攀达穹顶体系的运动过程分析

可变体系的展开过程既包含了机构运动又包含了弹性变形。该文采用了以自然坐标描述的多体系统动力学的有限元方法,根据最小应变能原理与拉格朗日乘子法给出了多体系统运动学基本方程的建立方法,并基于Hamilton原理给出了考虑机构运动与弹性变形的动力学方程。通过对简化的攀达穹顶模型展开过程的数值模拟,验证了理论方法的可行性,表明了结构构形与受力状况在体系展开过程中产生较大的变化。算例结果表明:攀达穹顶体系的展开程度与体系设计相关,“过度”的展开会使结构处于不利的受力状态。     

Z型折叠板内共振下非线性振动特性研究

Z型折叠板是一类复杂多体结构,在工程实际中应用广泛。以大型的空间可展开结构为实际工程背景,考虑了Z型折叠板折叠过程中各部件的运动耦合关系,基于Reddy经典板理论和von-Karman几何非线性应变位移关系,利用Hamilton原理建立了Z型折叠板的非线性动力学控制方程。利用有限元分析得到了Z型折叠板结构的模态函数,运用二阶Galerkin截断,得到了Z型折叠板二自由度的非线性常微分方程。考虑系统主参数共振-1∶2内共振的情况,通过摄动分析得到系统四维直角坐标形式的平均方程,最后利用数值模拟方法研究了横向激励对Z型折叠板非线性动力学特性的影响。     

多刚体动力学在结构地震响应分析中的应用

该文将多刚体系统动力学理论应用于结构的地震响应分析中;将结构进行多刚体离散,建立了结构的多刚体-铰链-弹簧系统模型,并给出了多刚体离散化模型中弯曲弹簧的等效刚度系数的计算公式;运用多刚体动力学推导了求解结构地震响应的动力学方程,该方程与传统动力学方程的形式相似,可用一般的数值方法求解。该文最后对一单榀建立墙以及一10层剪力墙结构进行了地震响应的时程分析,并将计算结果与有限元方法计算结果进行了比较,两种方法的误差较小。算例结果表明,该文所提出的多刚体动力学用于结构地震反应分析的方法是可行且有效的。     

变拓扑空间可展桁架多体系统动力学建模与分析

随着空间折叠式桁架可展长度的增大与结构的复杂化,对空间大型展开机构动力学分析的计算规模逐渐增大。为了减少系统的广义坐标个数,该研究取铰的相对坐标为系统的广义坐标,基于单向递推组集方法建立太空望远镜桁架展开过程的动力学模型。利用Jourdain速度变分原理建立了各柔性部件的动力学变分方程,根据各柔性部件之间的运动学递推关系,并引入切断铰的约束方程,建立了柔性多体系统的刚-柔耦合动力学方程。针对柔性部件展开锁定时容易出现的数值计算问题,提出了在缓冲减速的基础上施加相对角约束的变拓扑方法。基于动力学模型对11节桁架单元的太空望远镜桁架展开过程进行数值仿真。为了进一步缩减计算规模,根据系统结构的对称性和纵向载荷分布的均匀性,将多个桁架和主镜组成的多体系统简化为单个桁架与主镜的一部分组成的系统进行数值仿真。将单个桁架系统展开过程的数值仿真结果与多个桁架系统的仿真结果进行对比,验证了简化动力学模型的准确性和有效性。在此基础上进一步对30节桁架单元的桁架展开过程进行数值仿真,通过对比柔性桁架与刚性桁架在展开和碰撞锁定过程中仿真结果的差异,分析了弹性变形对系统动力学特性的影响。     

计及应力刚化效应的空间大运动曲梁动力学建模与分析

从连续介质力学非线性位移-应变关系出发,导出计入应力刚化效应的空间柔性梁变形能表达式。利用浮动框架有限元方法和哈密顿变分原理推导了满足小变形假设的空间曲梁的一般运动动力学方程,并利用模态缩减法对动力学方程进行了维数降阶。所推导的动力学方程可用于高速旋转一般运动空间柔性曲梁动力学问题的求解。通过数值仿真讨论了应力刚化效应对大范围运动小变形空间柔性曲梁动力学特性的影响,并与ADAMS软件和ABAQUS软件的仿真结果进行了对比,指出了ADAMS软件在高速旋转柔性多体系统数值计算方面的一些缺陷。所提出的计及应力刚化效应的空间曲梁动力学建模方法为高速旋转一般运动柔性多体系统动力学建模和分析提供了参考。     

垂直热发射过程弹架耦合作用研究

研究裸弹垂直热发射过程系统的动态响应及其对导弹运动的影响。对车载导弹发射系统进行了简化和等效建模,进行了导弹起飞过程的理论分析,基于动力学和有限元软件建立了系统刚柔耦合多体动力学模型,对发射过程展开了动力学仿真与分析,并进行了多刚体与刚柔耦合两类模型计算结果对比。数值模拟结果表明,导弹起飞过程与发射车的耦合作用明显,系统振动对导弹起飞姿态产生影响,发射车振动衰减特性良好,柔性发射台模型能够较好反映发射过程系统动态响应以及弹架耦合特性。     

基于多体动力学方法大型风力机台风致响应特性与偏航影响

为研究强台风下考虑偏航效应的大型风力机气动力及动态响应特征,以美国可再生能源实验室5 MW风力发电机组为研究对象,基于多体动力学及混合多体系统建模方法,建立了整机刚-柔混合多体动力学模型,并对该模型进行了动力特性分析与模型有效性验证。同时,基于谱分解法模拟了台风眼壁区域强干扰阶段的三维随机风场,并基于叶素-动量理论对7种偏航工况下风力机体系气动力进行数值模拟,分析了偏航对强台风下整机气动荷载的影响。最后,基于多体动力学模型对考虑不同偏航的大型风力机体系进行了动力时程分析,提炼了偏航对于结构风致响应的影响规律。结果表明,本文建立的多体动力学模型使用较少的自由度能有效描述了5 MW大型风力机的动力特性;当大型风力机处于30°和120°停机偏航角时,结构的台风致风荷载和风振响应显著增大,属于典型的不利工况,应在风电场实际控制时予以避免。主要研究结论可为强台风极端风况下大型风力机抗风设计提供科学依据。     

基于有限元法的齿轮强度接触研究分析

本文首先介绍了针对齿轮接触的有限元原理,其次根据齿轮结构特性及相关理论导出渐开线齿廓方程和齿轮啮合位置方程,在此基础上利用有限元方法进行模型构建,进行数值模拟,最后对数值模拟与仿真计算结果展开分析,结论与齿轮实际情况相吻合,以期对齿轮接触强度有限元分析领域有所贡献。     

基于非均匀分布复弹簧单元的螺栓连接薄板结构动力学有限元建模

在创建螺栓连接结构动力学模型时,如何有效地模拟螺栓影响区对结构动力学特性的贡献至关重要。提出用非均匀分布复弹簧单元来模拟螺栓影响区力学特性,在此基础上针对一种螺栓连接薄板结构建立有限元模型并对其进行线性动力学分析。在确定螺栓影响区面积的基础上,分别假定了三种刚度非均匀分布的复弹簧单元来模拟螺栓结合部的力学特性,并提出用反推辨识技术确定复弹簧单元刚度及阻尼参数的方法。通过自编有限元程序创建了螺栓连接薄板结构线性动力学分析模型,重点描述了将非均匀分布复弹簧单元引入连接薄板动力学方程的方法。最后,以一个具体的螺栓连接薄板结构为对象进行了实例研究,结果表明:用所创建的有限元模型计算获得的固有频率、模态振型以及频响函数值与实测值均较为接近,从而证明了用非均匀分布复弹簧单元模拟螺栓影响区进而实施有限元建模可实现较高的仿真计算精度。     

气浮台-薄板刚-柔耦合系统动力学建模和实验研究

本文对气浮台和大变形薄板多体系统动力学建模理论和实验方法进行研究。基于非线性应变和位移关系,从曲率的精确表达式出发,用绝对节点坐标法建立了大变形矩形薄板的动力学变分方程。考虑结构阻尼,建立了气浮台和大变形薄板多体系统的动力学方程。利用非接触式的运动测量仪测量特征点的速度和气浮台的角速度,利用应变仪测量特征点的应变,通过理论和实验结果的数值对比验证了本文几何非线性动力学模型的正确性。     

A novel nonsmooth dynamics method for multibody systems with friction and impact based on the symplectic discrete format

As multibody systems often involve unilateral constraints, nonsmooth phenomena, such as impacts and friction, are common in engineering. Therefore, a valid nonsmooth dynamics method is highly important for multibody systems. An accuracy representation of multibody systems is an important performance indicator of numerical algorithms, and the energy balance can be used efficiently evaluate the performance of nonsmooth dynamics methods. In this article, differential algebraic equations (DAEs) of a multibody system are constructed using the D'Alembert's principle, and a novel nonsmooth dynamics method based on symplectic discrete format is proposed. The symplectic discrete format can maintain the energy conservation of a conservative system; this property is expected to extend to nonconservative systems with nonsmooth phenomena in this article. To evaluate the properties of the proposed method, several numerical examples are considered, and the results of the proposed method are compared with those of Moreau's midpoint rule. The results demonstrate that the solutions obtained using the proposed method, which is based on the symplectic discrete format, can realize a higher solution accuracy and lower numerical energy dissipation, even under a large time step.     

基于完全笛卡尔坐标的多体系统微分-代数方程符号线性化方法

多体系统动力学方程分为两类形式,即微分方程和微分-代数方程。这两类方程都是针对大位移系统,并且方程呈强非线性。为研究多体系统小位移或振动问题,从多体系统动力学方程出发,讨论微分-代数方程线性化计算机代数问题。利用完全笛卡尔坐标描述多刚体系统,建立多刚体系统动力学微分-代数方程。利用逐步线性化方法和计算机代数,分别对多体系统微分-代数方程的广义质量阵,约束方程和广义力阵在平衡位置附近进行Taylor展开。给出一种基于完全笛卡尔坐标的多体系统动力学微分-代数方程符号线性化方法。最后通过两个算例验证该方法的有效性。     

Interval uncertain method for multibody mechanical systems using Chebyshev inclusion functions

This study proposes a new uncertain analysis method for multibody dynamics of mechanical systems based on Chebyshev inclusion functions The interval model accounts for the uncertainties in multibody mechanical systems comprising uncertain‐but‐bounded parameters, which only requires lower and upper bounds of uncertain parameters, without having to know probability distributions. A Chebyshev inclusion function based on the truncated Chebyshev series, rather than the Taylor inclusion function, is proposed to achieve sharper and tighter bounds for meaningful solutions of interval functions, to effectively handle the overestimation caused by the wrapping effect, intrinsic to interval computations. The Mehler integral is used to evaluate the coefficients of Chebyshev polynomials in the numerical implementation. The multibody dynamics of mechanical systems are governed by index‐3 differential algebraic equations (DAEs), including a combination of differential equations and algebraic equations, responsible for the dynamics of the system subject to certain constraints. The proposed interval method with Chebyshev inclusion functions is applied to solve the DAEs in association with appropriate numerical solvers. This study employs HHT‐I3 as the numerical solver to transform the DAEs into a series of nonlinear algebraic equations at each integration time step, which are solved further by using the Newton–Raphson iterative method at the current time step. Two typical multibody dynamic systems with interval parameters, the slider crank and double pendulum mechanisms, are employed to demonstrate the effectiveness of the proposed methodology. The results show that the proposed methodology can supply sufficient numerical accuracy with a reasonable computational cost and is able to effectively handle the wrapping effect, as cosine functions are incorporated to sharpen the range of non‐monotonic interval functions. Copyright © 2013 John Wiley & Sons, Ltd.     

The benefits of parallel multibody simulation

To exploit the benefits of parallel computer architectures for multibody system simulation, an interdisciplinary approach has been pursued, combining knowledge of the three disciplines of dynamics, numerical mathematics and computer science. An analysis of the options available for the formulation and numerical solution of the dynamical system equations yielded a surprising result. A method initially proposed to solve the inverse problem of dynamics is the best choice to generate the system equations required for solving the simulation problem, when relying on implicit integration routines. Such routines have the particular advantage of handling stiff systems, too. The new O(N)-residual formalism, generating the system equations in a form required for implicit numerical integration, has a high potential to benefit from parallel computer architectures. Two strategies of medium and coarse grain parallelization have been implemented on a Transputer network to obtain a package for parallel multibody simulation. An analysis of the performance of this package demonstrates for typical multibody simulation problems that the new code is five times faster than existing codes when implemented on a serial computer. An additional speed-up by the same order of magnitude is obtained when the code is implemented on a Transputer network.     

Direct differentiation method for sensitivity analysis based on transfer matrix method for multibody systems

On one hand, the new version of transfer matrix method for multibody systems (NV‐MSTMM), has been proposed by formulating transfer equations of elements in acceleration level instead of position level as in the original discrete time transfer matrix method of multibody systems to study multibody system dynamics. This new formulation avoids local linearization and allows using any integration algorithms. On the other hand, sensitivity analysis is an important way to improve the optimization efficiency of multibody system dynamics. In this paper, a totally novel direct differentiation method based on NV‐MSTMM for sensitivity analysis of multibody systems is developed. Based on direct differentiation method, sensitivity analysis matrix for each kind of element is established. By assembling transfer matrices and sensitivity analysis matrices based on differentiation law of multiplication, the sensitivity analysis equation of overall transfer equation is deduced. The computing procedure of the proposed method is also presented. All these improvements as well as three numerical examples show that the direct differentiation method based on NV‐MSTMM is suitable for optimizing the dynamic sensitivity in multi–rigid‐body systems.     

A hybrid direct‐automatic differentiation method for the computation of independent sensitivities in multibody systems

The usefulness of sensitivity analyses in mechanical engineering is very well‐known. Interesting examples of sensitivity analysis applications include the computation of gradients in gradient‐based optimization methods and the determination of the parameter relevance on a specific response or objective. In the field of multibody dynamics, analytical sensitivity methods tend to be very complex, and thus, numerical differentiation is often used instead, which degrades numerical accuracy. In this work, a simple and original method based on state‐space motion differential equations is presented. The number of second‐order motion differential equations equals the number of DOFs, that is, there is one differential equation per independent acceleration. The dynamic equations are then differentiated with respect to the parameters by using automatic differentiation and without manual intervention from the user. By adding the sensitivity equations to the dynamic equations, the forward dynamics and the independent sensitivities can be robustly computed using standard integrators. Efficiency and accuracy are assessed by analyzing three numerical examples (a double pendulum, a four‐bar linkage, and an 18‐DOF coach) and by comparing the results with those of the numerical differentiation approach. The results show that the integration of independent sensitivities using automatic differentiation is stable and accurate to machine precision. Copyright © 2014 John Wiley & Sons, Ltd.     

受控线性多体系统传递矩阵法

受控线性多体系统的稳态运动是多体系统动力学的重要研究内容之一。本文以简单的受控多体系统为例，建立了受控线性多体系统传递矩阵法，能方便快捷地求解受控线性多体系统的稳态运动。建立了控制力作用下集中质量和弹簧阻尼铰的扩展传递矩阵和扩展传递方程。将牛顿法和受控线性多体系统传递矩阵法的计算结果进行了比较。实例表明，受控线性多体系统传递矩阵法不仅能用于受控线性多体系统的动力学分析，而且完整地保持了传递矩阵法的所有优点。     

A general formulation in rigid multibody dynamics

The dynamics of rigid multibodies is traditionally formulated by means of either minimal or redundant co-ordinates methods. An alternative approach is here proposed whereby a highly redundant set of coordinates is adopted. As a result, the equations of motion of the constrained bodies are decoupled. Several meaningful parameters are directly available and the constraint conditions are enforced in a very natural way. The first part of the paper presents the basic meanings and the theoretical developments of the formulation. The second develops a numerical approximation for the methodology proposed in the first part. The non-linear system of differential-algebraic equations governing the motion of the multibody is reduced to its weak form. It is linearized by applying a Newton–Raphson procedure and approximated through the method of finite elements in time. The details of the numerical application of this method are discussed and a solution procedure is presented. Finally, some numerical examples involving tree and closed loop topologies prove the capability of the present formulation in handling multibody dynamics.     

The global modal parameterization for non‐linear model‐order reduction in flexible multibody dynamics

In flexible multibody dynamics, advanced modelling methods lead to high‐order non‐linear differential‐algebraic equations (DAEs). The development of model reduction techniques is motivated by control design problems, for which compact ordinary differential equations (ODEs) in closed‐form are desirable. In a linear framework, reduction techniques classically rely on a projection of the dynamics onto a linear subspace. In flexible multibody dynamics, we propose to project the dynamics onto a submanifold of the configuration space, which allows to eliminate the non‐linear holonomic constraints and to preserve the Lagrangian structure. The construction of this submanifold follows from the definition of a global modal parameterization (GMP): the motion of the assembled mechanism is described in terms of rigid and flexible modes, which are configuration‐dependent. The numerical reduction procedure is presented, and an approximation strategy is also implemented in order to build a closed‐form expression of the reduced model in the configuration space. Numerical and experimental results illustrate the relevance of this approach. Copyright © 2006 John Wiley & Sons, Ltd.