空间展开折叠桁架结构动力学分析研究

本文以笛卡尔坐标系下节点自然坐标为未知量,建立了桁架结构系的基本运动力学方程,并首次推导出桁架结构中常用节点附加几何约束方程,相应约束Jacobi矩阵及其导数矩阵,采用奇异值分解法求约束Jacobi矩阵的零空间基和M-P广义逆,并由矩阵缩减法建立了带约束桁架体系的运动力学方程和求解方法。数值算例表明该方法适于可展折叠桁架结构运动力学分析。     

新的一个求解带孔薄板弹性问题的二维杂交应力单元

建立了一个新的求解带圆孔薄板弹性问题的二维杂交应力单元,该单元为四节点四边形平面单元,名为P-HS4-8β。由极坐标系下的物理方程和几何方程求解出了一个极坐标方向的应力,通过将这个应力带入由Hellinger-Reissner原理推导的极坐标系下平面应力问题的能量方程中,得到了消除了该应力的能量方程,基于这个能量方程建立了杂交应力单元列式。根据圆孔边无外力条件和相容方程,推导了适用于求解带圆孔薄板问题的极坐标系下的二应力插值矩阵,并将此矩阵应用于新的有限单元列式中。数值算例表明新单元在求解孔边附近的应力时具有较高的精度。     

超空泡运动体圆柱薄壳的非线性动力屈曲分析

超空泡运动体的动力屈曲失稳具有隐蔽性、突发性和危险性, 因而必须研究清楚运动体的失稳区域边界及失稳振幅. 将超空泡运动体模拟成受轴向周期载荷作用的细长圆柱薄壳, 给出非线性几何方程、物理方程和平衡方程, 建立细长圆柱薄壳带有非线性项的动力屈曲微分方程组; 依据非线性项的形式, 给出合理的非线性位移表达式, 得到具有周期性系数的非线性横向振动微分方程; 采用伽辽金变分法和和鲍洛金方法, 获得带有周期性系数和非线性项的马奇耶方程; 求解非线性马奇耶方程, 得到第一、第二阶不稳定区域内的定态振动振幅的解析表达式; 绘制超空泡运动体的非线性参数共振曲线, 分析航行速度、载荷比例系数、轴向载荷频率和振型对参数共振曲线的影响. 以上研究为建立基于参数共振的圆柱薄壳动力失稳的可靠性分析及基于参数共振可靠性的结构动力优化设计的奠定了理论基础.      

Timoshenko-Euler楔形梁有限元

本文首先建立楔形梁包含轴力和剪切变形效应的平衡微分方程，由于该方法是二阶变系数微分方程，其争析解很难得到，本文通过将该方程中的变系数和方程的解用Chebyshev多项式逼近得到了Timoshenko-Euler楔形梁的单元刚度方程，最后通过算例检验了所得单元刚度方程的对称性，以及验证了计算悬臂梁挠度和悬臂柱弹性临界力的正确性及其收敛性，本文提出的方法可适用于任意变截面Timoshenko-Euler梁单元刚度方程的求解，运用此方法，除可以考虑轴力和剪切变形的影响外，还可以减少结构分析中的单元数和自由度，提高包含楔形构件的结构分析的精度和速度。     

含铰接杆系结构几何非线性分析子结构方法

将细长杆系结构按长度方向划分为多个子结构,由于在子结构坐标系下的节点位移均是小位移,可以将子结构内部自由度凝聚到边界. 考虑到子结构端面在变形过程中保持为刚性截面,将端面节点自由度进一步凝聚到端面形心点,这样每一个子结构就减缩成形式上只有两个节点的广义梁单元,大大减缩了自由度. 大位移大转动是细长杆系结构产生几何非线性效应的一个重要原因,基于共旋坐标法,建立了随单元一起运动的随动坐标系,推导了子结构单元的节点力平衡方程及其切线刚度阵. 同时,考虑到工程机械中细长杆系结构含有相互铰接的刚体加强块,给出了非独立自由度节点力转换到独立参数下的广义节点力及其导数. 最后,通过履带式起重机的副臂工况算例,给出了其在不同载荷下的臂架结构位移,验证了方法的正确性.      

直升机不平衡旋翼动力学建模与轴心运动轨迹分析方法研究

研究了Johnson提出的倾转旋翼不平衡载荷前飞动力学模型,将其桨叶分析方法应用于直升机旋翼系统模态分析。在刚性条件假设下推导了直升机旋翼弹性阻尼和惯性力综合作用时桨叶的挥舞和摆振运动方程,给出了固定和旋转坐标系下对应的运动方程。通过引入均匀入流和线性扭转假设,获得了运动方程的理论解析解。利用叠加原理,得到了桨毂轴心运动方程;采用Newmark法进行振动微分方程求解,最终得到了直升机旋翼的轴心运动轨迹。以某型直升机旋翼系统为例,验证了本研究所提出旋翼桨叶模态分析方法的准确性,给出了兼顾计算精度和效率的最佳求解步长选取方法;预测了典型飞行状态下的桨毂轴心运动轨迹,为直升机旋翼系统设计提供了基础方法和技术参考。     

冰载荷下不锈钢复合板挠度特性分析

以复合板中面的挠度响应作为不锈钢复合板抗冲击性能的评价指标,基于能量法和经典层合板理论,考虑层间结构参数设计,通过横向载荷下的弯曲平衡微分方程,建立冰载荷下不锈钢复合板挠度响应简化解析模型。该分析模型将整个动态响应分析过程分为冰载荷计算分析和动力学方程求解两个阶段。分析了冰载荷模型的面倾角、冲击速度和碰撞位置对冰载荷的影响,确定极端工况参数,汇总接触面的节点力数据;分析了层厚比对挠度响应的影响规律;基于LS-DYNA有限元仿真以及数值算例分析,对比挠度响应仿真结果和解析计算值,验证了本文简化解析模型的准确性,研究结果对不锈钢复合板抗冲击性能分析和评估具有一定的参考价值。     

复合载荷作用下圆板大挠度弯曲问题的伽辽金法

1.引言 关于复合载荷作用下圆板的大挠度弯曲问题,文献[1,2]曾分别选取不同的参数用摄动方法给予求解。本文用一个简便的方法来分析此问题。即先假设一个挠度试函数,使相容方程完全满足,求出薄膜力;然后再用伽辽金加权残数法求解平衡微分方程。 已知均布荷载及中心集中力联合作用下圆板的大挠度方程为     

约束多体系统独立广义坐标的数值选取

多体系统的完整约束定义了一个嵌入到欧氏空间的微分流型,多体系统独立的广义坐标选取问题等价于该流型的坐标选取问题。据此,本文提出了一种新的独立广义坐标数值选取理论,可将多体系统的微分-代数混合型运动方程转化为较易求解的纯微分方程,并且不以求解非线性方程组作为必须的手段。     

航行体水下发射流固耦合效应分析

对于水下发射过程来说,掌握水动力载荷形成机理与结构响应特征是一个亟待解决的问题.研究该问题需要考虑含相变的复杂多相流动,变约束的结构运动以及这二者之间的耦合效应.本文采用松耦合的方法,以流体求解器为主体,将自编的固体结构程序接入流体求解器中,在每个时间步长内分别对流体动力学方程和固体结构动力学方程进行求解,通过流固界面之间的数据交换实现耦合计算.其中,流体求解器基于雷诺平均纳维斯托克斯方程,采用单流体模型处理多相流问题,引入空化模型描述空化相变,采用修正的湍流模型模拟混合物的湍流效应,并采用动网格技术处理移动边界问题.航行体的刚体运动和结构振动分开求解.结构求解器采用等效梁模型描述结构的振动,通过坐标变换给出了随体坐标系下的结构振动方程,求解方法采用时域积分法.所建立的流固耦合方法不仅能够捕捉到自然空化的演化情况,还可获得航行体所受水动力、结构振动响应以及截面的弯矩,获得了实验的验证.基于该方法研究了结构刚度、发射速度对空泡溃灭与结构振动耦合效应的影响规律.结果表明,同步溃灭是影响结构载荷的主要因素,包括溃灭压力幅值,溃灭压力作用位置,以及溃灭压力与结构振动的相位关系.     

On the stability of an equilibrium position and rotational motion of a gyrostat

This article is devoted to study the compulsory stability of equilibrium position and rotational motion of a rigid body containing fluid with the help of three rotors carried on the body. The control moments on the rotors using that condition which impose the stabilization of equilibrium position of the rigid body and rotational motion are obtained.     

Numerical algorithm for rigid body position estimation using the quaternion approach

This paper deals with rigid body attitude estimation on the basis of the data obtained from an inertial measurement unit mounted on the body. The aim of this work is to present the numerical algorithm, which can be easily applied to the wide class of problems concerning rigid body positioning, arising in aerospace and marine engineering, or in increasingly popular robotic systems and unmanned aerial vehicles. Following the considerations of kinematics of rigid bodies, the relations between accelerations of different points of the body are given. A rotation matrix is formed using the quaternion approach to avoid singularities. We present numerical procedures for determination of the absolute accelerations of the center of mass and of an arbitrary point of the body expressed in the inertial reference frame, as well as its attitude. An application of the algorithm to the example of a heavy symmetrical gyroscope is presented, where input data for the numerical procedure are obtained from the solution of differential equations of motion, instead of using sensor measurements.     

Finite amplitude, free vibrations of an axisymmetric load supported by a highly elastic tubular shear spring

The finite amplitude, free vibrational characteristics of a simple mechanical system consisting of an axisymmetric rigid body supported by a highly elastic tubular shear spring subjected to axial, rotational, and coupled shearing motions are studied. Two classes of elastic tube materials are considered: a compressible material whose shear response is constant, and an incompressible material whose shear response is a quadratic function of the total amount of shear. The class of materials with constant shear response includes the incompressible Mooney-Rivlin material and certain compressible Blatz-Ko, Hadamard, and other general kinds of models. For each material class, the quasi-static elasticity problem is solved to determine the telescopic and gyratory shearing deformation functions needed to evaluate the elastic tube restoring force and torque exerted on the body. For all materials with constant shear response, the differential equations of motion are uncoupled equations typical of simple harmonic oscillators. Hence, exact solutions for the forced vibration of the system can be readily obtained; and for this class, engineering design formulae for the load-deflection relations are discussed and compared with experimental results of others'. For the quadratic material, however, the general motion of the body is characterized by a formidable, coupled system of nonlinear equations. The free, coupled shearing motion for which either the axial or the azimuthal shear deformation may be small is governed by a pair of equations of the Duffing and Hill types. On the other hand, the finite amplitude, pure axial and pure rotational motions of the load are described by the classical, nonlinear Duffing equation alone. A variety of problems are solved exactly for these separate free vibrational modes, and a number of physical results are presented throughout.     

Control of the rotational motion of the rigid body with the help of internal rotors using Rodrigues-Caley parameters

The purpose of this paper is to study the control of the rotational motion of the rigid body with the help of three rotors attached to the principal axes of the body. In such study the asymptotic stability of this motion is proved by using the Lyapunov technique. As a particular case of our problem, the equilibrium position of the rigid body, which occurs when the principal axes of inertia of the body coincide with the inertial axes, is proved to be asymptotically stable. The control moments that impose the stabilization of the rotational motion and equilibrium position are obtained.     

Variational Characterization of a Quasi-rigid Body

The rigidity of a body usually is characterized by the kinematical assumption that the mutual distance between any two of its particles remains unaltered in any possible deformation. However, from this alone nothing can be said about the internal contact forces exerted between adjacent sub-bodies. Therefore, the determination and form of an internal state of stress for a rigid body is problematical. Here, we will show that by considering such a kinematical characterization as an internal constraint for an elastic body, the constrained body inherits the mechanical structure of the elastic parent theory, i.e., the internal constraint generates an associated set of Lagrange multiplier fields which can be interpreted as an internal constraint reaction pseudo-stress field with the same structure as the state of stress in the parent elastic body. Thus, although the final deformation is the same for both the rigid body and the rigidly constrained elastic body, the latter corresponds to a richer model and, to emphasize this distinction, we refer to it as a quasi-rigid body. While in equilibrium the pseudo-stress field of a quasi-rigid body will satisfy equations identical to the equilibrium equations for the stress field in the elastic parent theory, such equations are not, in general, sufficient to assure uniqueness. In order to overcome this indeterminacy, we consider the quasi-rigid body as the limit of a sequence of deformable bodies, where each member of the sequence is identified by a material parameter such that, as this parameter tends to infinity, the body to which it refers is rigidified. Our approach is variational, i.e., we consider a sequence of minimization problems for hyperelastic bodies whose elastic strain energy is multiplied by a penalty term, say 1/ε . As ε→?0, body distortions are more and more penalized so that the sequence of the displacement fields tends to a rigid displacement field, whereas the sequence of the associated stress fields tends to a definite non-zero limit. It will be shown that among all pseudo-stress fields that satisfy the equilibrium equations for the quasi-rigid body, the unique limit of the sequence as ε→0 minimizes a functional analogous to the complementary energy functional in classical linearized elasticity. This result permits its unique determination without having to consider the whole sequence of penalty problems.     

New solutions of classical problems in rigid body dynamics

The equations of motion of a rigid body acted upon by general conservative potential and gyroscopic forces were reduced by Yehia to a single second-order differential equation. The reduced equation was used successfully in the study of stability of certain simple motions of the body. In the present work we use the reduced equation to construct a new particular solution of the dynamics of a rigid body about a fixed point in the approximate field of a far Newtonian centre of attraction. Using a transformation to a rotating frame we also construct a new solution of the problem of motion of a multiconnected rigid body in an ideal incompressible fluid. It turns out that the solutions obtained generalize a known solution of the simplest problem of motion of a heavy rigid body about a fixed point due to Dokshevich.     

Biquaternion solution of the kinematic control problem for the motion of a rigid body and its application to the solution of inverse problems of robot-manipulator kinematics

The problem of reducing the body-attached coordinate system to the reference (programmed) coordinate system moving relative to the fixed coordinate system with a given instantaneous velocity screw along a given trajectory is considered in the kinematic statement. The biquaternion kinematic equations of motion of a rigid body in normalized and unnormalized finite displacement biquaternions are used as the mathematical model of motion, and the dual orthogonal projections of the instantaneous velocity screw of the body motion onto the body coordinate axes are used as the control. Various types of correction (stabilization), which are biquaternion analogs of position and integral corrections, are proposed. It is shown that the linear (obtained without linearization) and stationary biquaternion error equations that are invariant under any chosen programmed motion of the reference coordinate system can be obtained for the proposed types of correction and the use of unnormalized finite displacement biquaternions and four-dimensional dual controls allows one to construct globally regular control laws. The general solution of the error equation is constructed, and conditions for asymptotic stability of the programmed motion are obtained. The constructed theory of kinematic control of motion is used to solve inverse problems of robot-manipulator kinematics. The control problem under study is a generalization of the kinematic problem [1, 2] of reducing the body-attached coordinate system to the reference coordinate system rotating at a given (programmed) absolute angular velocity, and the presentedmethod for solving inverse problems of robotmanipulator kinematics is a development of the method proposed in [3–5].     

万有引力场中带挠性板非轴对称航天器的姿态稳定性

本文讨论由非轴对称主刚体和矩形挠性板组成的航天器在万有引力场中的姿态运动。利用Ｇａｌｅｒｋｉｎ方法对动力学方程离散化，并利用Ｋｅｌｖｉｎ－Ｔａｉｔ－Ｃｈｅｔａｙｅｖ定理判断航天器在轨道坐标系内相对平衡的稳定性。导出适用于任意阶模态的解析形式稳定性充分条件。