计及二阶效应的刚柔耦合连杆系统动力学分析

根据虚功原理和达郎伯原理推导了计及二阶效应的柔性单元运动方程,并利用刚化条件得到了刚性梁单元运动方程,给出了刚柔耦合连杆系统动力学建模与分析的方法.对构件刚度相差悬殊的多体系统进行动力学分析时,如若当作多刚体系统分析,会因忽略弹性变形导致结果不准确;当作多柔体系统建模分析求解,则因自由度太多导致方程庞大难求解.可行的方法是:将刚性单元与柔性单元耦合建模,在多柔体系统基础上,引入刚性单元和刚性约束条件,对刚性构件自身的动力学特性进行等效,然后按照一般弹性系统有限元方法集成得到虚拟柔性系统动力学方程,建立过渡坐标与广义坐标关系,消除非独立坐标,得到真实的系统运动方程,降低系统方程维数,提高分析效率.以曲柄滑块机构为例,介绍了计及二阶效应的刚柔耦合系统动力学的建模分析过程.     

考虑二阶效应的履带起重机桁架臂系统动力学分析

以有限元理论为基础,对单元横向位移场采用三次Hermite插值函数,利用柔性多体系统动力学的方法,准确描述梁单元的运动状态,并推导了梁单元在局部坐标系下考虑二阶效应的运动方程。利用两节点梁单元对桁架臂系统底节、标准节与顶节分别进行等效,在考虑桁架臂受二阶效应产生的影响下,利用Lagrange方程建立动力学方程。以QUY750型号起重机桁架臂作为研究对象,选择典型变幅工况进行实例分析,利用Simulink对动力学方程进行求解,并通过ADAMS对臂架进行动力学仿真,对比桁架臂系统在变幅过程中起重臂节点位移与速度。计算结果表明,在考虑二阶效应下,对于桁架臂系统位移和变形的动力学方程计算的数值解与ADMAS仿真结果相符。因此,在分析履带起重机桁架臂系统的运动过程中考虑二阶效应产生的弹性变形是十分必要的。     

大位移弹性多体系统的动力非线性分析

对运动弹性多体系统进行分析时,采用对运动刚体系统计算的结果叠加弹性系统静力分析结果的方法,有明显的缺点。本文推导了梁杆单元在大幅度运动情况下局部坐标的变形场和绝对坐标中位移场的表达形式,建立了具有普遍意义的大位移弹性梁杆单元的运动方程,有实用价值。     

作大运动的空间桁架结构动力有限元分析

作大运动的空间桁架,由于运动和变形的耦合将产生动力刚化现象,传统的动力学难以及这种影响,在有限元方法中首次引入单元耦合形函数（阵）将单元弹性位移表示成为单元结点位称的二阶小量形式,利用几何非线性应变－位移关系式,在小变形假设条件下确定单元耦合形函数。根据Ｋａｎｅ方程,运用模态坐标压缩,并通过适当的线性处理,得到了一致线性化的动力学方程,编制空间桁架结构动力刚度有限元分析程序。仿真算例证明理论和算法     

3-RRR平面柔性并联机构动力学分析

针对柔性并联机构动力学模型时变、刚-柔耦合、非线性的特点,以3-RRR平面柔性并联机构为研究对象,建立了一种基于有限元法、浮点坐标系和KED法的机构弹性动力学方程。首先,运用有限元法的理论,将机构的柔性杆件划分为一系列离散的梁单元模型,建立梁单元的动力学方程。然后,运用KED法,得到机构的约束关系式和装配关系式,从而得到机构在浮点坐标系下的弹性动力学方程。最后,分别对采用简化KED法和这里方法建立的机构动力学模型进行仿真分析,对比机构动平台的弹性位移/转角曲线和最大应力曲线,验证了这里建模方法的有效性。     

刚体—微梁系统的动力学特性

由于微尺度领域材料的力学性能存在尺度效应,使得微梁的动力学性态较传统的大尺寸柔性梁的动力学性态呈现明显的不同。对中心转动刚体、柔性微梁组成的刚体—微梁一类刚柔耦合系统的动力学特性进行研究。在柔性微梁变形位移中,计及横向位移引起轴向缩短的耦合变形量,采用偶应力理论(又称Cosserat理论)研究微梁动力学特性的尺度效应,由Hamilton原理推导出系统考虑尺度效应的刚柔耦合动力学方程。在此基础上,分析微梁固有频率对微尺度的依赖性,比较在不同转速下零次近似模型和一次近似模型振动频率的差异,从而确定在考虑尺度效应的微尺度下零次近似模型的适用范围,最后分析尺度效应和耦合变形量对微梁刚度的影响。研究表明,尺度效应提高微梁的固有频率,尺度效应对微梁刚度的影响是静态的,耦合变形量对微梁的刚度的影响与转速有关。     

弹性约束悬臂压弯梁的稳定性及最大二阶弯矩

利用变形微分方程，对弹性约束悬臂压弯梁的稳定性进行分析，给出了其临界载荷的精确计算式和实用近似计算式，推导了弹性约束悬臂压弯梁约束端二阶弯矩的精确计算式，并讨论了《塔式起重机设计规范》中的非弹性约束压弯梁的最大二阶弯矩近似计算式在考虑了约束端弹性时的适用性。     

机械系统动力刚化机理分析

采用计及变形约束的非线性运动学分析方法及传统分析方法建立简单柔性机械臂线性化的动力学方程。笔者认为：运动的柔性机械构件春变形运动的耦合产生动力刚化，传统分析方法失去了刚体运动与弹性振耦合的动力刚化项；如果在建立运动学方程时，计及运动学的非线性项，至少要计及振动坐标的二阶小量，将非线性保留到适当阶段，再线性化，熊猫是到一致化性化的动力学方程，这种方法适合于机械系统件的小变形问题，对动力刚化的研究实际     

改进的绝对节点坐标平面梁有限元传递矩阵法

针对大运动柔性梁的动力学问题,采用绝对节点坐标有限元法建立了非线性单元动力学方程。在单元动力学方程中节点广义加速度和节点广义内力之间呈线性关系,基于此并结合结构力学传递矩阵法,提出了全新的绝对节点加速度平面梁有限元传递矩阵法。与传统有限元传递矩阵法相比,方法的传递矩阵和时程积分方法无关,便于不同常微分方程数值方法的引入。最后通过大运动小变形梁算例验证了此法。     

非线性变形对大范围平面运动梁动力学特性的影响

根据柔性梁的几何非线性变形理论,从连续介质的力学原理出发,针对大范围运动的平面柔性梁,考虑了弯曲的非线性因素对横向变形的影响,得到了较为精确的变形模式。利用Lagrange方程建立了非线性变形模式下的动力学方程。仿真算例说明横向变形的非线性因素会对柔性梁的变形位移产生影响。     

计及变形耦合的双连杆柔性机械臂动力学模型

根据连续介质的几何非线性变形原理,结合柔性多体系统建模理论的最新进展,在柔性梁的纵向、横向变形位移中均考虑了横向弯曲变形以及轴向伸缩变形的耦合作用,对一双连杆柔性机械臂系统,将其简化为柔性梁结构,利用有限元法和Lagrange方程,得出不同于传统零次近似方程,也不同于一次耦合动力学方程的新方程, 并可将此方程拓展到多杆机械臂系统。模型包含了二次耦合附加项,并且由于增加了变形耦合量,对柔性梁产生了“软化”作用,使得柔性机械臂模型不同于传统动力学模型。最后,计算仿真说明了这种差异,揭示了新模型的特点和有效性。     

考虑热效应的柔性多体系统的动力学分析

机械系统因热膨胀和热弯曲引起的热误差是工程研究的一个重要问题。为了研究热效应对柔性多体系统动力学特性的影响,本文首先从虚功原理出发,用假设模态法对平面梁进行离散,在温度变化和y方向的温度梯度已知的情况下,建立了单个柔性梁的动力学变分方程,然后根据各柔性体之间的运动学约束关系,引入拉格朗日乘子,建立了柔性多体系统的第一类拉格朗日动力学方程,并推导了约束力的计算公式。曲柄滑块机构的数值仿真表明:温度变化对系统动力学特性的影响不仅与温度变化率和系统惯量有关,还取决于几何位置。当运动机构趋近于奇异位置时,热效应最为显著。进一步研究表明,温度梯度引起横向变形和横向约束力平均值的变化。     

Dynamic finite element method for generally laminated composite beams

A dynamic finite element method for free vibration analysis of generally laminated composite beams is introduced on the basis of first-order shear deformation theory. The influences of Poisson effect, couplings among extensional, bending and torsional deformations, shear deformation and rotary inertia are incorporated in the formulation. The dynamic stiffness matrix is formulated based on the exact solutions of the differential equations of motion governing the free vibration of generally laminated composite beam. The effects of Poisson effect, material anisotropy, slender ratio, shear deformation and boundary condition on the natural frequencies of the composite beams are studied in detail by particular carefully selected examples. The numerical results of natural frequencies and mode shapes are presented and, whenever possible, compared to those previously published solutions in order to demonstrate the correctness and accuracy of the present method.     

Investigation on steady state deformation and free vibration of a rotating inclined Euler beam

The steady state deformation and infinitesimal free vibration around the steady state deformation of a rotating inclined Euler beam at constant angular velocity are investigated by the corotational finite element method combined with floating frame method. The element nodal forces are derived using the consistent second order linearization of the nonlinear beam theory, the d'Alembert principle and the virtual work principle in a current inertia element coordinates, which is coincident with a rotating element coordinate system constructed at the current configuration of the beam element. The rotating element coordinates rotate about the hub axis at the angular speed of the hub. The equations of motion of the system are defined in terms of an inertia global coordinate system, which is coincident with a rotating global coordinate system rigidly tied to the rotating hub. Numerical examples are studied to demonstrate the accuracy and efficiency of the proposed method and to investigate the steady state deformation and natural frequency of the rotating inclined beam.     

平面柔性并联机器人动力学建模

利用有限元理论研究柔性并联机器人动力学建模的理论和方法,分析各支链的弹性位移及其耦合关系,建立柔性并联机器人系统的运动约束条件和动力约束条件。综合考虑构件的分布质量、集中质量以及杆件的剪切变形、弯曲变形、拉压变形和横向位移的影响,运用运动弹性动力学理论和Lagrange方程,推导出平面柔性并联机器人的动力学方程。以平面3-RRR柔性并联机器人为例,说明该动力学模型能正确反映柔性并联机器人的弹性振动特性,杆件的弹性变形对机器人动平台的位置误差和方向误差具有重要影响。     

Dynamic stability of a rotating shaft embedded in an isotropic winkler-type foundation

The dynamic instability of a rotating shaft subjected to axial periodic forces and embedded in an isotropic, Winkler-type elastic foundation is studied by the finite element technique. The equations of motion for such a rotating shaft element are formulated using deformation shape functions developed from the Timoshenko beam theory. The effects of translational and rotatory inertia, gyroscopic moments, bending and shear deformation are included in the mathematical model. The numerical results show that the elastic foundation can shift the regions of dynamic instability away from the dynamic load factor axis and thus reduces the sizes of these regions, whereas the effect of gryoscopic moments is to shift the boundaries of the regions of dynamic instability outwardly and, therefore, increases the sizes of these regions.     

Dynamic modeling of flexible-links planar parallel robots

This paper presents a finite element-based method for dynamic modeling of parallel robots with flexible links and rigid moving platform. The elastic displacements of flexible links are investigated while considering the coupling effects between links due to the structural flexibility. The kinematic constraint conditions and dynamic constraint conditions for elastic displacements are presented. Considering the effects of distributed mass, lumped mass, shearing deformation, bending deformation, tensile deformation and lateral displacements, the Kineto-Elasto dynamics (KED) theory and Lagrange formula are used to derive the dynamic equations of planar flexible-links parallel robots. The dynamic behavior of the flexible-links planar parallel robot is well illustrated through numerical simulation of a planar 3-RRR parallel robot. Compared with the results of finite element software SAMCEF, the numerical simulation results show good coherence of the proposed method. The flexibility of links is demonstrated to have a significant impact on the position error and orientation error of the flexible-links planar parallel robot.     

The dynamic analysis of nonuniformly pretwisted Timoshenko beams with elastic boundary conditions

The coupled governing differential equations and the general elastic boundary conditions for the coupled bending–bending forced vibration of a nonuniform pretwisted Timoshenko beam are derived by Hamilton's principle. The closed-form static solution for the general system is obtained. The relation between the static solution and the field transfer matrix is derived. Further, a simple and accurate modified transfer matrix method for studying the dynamic behavior of a Timoshenko beam with arbitrary pretwist is presented. The relation between the steady solution and the frequency equation is revealed. The systems of Rayleigh and Bernoulli–Euler beams can be easily examined by taking the corresponding limiting procedures. The results are compared with those in the literature. Finally, the effects of the shear deformation, the rotary inertia, the ratio of bending rigidities, and the pretwist angle on the natural frequencies are investigated.     

旋转悬臂梁动力学的B样条插值方法

采用B样条插值方法对旋转悬臂梁的动力学特性进行研究。考虑柔性梁的纵向拉伸变形和横向弯曲变形,计入由于横向弯曲变形引起的纵向缩短,即非线性耦合项。利用B样条插值方法对柔性梁的变形场进行离散。采用Lagrange方程建立系统的动力学方程,并编制旋转悬臂梁动力学仿真软件。进行动力学仿真,将B样条插值方法的仿真结果与假设模态法、有限元法进行比较分析,验证了提出的方法的正确性,并表明B样条插值方法作为变形体离散法在柔性多体系统动力学中具有优良性能和应用价值。     

Dynamic analysis of an axially moving beam subject to inner pressure using finite element method

A dynamic model of an axially moving flexible beam subject to an inner pressure is present. The coupling principle between a flexible beam and inner pressure is analyzed first, and the potential energy of the inner pressure due to the beam bending is derived using the principle of virtual work. A 1D hollow beam element contain inner pressure is established. The finite element method and Lagrange’s equation are used to derive the motion equations of the axially moving system. The dynamic responses are analyzed by Newmark-β time integration method. Based on the computed dynamic responses, the effects of inner pressure on beam dynamics are discussed. Some interesting phenomenon is observed.