扁担挑物的动力学分析

建立了扁担挑物的动力学模型和动力学方程,并进行了数值求解。扁担挑物时存在三种频率,即重物类似于单摆的振动频率、挑运者的步行频率和扁担-重物系统铅垂方向的振动频率。计算结果表明,为了获得较好的挑担体验,三种频率应该相互协调。当人挑担行走的频率为扁担-重物系统铅垂方向振动频率的70%～80%时,肩部铅垂附加动反力为重物重力的30%左右且与肩部铅垂运动同相,当重物类似于单摆的振动频率为人步行频率的25%～30%时,重物的摆角和肩部受到的水平附加动反力均较小,从而有利于人挑担行走。     

DYNAMIC ANALYSIS OF A LOADED SHOULDER-POLE DURING WALKING

建立了扁担挑物的动力学模型和动力学方程,并进行了数值求解。扁担挑物时存在三种频率,即重物类似于单摆的振动频率、挑运者的步行频率和扁担-重物系统铅垂方向的振动频率。计算结果表明,为了获得较好的挑担体验,三种频率应该相互协调。当人挑担行走的频率为扁担-重物系统铅垂方向振动频率的70%,$\sim$,80%时,肩部铅垂附加动反力为重物重力的30%左右且与肩部铅垂运动同相,当重物类似于单摆的振动频率为人步行频率的25%,$\sim$,30%时,重物的摆角和肩部受到的水平附加动反力均较小,从而有利于人挑担行走。     

柔性牵引杂谈

动力源柔性牵引工作部件方式广为使用.悬挂的撞木摆动可减轻地面不平对冲车的影响,周期性地施加载荷可使摆幅增大, 得到较高撞击速度.大锤软柄的弹性变形延缓锤头加速、降低瞬间出力,而变形恢复又可使锤头进一步加速,且能减缓作用于手的反震力.扁担振动可使挑担者在肩部承载较小时迈步向前. 操作节奏是实现柔性牵引优良性能的关键.     

考虑剪应变的弹性薄壁杆件的振动理论

对于开口截面彈性薄壁杆件的振动問題,符拉索夫在1940年提出的理論,是基于下列两个基本假設:(1)截面具有剛硬不可变形的周綫;(2)中曲面无剪应变。其后,有些学者也曾提出过相同的理論(例如.R.海里格).由于忽略了中曲面的剪应变,我們可以估計得到,符拉索夫的理論只适用于研究低频率的固有振动和強迫振动,而不适用于研究高频瘁的振动。由于行动載荷和冲击载荷必然引起各个固有频率的振动,因此符拉索夫的理論也不适用于研究这些載荷作用下的振动問題。为了要更好地研究这些問題,必須要考慮剪应变的影响。     

风洞实验中翼型大迎角气动力分散性的机理分析

基于$k$-$\omega$的SST两方程湍流模型, 求解雷诺平均N-S方程获得定常和非定常气动力, 耦合 翼型弹性振动方程, 在时间域内模拟了不同的翼型非定常流动, 重点研究了大迎角下的分离 流问题, 研究结果表明: 在百万雷诺数条件下, 由于振动引起分离涡的不规律脱落, 可能导 致气动力平均值的变化; 而厚度大于20\%的翼型在一定大迎角范围内, 会出现分离涡流场平 衡态的转化, 从流体力学稳定性的角度, 解释了风洞实验中大迎角气动力数据的分散性, 为 大迎角气动力风洞实验的重复性和数据分散性给出了一种新解释.     

扁担是否真的省力?

围绕传统工具扁担是否省力的问题进行了分析.从刚体的静力学受力可知,扁担可以改变负重的传递路径,使承载时人体参与受力的肌肉和骨骼更少,且腰部所受弯矩很小;挑担行走的过程可以简化为一个弹性系统的受迫振动问题,人体的受力是更舒适的周期性动载荷;扁担的结构和材料本身,也有经验性的优化设计,尽量减少了肩膀处的局部压力.     

复合材料圆柱壳失稳载荷的振动监测

本文根据结构振动与稳定性的相关性，以振动频率测试值作为监控参数进行了复合材料圆柱壳的失稳状态监测。该方法首先利用模态试验，测量得到了复合材料圆柱壳在轴压和外压栽荷作用下的模态特性变化特性，进而利用一阶固有频率在低载荷下的这种变化特性，采用多项式拟合法，无损预估了复合材料圆柱壳的轴压和外压屈曲栽荷，估计值与试验测试结果比较一致。     

某型机跨音速等幅振动研究

针对某型机定型试飞中遇到的跨音速等幅振动现象,对该机的颤振分析和试飞实测振动数据进行了研究.结果表明,该型飞机跨音速等幅振荡现象主要是由于外挂物连接间隙引起的,文中对采取的排故措施进行了描述,验证试飞结果表明该振动现象已被排除.从而保证了定型试飞的顺利进行.     

低频微幅偏航与侧滑振动机翼的低速升力面理论

本文利用与机翼固连的坐标系,提出偏航振动机翼低速绕流的数学问题,对翼后蛇形尾涡作了仔细研究.在低频振动的情况下,利用非定常涡格法进行数值求解.本方法可以用来计算机翼因偏航与侧滑振动而引起的滚转力矩气动导数.某些导数的计算结果与实验结果作了比较.     

具非对称截面单体的双体船的对称波激响应

本文研究了具非对称截面单体的双体船的对称波激响应,包括船体的刚体运动,即升沉和纵摇(沿纵向铅垂面的垂向平移及绕重心的转动),以及振动。一方面由于船体截面的主惯性轴与船体的升沉运动不重合,即振动平面与刚体运动平面不重合。另一方面由于两个单体是通过两个定点相互约束的(即每个单体不但受分布的外荷而且受到集中的外荷),从而使得按照Bishop的水弹性理论研究此波激响应问题变得不可行了。本文推导出此类问题的运动微分方程,提出了解决此类问题水动力的计算方法,把Bishop的理论向前推进了一大步。并对一条对开式泥船进行了计算。     

THE FRICTIONLESS SLIDING OF AN OBJECT ALONG A ROPE

提出了物体在无摩擦情况下沿一段柔性绳索下滑运动力学问题的分析方法,利用牛顿第二定律建立耦合运动方程组,采用龙格-库塔（Runge-Kutta）方法编写程序对已建方程组进行求解,用Matlab 中的曲线拟合命令对方程组的数值解进行公式拟合,用得到的物体运动公式结合耦合运动方程组可求出物体下滑各时段绳索的内力. 提出的分析方法对物体在不同初始状态下的计算结果表明：绳索内力随物体的简谐振动呈周期性变化;物体下滑高度越高,经过相同位置时速度、加速度和绳索内力就越大.     

Propagation of longitudinal deformation wave along a lifting rope of variable length

The problem of motion of the rope of variable length consists of solving the boundary value problem with a variable boundary for the one-dimensional wave equation. A change of the rope length is caused by the force acting at the upper cross section of the rope. Studying the wave propagation process along the rope is based on the known integro-differential relation. The problem is reduced to solving two ordinary differential equations with a retarded argument that describe the variable length of the rope and the position of its lower end. The value of argument for functions involved in the right-hand side of the equations lag behind the argument value in the left-hand side of the equations by a time interval it takes for a propagation of the deformation wave throughout the current rope length. The problem is solved by using a technique of the sequential continuation of solution in the cyclic mode for each of the equation alternately. A computer realization of this technique presents no problem. A pilot computer program has been developed for solving the problem. Results of the numerical solution are presented in the case that the active force varies with time according to a piecewise linear relation.     

The Hanging Rope of Minimum Elongation for a Nonlinear Stress-Strain Relation

We consider the problem of determining the shape that minimizes the elongation of a rope that hangs vertically under its own weight and an applied force, subject to either a constraint of fixed total mass or fixed total volume. The constitutive function for the rope is given by a nonlinear stress-strain relation and the mass-density function of the rope can be variable. For the case of fixed total mass we show that the problem can be explicitly solved in terms of the mass density function, applied force, and constitutive function. In the special case where the mass-density function is constant, we show that the optimal cross-sectional area of the rope is as that for a linear stress-strain relation (Hooke's Law). For the total fixed volume problem, we use the implicit function theorem to show the existence of a branch of solutions depending on the parameter representing the acceleration of gravity. This local branch of solutions is extended globally using degree theoretic techniques.     

Dynamic stability of pre-twisted beams with non-constant spin rates under axial random forces

This paper investigates the dynamic stability of a pre-twisted cantilever beam spinning along its longitudinal axis with a periodically varying speed and acted upon by an axial random force at the free end. The spin rate of the beam is characterized as a small periodic perturbation superimposed on a constant speed, and the axial force is assumed as the sum of a static force and a weakly stationary random process with a zero mean. Both the periodically varying spin rate and the axial random force may lead to parametric instability of the beam. In this work, the finite element method is applied first to get rid of the dependence on the spatial coordinate. The method of stochastic averaging is then adopted to obtain Ito’s equations for the system response under different resonant frequency combinations. Finally, the first-moment and the second-moment stability conditions of the beam are derived explicitly. Numerical results are presented for a simple harmonic speed perturbation and a Gaussian white noise axial force.     

基于参变量变分原理的直升机系留载荷高性能计算方法

为了保证直升机在舰船上的安全性,必须使用系留设备将直升机系留在舰船上。直升机的系留问题可简化为由机身刚体、索具和起落架组成的杆件系统,索具只承受拉力而不承受压力,起落架只承受压力而不承受拉力。因此,直升机系留问题为典型的强非线性问题,需要发展有效的求解算法。在考虑大变形的情况下,基于参变量变分原理建立了求解直升机系留载荷的高性能计算方法。 该方法利用参变量变分原理能够准确判断索具和起落架的拉压状态,并将材料非线性静力问题转换为线性静力互补问题求解,极大地提高了结果的收敛性。数值算例中,通过与有限元通用软件NASTRAN和ABAQUS计算结果比较,证实了该方法的精确性、收敛性及高效性。     

The mechanical behavior of a wire rope with an independent wire rope core

A new model for simulating the mechanical response of a wire rope with an independent wire rope core is presented. The rope is subjected to both an axial load and an axial torque. In contrast with previous models that consider the effective response of wound strands, the present model fully considers the double-helix configuration of individual wires within the wound strand. This enables to directly relate the wire level stress to the overall load applied at the rope level. The model assumes a fiber response of individual wires. Two alternative kinematics of the wires are considered, and are used to predict the elastic response of the rope. The postulated kinematics are theoretically validated and the predicted rope response is in agreement with new experimental data. The new model enables the extraction of the stress at the wire level that can be used in turn to estimate global features of the rope such as force interaction between wires, rope stiffness, strength, and fatigue life.     

Helical Birods: An Elastic Model of Helically Wound Double-Stranded Rods

We consider a geometrically accurate model for a helically wound rope constructed from two intertwined elastic rods. The line of contact has an arbitrary smooth shape which is obtained under the action of an arbitrary set of applied forces and moments. We discuss the general form the theory should take along with an insight into the necessary geometric or constitutive laws which must be detailed in order for the system to be complete. This includes a number of contact laws for the interaction of the two rods, in order to fit various relevant physical scenarios. This discussion also extends to the boundary and how this composite system can be acted upon by a single moment and force pair. A second strand of inquiry concerns the linear response of an initially helical rope to an arbitrary set of forces and moments. In particular we show that if the rope has the dimensions assumed of a rod in the Kirchhoff rod theory then it can be accurately treated as an isotropic inextensible elastic rod. An important consideration in this demonstration is the possible effect of varying the geometric boundary constraints; it is shown the effect of this choice becomes negligible in this limit in which the rope has dimensions similar to those of a Kirchhoff rod. Finally we derive the bending and twisting coefficients of this effective rod.     

晃动基座行进间对准问题的QUEST算法

针对惯导系统晃动基座行进间初始对准问题,提出了一种基于重力矢量的QUEST(Quaternion Estimator)姿态最优估计算法。在传统基于重力矢量的初始对准方法基础上,将方向余弦矩阵的求解过程转换为Wahba问题,实现对重力矢量信息的充分利用,并通过QUEST算法实现了晃动基座下行进间粗对准的最优算法,改善了原有算法鲁棒性以及实时性等方面的问题。仿真和湖试实验验证表明,更改后的算法能够明显提高惯导系统在动基座下的姿态估计速度和精度,特别在周期性线振动环境下的对准精度能够提高一个数量级。多航次的湖试实验结果表明,改进后的算法能够有效提高航向对准精度,综合导航速度精度能够提高50%左右。     

Application of the Kantorovich-Galerkin Method for Solving Boundary Value Problems with Conditions on Moving Borders

The approximate Kantorovich-Galerkin method is considered for solving problems describing the vibrations of viscoelastic objects with conditions on moving boundaries and analyzing the resonance properties of these objects. The method makes it possible to take into account the effect of forces of environmental resistance on the system, flexural rigidity, and also boundary conditions with weak nonstationarity. The mathematical formulation of the problem involves a partial differential equation with respect to the desired displacement function and inhomogeneous boundary conditions. The Kantorovich-Galerkin method makes it possible to take into account the initial conditions, but they do not affect the resonance properties of linear systems, so in this case they are not taken into account. By introducing a new function into the problem, the boundary conditions are reduced to homogeneous ones. The solution is carried out in dimensionless variables to within a second order of smallness with respect to small parameters characterizing the velocity of the boundary motion and viscoelasticity. Using the Kantorovich-Galerkin method, an approximate solution of high accuracy of the problem of forced longitudinal vibrations of a viscoelastic rope of variable length, one end of which is wound on a drum, and the second is rigidly fixed, is found. The results obtained for the amplitude of oscillations corresponding to the nth dynamical mode are presented. The phenomenon of steady resonance and passage through resonance is investigated using numerical methods. A graphical dependence of the maximum amplitude of the rope oscillations as it passes through the resonance, depending on the coefficient characterizing the viscoelasticity of the object based on the Voigtmodel, is presented. The accuracy of the Kantorovich-Galerkin method is estimated.