Dynamics of digging in wet soil

Numerous animals live in, and locomote through, subsea soils. To move in a medium dominated by frictional interactions, many of these animals have adopted unique burrowing strategies. This paper presents a burrowing model inspired by the Atlantic razor clam (Ensis directus), which uses deformations of its body to cyclically loosen and re-pack the surrounding soil in order to locally manipulate burrowing drag. The model reveals how an anisotropic body - composed of a cylinder and sphere varying sinusoidally in size and relative displacement - achieves unidirectional motion through a medium with variable frictional properties. This net displacement is attained even though the body kinematics are reciprocal and inertia of both the model organism and the surrounding medium are negligible. Our results indicate that body aspect ratio has a strong effect on burrowing velocity and efficiency, with a well-defined maximum for given kinematics and soil material properties.     

Development of a solution method for frictional contact problems with complex loading

In this work, solution methods for frictional contact problems are extended to the case of moving punches and to the external loading history-dependent system states. To solve the frictional contact problems in the contact area, an iterative method is developed and implemented. Solutions of two-dimensional problems are constructed using the boundary element method. Numerical analysis is aimed at the quantitative study of effects such as the interaction of contact pressure and friction forces, estimates of the friction force differences due to the differences in the choice of local basis for the calculation of normal pressure and friction forces, and evaluation of the effects of complex loading (rotation of the rigid punch after its preliminary penetration into the solid). We find that, for the same definition of the friction force, different initial approximations lead to the same solution. At the same time, the friction forces defined either as projections onto the common tangent plane or as projections onto the plane tangent to the punch can differ quite substantially. Similar conclusions are derived for the solutions corresponding to single or multiple loading steps. The work relies on the variational principle for the solution of contact problems and numerical algorithms developed for the problems with one-sided constraints. The variational principle was first applied by Signorini [1] to the determination of the stress-strain state in a linearly deformed body in a rigid smooth shell. The modern view of the problem and its generalizations to the frictional problems and some other problems involving unilateral constraints in given in the monograph [2]. Finite difference and finite element methods in application to the problems with unilateral constraints are described in [3]. Analytical solution methods are developed in the monographs [4–6].     

Biomechanical analysis and numerical calculation of earthworm crawling

蚯蚓是典型的多体节动物。本文从生物力学的角度,分析了蚯蚓在静止和运动状态下的体壁应力,又分析了蚯蚓爬行过程中的变形以及与地面之间的摩擦力,给出了蚯蚓在地表爬行的动力学模型。进一步,又数值计算了一定质量范围的蚯蚓在静止和运动状态下体壁承受的最大应力和动力学模型方程,得到蚯蚓爬行的平均速度与质量的关系。计算结果与实验观测值基本一致。     

蚯蚓爬行的生物力学分析与数值计算

蚯蚓是典型的多体节动物。本文从生物力学的角度,分析了蚯蚓在静止和运动状态下的体壁应力,又分析了蚯蚓爬行过程中的变形以及与地面之间的摩擦力,给出了蚯蚓在地表爬行的动力学模型。进一步,又数值计算了一定质量范围的蚯蚓在静止和运动状态下体壁承受的最大应力和动力学模型方程,得到蚯蚓爬行的平均速度与质量的关系。计算结果与实验观测值基本一致。      

A comprehensive study on the behavior of a rigid block on an oscillating ground with friction,elastic and viscous forces

This paper investigates the behavior of a non-linear mechanical model where a block is driven by an oscillating ground through Coulomb friction, a linear viscous damper and a linear spring. The governing equation is solved analytically for different partial configurations: friction only, friction with viscous damping, friction with a linear restoring force, and for the complete model. Using dimensionless groups, the analysis of the block motion provides a comprehensive set of information on the motion regime (stick, stick-slip or permanent sliding), on the dominant energies or forces, on the resonance and on the amplification of the ground oscillation by the system. The limit between the stick-slip regime and the permanent slipping regime is found either analytically or numerically. It is also shown that there exists a set of parameters for which the friction force, the viscous dissipative force and the elastic restoring force are equal.     

Strain and work-hardening in a coulomb-type granular medium

Equations are given for the elastoplastic strain of a granular medium together with experimental relationships for sands. Equations for the characteristics are drawn up in general form for the two-dimensional case. It is shown that experimental data on the dilatancy rate as a function of the angle of internal friction reflect the condition for orthogonality of the characteristics of the velocity distribution to the direction of the dry-friction forces in the sliding areas. The flow in a shear tester is discussed. The calculation from the universal relationships agrees with experiment.     

Boundary layer on the moving surface of a cylinder

A study is made of the problem of the boundary layer on a cylinder with a moving surface when the cylinder moves with constant velocity in an incompressible fluid. Expressions are obtained for the distributions of the frictional stress on the surface of the cylinder and the coordinate of the singular point in the solution of the boundary layer equations that indicates the appearance of a region of reverse flow for different values of the relative velocity of the motion of the surface of the cylinder. Numerical calculations have been made of the work of the force of friction associated with displacement of the cylinder, the work expended on the motion of its surface, and, in the case of flow separation, the work of the pressure forces (it being assumed here that the pressure and friction on the wall behind the singular point are constant and equal to the pressure and friction at the singular point).     

Unilaterality and Dry Friction: A Geometric Formulation for Two-Dimensional Rigid Body Dynamics

The dynamics of a rigid body simply supported on a moving rigid ground in the presence of dry friction is investigated. Rigid body kinematics, in terms of generalized coordinates, and features of contact are discussed. According to the contact laws, a variational formulation is adopted to describe the dynamics and to analyze, in the case of contact, the connection between dynamically possible motions and actual evolution of the system. A geometric method is then proposed which allows the dynamic evolution to be determined without any direct evaluation of the contact forces. Though different situations are possible, depending on the instantaneous values of relative position, velocity and active forces, a unique solution is identified. Examples illustrating applications of the theory are presented.     

Comparisons of rotordynamic coefficients in stepped labyrinth seals by using Colebrook-White friction factor model

The objective of this work is to observe the effects of friction factors for the stepped labyrinth seals. The gas flow through the seals creates net pressure and shear forces acting on the rotor. It is necessary to predict these forces for reliably operating turbomachinery. So we investigated the effect of shear forces on the calculation of rotordynamic coefficients by comparing the results in the case shear forces are considered and in the case they are neglected. We also compared our results, obtained with the Colebrook–White friction factor model, with some reference experimental and computational results.     

环空大挠度钻柱力学分析的动坐标迭代法及其简化应用

应用动坐标迭代法分析环空钻柱的边界待定问题与几何非线性受力变形问题。将摩擦引入平衡计算中，导出了三维分析模型。计算说明该方法和模型简便可靠，实际应用可以简化计算。     

Non-linear dynamics of a mechanical system with a frictional unilateral constraint

We analyze the dynamics of a two-dimensional system constituted by two masses subjected to elastic, gravitational and viscous forces and constrained by a moving frictional mono-lateral surface. The model exhibits a time-varying dynamics capable of reproducing the hopping phenomenon, an unwanted phenomenon observed in many applications such as the motion of a robotic arm on a surface or that of a wiper on a windscreen. The system dynamics, besides being affected by geometrical non-linearities, has a non-smooth nature due to the impact and friction laws involved in the model. The complexity of the resulting equations and of the transition conditions require the problem to be solved numerically. Various periodic motions are found and the effect of varying the system parameters, in particular the friction coefficient, is investigated. Finally, simulations are used to gain some insight the behavior of the windscreen wiper.     

Calibration of granular material parameters for DEM modelling and numerical verification by blade-granular material interaction

The discrete element method (DEM) is a promising approach to model blade-granular material interactions. The accuracy of DEM models depends on the model parameters. In this study, a calibration process was developed to determine the parameter values. The particle size was the same as the real material and the particle shape was modelled using two spherical particles rigidly clumped together to form a single grain. Laboratory shear tests and compressions tests were used to determine the material internal friction angle and stiffness, respectively. These tests were replicated numerically using DEM models with different sets of particle friction coefficients and particle stiffness values. The shear test results are found to be dependent on both the particle friction coefficient and the particle stiffness. The compression test results show that it is only dependent on the particle stiffness. The combination of shear test and compression test results can be used to determine a unique set of particle friction and particle stiffness values. The calibration process was validated experimentally and numerically by modelling a blade moving through granular material. Results show that the forces acting on the blade can be accurately modelled with DEM and the maximum error is found to be 26%. The relative particle-blade displacements were used to predict the position and shape of the shear lines in front of the blade. A good qualitative correlation was achieved between the experiments and the DEM simulations.     

Experimental Studies of the Flow of Ferrofluid in Porous Media

This paper presents laboratory-scale experimental results of the behavior of ferrofluids in porous media consisting of sands and sediments. Ferrofluids are colloidal suspensions of magnetic particles stabilized in various carrier liquids. In the presence of an external magnetic field, a ferrofluid becomes magnetized as the particles align with the magnetic field. We investigate the potential for controlling fluid emplacement in porous media using magnetic fields. These experiments show that in laboratory-scale porous media experiments (up to 0.25m), with both vertical gravitational forces and lateral magnetic forces acting simultaneously, the magnetic field produces strong attractive forces on the ferrofluid, particularly in the vicinity of the magnet. These holding forces result in a predictable configuration of the fluid in the porous medium which is dependent on the magnetic field and independent of flow pathway or heterogeneity of the porous medium. No significant retention effects due to flow through variably saturated sands are observed. While the proposed field engineering applications of ferrofluids are promising, the observations to date are particularly relevant at the laboratory scale where the decrease in magnetic field strength with distance from a magnet is less of a limitation than in larger scale applications. Ferrofluids may find immediate application in any situation where it is desirable to control the motion or final configuration of fluid in an experimental flow apparatus without direct physical contact.     

Kinematics and dynamics of a particle on a non-simple harmonic vibrating screen

The motion of a particle on a screen is directly affected by the motion of the screen if airflow and intergranular friction are ignored. To study this effect, a mathematical model was established to analyze the motion of a planar reciprocating vibrating screen, and a matrix method was employed to derive its equation of motion. The motion of the screen was simulated numerically and analyzed using MATLAB. The results show that the screen undergoes non-simple harmonic motion and the law of motion of each point in the screen is different. The tilt angle of the screen during screening is not constant but varies according to a specific periodic function. The results of numerical simulations were verified through experiments. A high-speed camera was used to track the motion of three points in the longitudinal direction of the screen. The balance equation for forces acting on a single particle on the screen was derived based on the non-simple harmonic motion of the screen. These forces were simulated using MATLAB. Different types of particle motion like slipping forward, moving backward, and being tossed to different parts of the screen were analyzed. A vibro-impact motion model for a particle on the non-simple harmonic vibrating screen was established based on the nonlinear law of motion of the particle. The stability of fixed points of the map is discussed. Regimes of different particle behaviors such as stable periodic motion, period-doubling bifurcation motion, Hopf bifurcation motion, and chaotic motion were obtained. With the actual law of motion of the screen and the behavior of a particle on the screen, a theoretical basis for design optimization of the screen is provided.     

Analytic solution of the problem of rotation of a sphere in a rarefied molecular gas with allowance for the accommodation coefficients

In the case of the slip flow regime expressions both for the mass velocity of a rarefied molecular gas entrained by a rotating sphere and for the moment of the friction forces exerted on the sphere by the gas are obtained with allowance for the second-order correction with respect to the Knudsen number. It is demonstrated that these quantities depend on the Prandtl number and the accommodation coefficients of the tangential impulse of the gas molecules and its flux toward the sphere surface. The results are compared with analogous results obtained in the case of diffuse reflection of the gas molecules by the sphere surface.     

微/纳尺度粘着滑动接触的多尺度分析

采用分子动力学与有限元耦合的多尺度方法,求解二维刚性圆柱表面压头与弹性平面的微/纳尺度粘着滑动接触问题,通过与全分子动力学模拟结果的比较验证了多尺度方法的有效性。对压头半径、滑动速度、下压深度以及是否考虑粘着效应等对滑动接触性能的影响进行了全面研究,通过不同条件下摩擦力及接触力分布的比较,揭示了上述各参数对粘着滑动接触...     

Oscillation pattern of stick-slip vibrations

This paper studies the stick-slip oscillations of discrete systems interacting with translating energy source through a non-linear smooth friction curve. The stick-slip limit cycle oscillations of a single degree-of-freedom model are examined by means of numerical time-integration and analytical methods. Similar approaches are also applied to the model of the coupled friction oscillator. Particularly, it is found that the steady-state response of the coupled oscillator can be divided into two different forms of oscillation (mode-merged and mode-separated oscillations) according to the frequency separation of two modes. The oscillation pattern of the steady-state response is shown to depend on system parameters such as detuning factor, energy source speed, and normal contact load.     

基于虚拟变形法的车-桥耦合系统移动质量识别

利用双自由度质量-弹簧阻尼模型模拟移动车辆, 并基于虚拟变形(VDM)方法的结构快速重分 析思想, 提出一种车-桥耦合系统的移动质量快速识别的有效方法. 该方法以双自由度车体模 型的质量为变量, 通过最小化桥体结构实测响应和计算响应的平方距离来识别移动质量 (载荷), 避免了识别载荷时常遇到的病态问题, 对噪声鲁棒性强, 且需要传感器信息少. 每步优化 中, 利用在VDM方法基础上提出的移动动态影响矩阵概念, 无需时时重构车-桥耦合系统的时 变系统参数矩阵, 显著提高了计算效率. 利用数值框架梁模型, 通过比较不同车辆简化模型 对移动体质量及等效移动载荷的识别效果, 验证了该方法的可行性和有效性, 即使在5% 的噪声影响下, 利用一个传感器可以准确地识别多个移动体的质量.     

Motion of a circular cylinder in a rectangular channel

When bodies move in fluids, the parameters of their motion depend strongly on the interaction of the bodies with the surrounding fluid [1, 2]. The present paper is devoted to determination of the hydrodynamic forces that act on a cylinder moving in an infinite rectangular channel in an ideal incompressible fluid that is at rest.     

Momentum and heat transfer over a continuous moving surface in a non-Darcian fluid

The momentum and heat transfer characteristics associated with the boundary layer on a continuous moving flat surface in a non-Darcian fluid have been investigated exploiting a local similarity solution procedure. The full boundary layer equations, which describe the effects of convective inertia, solid boundary, and porous inertia in addition to the Darcy flow resistance, were solved using novel transformed variables, deduced from a scale analysis on the momentum and energy conservation equations. Details are provided for the effects of convective inertia and porous inertia on the velocity and temperature profiles. The resulting friction and heat transfer characteristics are found to be substantially different from those of forces convection over a stationary flat plate. Furthermore, useful asymptotic expressions for the local Nusselt number are presented in consideration of possible physical limiting conditions.