的运动响应进行仿真,分岔图和 Poincaré图表明：随着平均带速和波动 幅值的变化,系统出现周期振动和混沌振动,倍周期分岔是产生混沌振动的途径．     

受电压激励的复合材料悬臂板的分叉分析

以飞行器机翼作为工程背景,将机翼简化为悬臂板模型,研究了受横向电压激励、基础激励、面内激励联合作用下复合材料层合悬臂板的非线性动力学问题.首先建立其动力学模型,考虑冯-卡门大变形理论,利用Hamilton原理建立复合材料层合悬臂板的非线性动力学方程;选择符合边界条件的模态函数,利用Galerkin方法对系统进行四阶离散,得到四自由度非线性常微分方程;代入系统实际物理参数,应用MATLAB软件数值模拟得到系统振动幅值随电压激励变化的分叉图,由图可知,电压激励使系统从混沌运动变为倍周期运动,降低了系统振幅,保持系统的稳定.     

风力机叶片大挠度挥舞振动特性分析

分析了风力机叶片大挠度挥舞振动特性.基于Hamilton原理,建立了叶片大挠度挥舞振动控制方程,其中非稳态气动力由Greenberg公式得出.使用瑞利-利兹法求解振动特征问题,得到振动的频率和无阻尼模态函数.基于得出的模态函数,使用Galerkin方法将控制偏微分方程离散,得到模态坐标方程.将振动位移分解为静态位移和动态位移,得到了静态位移和动态位移方程,考查了入流速度比对静态位移和气动阻尼的影响,并对大挠度挥舞振动动态响应进行了分析,得到如下结论：大挠度挥舞振动静态位移沿叶片展向随入流速度比的增大而增大,叶尖处位移最大；当入流速度比较小时,振动为小振幅的周期运动,入流速度比较大时,振动为大振幅的拟周期运动.     

轴向运动粘弹性夹层梁的横向振动

研究了小扰度下轴向匀速运动粘弹性夹层梁的振动模态和固有频率.基于Kelvin粘弹性本构方程,建立了轴向运动粘弹性夹层梁横向振动控制方程.分别采用Galerkin截断和复模态分析方法,研究两端简支的粘弹性夹层梁的固有频率和模态函数,讨论了轴向运动速度、夹心层与约束层厚度比、初始轴力等参数对夹层梁固有频率、临界速度及稳定性的影响.     

基于延拓方法的悬索非线性振动分析

研究了受谐波激励作用下悬索的非线性响应.基于索的拟静态假设,同时考虑悬索的几何非线性,首先利用Hamilton变分原理得到了悬索面内运动的非线性方程.然后把悬索的位移展开成固有模态的级数和.并利用Galerkin方法得到一个有限维的动力系统.再利用打靶法和延拓方法研究了悬索的周期运动.同时利用数值积分研究了超谐波共振区的一些非周期运动.最后讨论了激励幅值对悬索周期运动的影响.     

轴向运动薄板非线性振动及其稳定性研究

应用增量谐波平衡法(IHB法)研究轴向运动薄板横向非线性振动特性及其稳定性.通过Hamilton原理推导出了非惯性参考系下四边简支轴向运动薄板的横向振动微分方程,然后利用Galerkin方法离散运动方程.对离散后的非线性方程组应用IHB法进行非线性振动分析,研究了在固有频率之比ω20/ω10接近于3:1情况下,外激励频率ω在ω10附近的具有内部共振的基谐波响应.最后用多元Floquet理论分析了系统周期解的稳定性,其中采用Hsu方法来计算转移矩阵.通过对具体例子的数值计算,分别得到了自由振动和不同外激励下的频幅相应曲线,通过对比运动梁模型和运动薄板模型的计算结果,分析了各种模型的适用范围.     

地基波动影响下非线性粘弹性桩的混沌运动分析

研究了在地基波动影响下非线性粘弹性桩中的混沌运动．假定桩体材料满足Leaderrnan非线性粘弹性本构关系,得到在轴向载荷作用下满足Winkler条件的地基土波动方程、桩与地基土耦合振动方程;利用Galerkin方法将非线性积分一微分方程简化,并进行了数值计算,揭示了非线性粘弹性桩包括混沌运动在内的动力学行为．     

轴向运动梁横向非线性振动研究

应用增量谐波平衡法(IHB法)研究轴向运动梁横向非线性振动的内部共振．根据哈密顿原理建立非惯性参考系下轴向运动梁的横向振动微分方程,采用分离变量法分离时间变量和空间变量并利用Galerkin方法离散运动方程,再应用IHB法进行非线性振动分析,研究了在固有频率之比ω20／ω10接近于3：1情况下,外激励频率ω在ω10,ω20附近的具有内部共振的基谐波和次谐波响应．数值结果表明了IHB法是一个求解轴向运动体系非线性振动的非常有效的半解析、半数值的方法。     

Simulation of Motion of Constrained Multibody Systems Based on Projection Operator

This paper presents an efficient dynamic formulation for solvingDifferential Algebraic Equations (DAE) by using the notion of orthogonalprojection. Firstly, the constraint equations are expressed explicitlyat acceleration level by using the notion of the orthogonal projection.Secondly, the Lagrangian multiplier is eliminated from the dynamicsequation by the projection operator. Then, the resultant equations areconsolidated into one equation which explicitly correlates theacceleration to the generalized force through a so-called constraint mass matrix. It is proved that the constraint mass matrix isalways invertible and hence the acceleration can be computed in aclosed-form manner even with the presence of redundant constraints or asingular configuration. The equation of motion is given explicitly in arelatively compact form, which can lead to computational efficiency. Italso has a useful physical interpretation, as the component of thegeneralized force contributing to motion dynamics is readily derivedform the formulation. Finally, results obtained from numericalsimulation of motion of a five-bar mechanism is documented.     

平面双连杆受限柔性机器人臂的动力学建模*

对一类平面双连杆受限柔性机器人臂的动力学建模问题进行研究，利用Ｄ’Ａｌｅｍｂｅｒｔ－Ｌａｇｒａｎｇｅ原理得到了一组描述该机器人系统运动性态的动力学方程。与已有的动力学模型相比，本文所建立的运动方程和振动方程具有模型准确、结构简单等特点，且具有与传统无约束刚性机器人类似的模型形式，因而有可能直接或间接利用现有的关于刚性机器人运动控制等方面的成果来研究复杂的受限柔性机器人的控制问题。     

正交各向异性叠层板的非线性主共振分析

研究了在四边简支的边界条件下,正交各向异性矩形叠层板在横向简谐激励作用下的非线性主共振及其稳定性问题．在给出了正交各向异性叠层板的振动微分方程的基础上,利用伽辽金法导出了相应的达芬型非线性强迫振动方程．应用平均法对主共振问题进行求解,得到了系统在稳态运动下的幅频响应方程．基于李雅普诺夫稳定性理论,得到了解的稳定性判定条件．作为算例,分别给出了不同条件下,系统运动的幅频响应曲线图、振幅-激励幅值响应曲线图和动相平面图,并对解的稳定性进行了分析,讨论了各参数对系统非线性振动特性的影响．     

一类参数激励和外激励联合作用下四边简支薄板的周期解

研究了一类参数激励和外激励联合作用下四边简支薄板在1:1内共振下的周期解分叉.首先,根据von Karman方程推导出四边简支薄板的运动控制方程,利用Galerkin方法得到参数激励和外激励联合作用下的两个自由度的运动方程.然后,通过引入周期变换和相应的Poincaré映射推广了次谐Melnikov方法.最后,对系统进行数值模拟验证了理论的正确性.     

Stability and joint stiffness analysis of legged robot’s periodic motion driven by McKibben pneumatic actuator

A McKibben-type pneumatic actuator is widely used as a convenient actuator for a robot with a simple actuator model and a simple control method. However, the effect of its characteristics on the stability of robot motion has not been sufficiently discussed. The purpose of our research is to analyze the influence that the various characteristics of a McKibben pneumatic actuator has on the stability of movements generated by the actuator. In this study, we focus on a periodic motion, which is one of the common movements of robots. We introduce a stability criterion for periodic motion similar to our previous work, in which stability of musculo-skeletal system was discussed, and show that the criterion is always satisfied. Next, we focus on a redundancy of air pressure inputs. As one of application of the redundancy, we investigate the joint stiffness of a robot and propose a design procedure of inputs based on a reference period trajectory and the desired joint stiffness. The stability analysis and design of joint stiffness are verified not only through numerical simulations but also through experiments with a developed 1-DOF legged robot.     

Robust Hybrid Control of Constrained Robot Manipulators via Decomposed Equations

Basing on a constraint Jacobian induced orthogonal decomposition of the task space and by requiring the force controller to be orthogonal to the constraint manifold, the dynamics of the constrained robots under hybrid control is decomposed into a set of two equations. One describes the motion of robots moving on the constraint manifold, while the other relates the constraint force with the hybrid controller. This decomposition does not require the solution of the constraint equation in partition form. In this setting, the hybrid control of constrained robots can be essentially reduced to robust stabilization of uncertain nonlinear systems whose uncertainties do not satisfy the matching condition. A continuous version of the sliding-mode controller (from Khalil [12]) is employed to design a position controller. The force controller is designed as a proportional force error feedback of high gain type. The coordination of the position controller and the force controller is shown to achieve ultimately bounded position and force tracking with tunable accuracy. Moreover, an estimate of the domain of attraction is provided for the motion on the constraint manifold. Simulation for a planar two-link robot constraining on an ellipse is given to show the effectiveness of a hybrid controller. In addition, the friction effect, viewed as external disturbance to the system, is also examined through simulations.     

索受外激励作用下索拱结构非线性动力学分析

研究索拱结构中索受外激励作用下索拱之间非线性动力学问题．利用已建立的索拱结构非线性动力学耦合面内运动微分方程,采用Galerkin方法把索拱结构的面内运动方程进行离散,然后利用多尺度法对离散的运动方程进行摄动得到索主共振情况下的平均方程,研究在索受到外激励作用下索振动对拱的振动产生的影响,同时对索拱结构内共振时的稳定、分叉及混沌情况进行了分析．结果表明：索某阶频率与拱某阶频率接近时可能出现内共振现象,能量在索拱之间相互传递,原本静止的拱也可能出现共振现象,共振频域区间内索拱振动将出现跳跃、分叉及混沌等复杂的非线性动力学行为．     

Shape and motion from simultaneous equations with closed-loop solution

This paper proposes a method for simultaneously estimating 2D image motion and 3D object shape and motion from only two frames. The problem is formulated in a system of equations, including the differential epipolar constraint, a newly derived optical flow equation and surface normal constraint, under the assumption of perspective projection, rigid motion, Lambertian reflectance and distant lighting. A closed-loop solver is constructed based on the simultaneous equations to export accurate estimate for optical flow as well as dense shape and motion. Experimental results are also provided.     

双周期参数系统的受迫振动响应

谐波减速器在制造过程中,如果柔轮齿与刚轮齿引入了周节累积误差,则谐波减速器在动力传递中将出现双周期时变扭刚度波动,形成双周期参数振动问题.本文引入基于组合频率的二重三角级数,逼近双周期参数系统受迫振动,应用谐波平衡,得到不含时间变量的谐波系数递推式,形成三维矩阵代数方程;采用矩阵降维法,将三维矩阵代数方程转化为两维矩阵代数方程,实现响应谐波系数的求解.研究结果对双周期参数振动中响应预测问题研究和工程应用具有一定的理论指导意义.     

弹性支撑浅拱的非线性动力行为分析

本文研究了两端转角均为转动弹簧支撑的铰支浅拱在外激励作用下的非线性动力学行为.基于弹性支撑浅拱的基本动力控制方程,采用多尺度法对内共振进行了摄动分析,并得到了极坐标形式的平均方程.弹性约束的刚度通过特征方程影响结构的自振频率和模态,且与平均方程的相关系数一一对应,文中还以最低两阶模态之间1:1内共振为对象进行了数值分析.结果显示系统存在模态交叉与转向两种内共振形式,另一方面结构参数处于某一范围之内时外激励激发的模态作用可导致出现准周期运动和混沌运动.