最速降线问题解充分性的证明

 利用可动边界的变分公式,通过广义环路积分导出Hilbert不变积分, 在此基础上说明了最速降线问题解的充分性.     

带式输送机弯曲变形阻力理论研究

为了减小带式输送机的弯曲阻力,基于黏弹性材料在动载荷下的能耗理 论,对输送带运行时的弯曲变形能耗机理进行了分析,推导出输送带弯曲变形阻力系数的近似理 论公式,并通过试验验证了公式的正确性. 利用公式对各因素对弯曲阻力系数 的影响规律进行了探讨,结果表明可以通过选配合适的输送带橡胶材料获得合适的 输送带黏弹性参数,并结合调整输送带、输送机的结构参数达到降低输送机弯曲阻力的目的.     

一种滞弹簧耗能的新型离散元滚动阻力模型研究

颗粒间滚动阻力对颗粒体系的稳定性起着重要作用. 在传统的离散元法中, 滚动阻力模型通常由转动弹簧、转动黏壶和摩擦元件表达, 颗粒滚动动能由黏滞力(矩)和摩擦力做功耗散. 由于黏滞力(矩)与滚动速度相关, 临近静止状态的颗粒滚动速度变小, 动能耗散减弱, 传统的离散元模拟得到颗粒由滚动到静止耗费的时间比试验观测的结果要长. 为解决这一问题, 基于摩擦学理论分析了滚动阻力产生的材料滞弹性机理, 将其引入离散元滚动阻力模型, 提出了一种速度无关型动能耗散的滞弹簧, 给出了滞弹簧的弹性恢复力计算公式, 建立了一种新型的离散元滞弹性滚动阻力模型(HDEM). 为验证新型滚动阻力模型的正确性, 通过一个光学物理试验对单个圆形颗粒试件的自由滚动过程进行了测量, 将测量数据与新型的滞弹型离散元模型和传统离散元模型计算结果进行了对比. 结果显示, 基于滞弹性滚动阻力模型HDEM计算结果与试验数据吻合程度更高, 而且模拟得到的颗粒摆动频率更符合试验现象.      

圆柱管道内运动的小球受到的黏滞阻力的数值分析

为了更好地运用落球法测量研究流体的黏滞系数,研究小球在黏性流体中下落的受力情况,本文对小球在充满黏性流体的圆柱管道的下落过程进行分析。利用COMSOL4.4仿真模拟,建立了合理的仿真模型,并分析了小球受到的黏滞阻力与小球的大小、下落位置的关系。结果表明:选择速度项二阶近似、压强项一阶近似的离散化方法,可以得到和理论值非常相符的仿真结果;当下落过程中小球球心始终在圆柱轴线上时,小球受到的黏滞阻力相对于Stokes力的修正系数,是小球半径与圆柱管道半径的比例函数,本文得到了更大范围的符合理论解的修正系数;当下落过程中小球的球心偏离圆柱轴线时,对于同样大小的小球,黏滞阻力、压强力、黏性力均随着球心到轴线的距离先减小后增大,且具有不同的极小值点。     

泡沫在圆管中层流阻力研究

泡沫具有粘度大,密度低的特点.根据连续介质运动方程导出了泡沫在圆管内层流流动时的阻力方程和摩擦阻力系数表达式.通过实验,证明了摩擦阻力系数方程的正确性.     

材料黏滞系数与损耗因子的频率相关性研究

针对黏弹性材料KV阻尼模型的黏滞系数与复阻尼模型的损耗因子间的关系,由单自由度体系的结构动力学分析,并基于结构振动响应的一致性,推导建立了黏滞系数与损耗因子在结构线性稳态简谐振动和自由振动时的一般关系式;并利用该关系式,试验研究了纤维混凝土材料黏滞系数和损耗因子的频率相关性.结果表明,黏滞系数与损耗因子间的关系在稳态简谐振动和自由振动时的表达形式相同,只是频率取值不同;纤维混凝土的损耗因子和黏滞系数都随频率增加而降低,且在0.5～1.0Hz频段降幅显著,而后渐趋平缓;相比于素混凝土,纤维混凝土的黏滞系数和损耗因子与激振频率的相关性更强.试验所得纤维混凝土频率相关的黏滞系数、损耗因子及推导所建立的两参数关系式为构建物理意义明确且又便于结构振动反应分析的阻尼系数或阻尼矩阵奠定了基础.      

剪切流下发生涡激振动的柔性立管阻力特性研究

利用缩尺模型试验的方法研究了线性剪切流下涡激振动发生时柔性立管的阻力特性.文中基于光纤光栅应变传感器测得的模型应变信息,采用梁复杂弯曲理论计算了立管的平均阻力,继而分析了阻力系数沿管长方向和雷诺数的分布特性以及涡激振动对阻力系数的放大效应,并提出了用于估算柔性立管发生涡激振动时阻力系数的经验公式.结果表明:涡激振动对阻力系数有放大效应,使得立管局部阻力系数高达3.2;平均阻力系数在1.0×104到1.2×105的雷诺数区间内的值为1.3~2.0,并随雷诺数的增大而减小.本文提出的经验公式可准确估算高雷诺数下涡激振动发生时柔性立管的阻力系数,此经验公式考虑了流速、涡激振动主导模态以及主导频率对阻力系数的影响.      

水平井变质量流研究进展

综述了水平井筒沿管壁具有流体流入的变质量流动的最新研究进展.内容包括:考虑油藏流体流入时井筒流动压力及产量的计算,具有不同流入时管壁摩擦系数的经验计算公式,以及流体径向流入井筒后流动阻力损失产生的机理分析等.重点介绍了水平井筒变质量流动阻力系数的计算,同时文中还介绍了井筒两相变质量流动损失产生的机理和数值模拟研究进展.      

粘土悬浮液明渠流的减阻现象

水和粘土悬浮液在水槽中的流动试验证明，在粗糙边界上的粘土悬浮液明渠流阻力明显小于清水流．在同样水力条件下粘土悬液的时均流速比清水流速大得多．当悬液浓度较高时，流动阻力系数比清水流阻力系数的一半还小．实验表明粘土悬液的高粘性和屈服应力抑制了紊动的发展，减小了紊动剪力，导致阻力降低．对于光滑边界湍流，粘土悬液的阻力系数与清水流的相近，不发生减阻现象     

基于LuGre摩擦模型的接触约束法旋转柔性梁斜碰撞研究

基于接触约束法和LuGre摩擦模型对在重力场作用下作大范围旋转运动的柔性梁系统和斜坡发生含摩擦斜碰撞的动力学问题进行研究. 首先运用刚柔耦合的多体系统动力学理论对大范围运动的柔性梁进行离散化和动力学建模, 在碰撞时采用冲量动量法求出跳跃速度, 其次在法向上引入接触约束求解出碰撞力, 在切向上采用LuGre摩擦模型分两种方式求解摩擦力, 第一种是在滑动时摩擦力由摩擦系数和碰撞力计算得出, 黏滞状态下引入切向约束计算拉格朗日乘子反应实际摩擦力, 根据黏滞/滑动切换判断计算出碰撞过程摩擦力(与Coulomb摩擦模型计算摩擦力一致); 第二种根据LuGre摩擦模型摩擦系数和法向碰撞力计算其摩擦力, 从而在碰撞时无需黏滞/滑动切换, 采用相同的摩擦力计算公式. 通过与Coulomb摩擦模型对比发现, LuGre摩擦模型描述碰撞切向摩擦过程更精确, LuGre摩擦模型黏滞时建立约束方程和碰撞采用统一的摩擦力公式这两种建模方式描述的斜碰撞动力学特性没有区别, 进而说明采用法向接触约束和LuGre摩擦模型具有满足碰撞非嵌入情况、避免黏滞/滑动切换、描述摩擦力相对准确的优势.      

The Okhotsimskii-Pontryagin method in control theory and analytical mechanics. Part II

The Okhotsimskii method for the differentiation of functionals in control theory is discussed on the basis of the Pontryagin formalism. The relation of this method to other approaches to solving control problems and to other methods of analytical mechanics is studied. Some typical cases of solving optimal control problems are considered. The brachistochrone problem is solved with consideration of viscous friction.     

Conditions for pure rolling of a heavy cylinder along a brachistochrone

Algebraic equations for the line of steepest descent of a cylinder are derived in parametric form. Conditions for rolling without slipping and separation of the cylinder along a brachistochrone are established based on the equations of motion with constraint reaction. The important conclusion is drawn that the center of mass of a cylinder moving along a brachistochrone describes a cycloid     

Brachistochrone for a rolling cylinder

The motion of a heavy homogeneous cylinder is considered as a no-slip rolling along the desired curve. We obtain a functional in the form of the total time of the cylinder rolling and solve the corresponding variational problem of minimizing this functional. We obtain an algebraic equation for the directional line of steepest descent, brachistochrone, in parametric form. We use the equation of motion of the cylinder with constraint reaction to determine the conditions of implementation of its pure rolling without separation and slip with respect to the brachistochrone.     

Brachistochrone with Coulomb friction as the solution of an isoperimetrical variational problem

The problem of finding the plane supporting curve (brachistochrone) along which a heavy particle released from rest at the given starting point slides with dry (Coulomb) friction and reaches the given destination point in least time, is stated as a variational isoperimetrical problem. The finite parametric equations of the extremal curve are obtained. This curve is the sought-for brachistochrone if the solution of the problem exists. Several numerical examples are given.     

Evolutionary solutions to the brachistochrone problem with Coulomb friction

The classical brachistochrone problem was originally proposed by Johann Bernoulli more than 300 years ago, and is still one of the most elegant problems in modern mathematics. This paper examines a generalisation of the original brachistochrone problem by the inclusion of a non-conservative force in the form of Coulomb friction. Solutions to this problem are found using an evolutionary computational technique based on Darwinian natural selection and survival of the fittest. These evolutionary solutions tend to indicate that as friction is introduced the optimum curves develop from cycloidal (the analytical solution for the conservative problem) toward straight lines. The flexibility of the evolutionary method to optimise for other objectives is then discussed.     

Cycloidal pendulum with a rolling cylinder

Free vibrations of a heavy homogeneous cylinder rolling in a cylindrical cavity whose directing curve is a brachistochrone are considered. The equation of motion of the cylinder is derived and the circular frequency of free vibrations of the cylinder center of mass is determined. An analogy between the cycloidal pendulum with a rolling cylinder and the classical cycloidal pendulum in the form of a material point is obtained.     

Brachistochrone with Coulomb friction

The classical brachistochrone is considered with the inclusion of a resistant force, which is due to Coulomb friction, in addition to the uniform gravitational force that is present. The solution to this problem is expressed in terms of standard functions, and it is developed in two separate ways by means of constrained variational calculus methods. These ways involve formulations of the problem in terms of temporal and spatial independent variables, respectively. The equations of motion that result in both cases are non-linear and coupled. The utilization of path variables is a central feature of the developments provided.     

Resolution of a Paradox Involving Viscous Dissipation and Nonlinear Drag in a Porous Medium

The modelling of viscous dissipation in a porous medium saturated by an incompressible fluid is discussed, for the case of Darcy, Forchheimer and Brinkman models. An apparent paradox relating to the effect of inertial effects on viscous dissipation is resolved, and some wider aspects of resistance to flow (concerning quadratic drag and cubic drag) in a porous medium are discussed. Criteria are given for the importance or otherwise of viscous dissipation in various situations.     

Efficiency of a vibroprotection system with an isochronous roller damper

Low-frequency vibrations of a vibroprotection “roller damper-movable bearing body” system of rigid bodies under the action of an external harmonic excitation are considered. The working surface of the damper working body is formed by a brachistochrone. The dynamic equations of common no-slip motion of the damper working body on a hinged roller and of the bearing body are formulated. The roller damper tuning parameters are determined.     

Brachistochronic motion of nonholonomic nonlinear mechanical system of the Chaplygin type

In this paper, the differential equations of brachistochronic motion of nonholonomic nonlinear system of the Chaplygin type were determined. The additional forces R_α realizing the corresponding motion of the system together with the given forces were also determined. Lastly, the brachistochrone was solved for a concrete model using mathematical numerical methods.