An inviscid model for vortex shedding from a deforming body

An inviscid vortex sheet model is developed in order to study the unsteady separated flow past a two-dimensional deforming body which moves with a prescribed motion in an otherwise quiescent fluid. Following Jones (J Fluid Mech 496, 405–441, 2003) the flow is assumed to comprise of a bound vortex sheet attached to the body and two separate vortex sheets originating at the edges. The complex conjugate velocity potential is expressed explicitly in terms of the bound vortex sheet strength and the edge circulations through a boundary integral representation. It is shown that Kelvin’s circulation theorem, along with the conditions of continuity of the normal velocity across the body and the boundedness of the velocity field, yields a coupled system of equations for the unknown bound vortex sheet strength and the edge circulations. A general numerical treatment is developed for the singular principal value integrals arising in the solution procedure. The model is validated against the results of Jones (J Fluid Mech 496, 405–441, 2003) for computations involving a rigid flat plate and is subsequently applied to the flapping foil experiments of Heathcote et al. (AIAA J, 42, 2196–2204, 2004) in order to predict the thrust coefficient. The utility of the model in simulating aquatic locomotion is also demonstrated, with vortex shedding suppressed at the leading edge of the swimming body.      

On the penetration of a rotating impactor into an elastic-plastic medium

This research is devoted to the modeling of high-speed rectilinear penetration of a rigid axisymmetric body (impactor with a flat bluntness) into an elastic–plastic media with account for its rotation about the axis of symmetry. The body has an arbitrary shape of the meridian. The resistance to the motion is represented as the sum of the body drag and the contribution of friction. The dynamic system governing the body motion is derived and the qualitative and numerical analysis of the projectile movement and perforation of a slab are performed. The problem of shape optimization of impactor with a flat bluntness is studied using evolutionary algorithm.     

Initial stage of the inclined impact of a smooth body on a thin fluid layer

The two-dimensional problem of the oblique impact of a free rigid body with a smooth flat bottom on a thin layer of an ideal incompressible fluid is considered. The initial stage of the impact when the body motion is accompanied by the formation of jets on the boundary of the body-fluid contact zone is investigated. The problem is solved jointly, i.e., the fluid flow initiated by the body motion and the motion of the body itself are determined simultaneously. A priori the “body-fluid” contact zone is unknown and determination of its time evolution represents a significant difficulty and the method of asymptotic matched expansions is used to overcome this difficulty. A system of integro-differential equations is obtained and the motion of the body under the action of hydrodynamic loads is investigated numerically on the basis of this system. It is shown that the hydrodynamic force exerted on the body during the impact is maximum precisely in the initial stage; therefore, the motion of the body varies fairly significantly in time considered.     

A Reconciliation of Viscous and Inviscid Approaches to Computing Locomotion of Deforming Bodies

We present a formulation for coupled solutions of fluid and body dynamics in problems of biolocomotion. This formulation unifies the treatment at moderate to high Reynolds number with the corresponding inviscid problem. By a viscous splitting of the Navier–Stokes equations, inertial forces from the fluid are distinguished from the viscous forces, and the former are further decomposed into contributions from body motion in irrotational fluid and ambient fluid vorticity about an equivalent stationary body. In particular, the added mass of the fluid is combined with the intrinsic inertia of the body to allow for simulations of bodies of arbitrary mass, including massless or neutrally buoyant bodies. The resulting dynamical equations can potentially illuminate the role of vorticity in locomotion, and the fundamental differences of locomotion in real and perfect fluids.     

An approximate decoupled dynamics and kinematics analysis of legless locomotion

We present a novel analysis technique to understand the dynamics of a recently described locomotion mode called legless locomotion. Legless locomotion is a locomotion mode available to a legged robot when it becomes high-centered, that is, when its legs do not touch the ground. Under these conditions, the robot may still locomote in the plane by swinging its legs in the air, rocking on its body, and taking advantage of the nonholonomic contact constraints. Legless locomotion is unique from all previously studied locomotion modes, since it combines the effect of oscillations due to controls and gravity, nonholonomic contact constraints, and a configuration-dependent inertia. This complex interaction of phenomena makes dynamics analysis and motion planning difficult, and our proposed analysis technique simplifies the problem by decoupling the robot’s oscillatory rotational dynamics from its contact kinematics and also decoupling the dynamics along each axis. We show that the decoupled dynamics models are significantly simpler, provide a good approximation of the motion, and offer insight into the robot’s dynamics. Finally, we show how the decoupled models help in motion planning for legless locomotion.     

Soft soil track interaction modeling in single rigid body tracked vehicle models

Single rigid body models are often used for fast simulation of tracked vehicle dynamics on soft soils. Modeling of soil-track interaction forces is the key modeling aspect here. Accuracy of the soil-track interaction model depends on calculation of soil deformation in track contact patch and modeling of soil resistive response to this deformation. An algorithmic method to calculate soft soil deformation at points in track contact patch, during spatial motion simulation using single body models of tracked vehicles, is discussed here. Improved calculations of shear displacement distribution in the track contact patch compared to existing methods, and realistically modeling plastically deformable nature of soil in the sinkage direction in single body modeling of tracked vehicle, are the novel contributions of this paper. Results of spatial motion simulation from a single body model using the proposed method and from a higher degree of freedom multibody model are compared for motion over flat and uneven terrains. Single body modeling of tracked vehicle using the proposed method affords quicker results with sufficient accuracy when compared to those obtained from the multibody model.     

On the problem of free deceleration of a rigid body in a resisting medium

A mathematical model of the influence of a medium on a rigid body with some part of its external surface being flat is considered with due allowance for an additional dependence of the moment of the medium action force on the angular velocity of the body. A full system of equations of motion is given under quasi-steady conditions; the dynamic part of this system forms an independent third-order system, and an independent second-order subsystem is split from the full system. A new family of phase portraits on a phase cylinder of quasi-velocities is obtained. It is demonstrated that the results obtained allow one to design hollow circular cylinders (“shell cases”), which can ensure necessary stability in conducting additional full-scale experiments.     

Transient thermo-mechanical analysis for bimorph soft robot based on thermally responsive liquid crystal elastomers

Thermally responsive liquid crystal elastomers(LCEs) hold great promise in applications of soft robots and actuators because of the induced size and shape change with temperature. Experiments have successfully demonstrated that the LCE based bimorphs can be effective soft robots once integrated with soft sensors and thermal actuators. Here, we present an analytical transient thermo-mechanical model for a bimorph structure based soft robot, which consists of a strip of LCE and a thermal inert polymer actuated by an ultra-thin stretchable open-mesh shaped heater to mimic the unique locomotion behaviors of an inchworm. The coupled mechanical and thermal analysis based on the thermo-mechanical theory is carried out to underpin the transient bending behavior, and a systematic understanding is therefore achieved. The key analytical results reveal that the thickness and the modulus ratio of the LCE and the inert polymer layer dominate the transient bending deformation. The analytical results will not only render fundamental understanding of the actuation of bimorph structures, but also facilitate the rational design of soft robotics.     

Water wave radiation by a submerged rough disc

A thin circular body is submerged below the free surface of deep water. The problem is reduced to a hypersingular integral equation over the boundary of the body. Using a perturbation method, the problem is then reformulated by a sequence of simpler hypersingular equations over a flat disc making it well suited for an efficient previously used solution method. The first order approximation is computed and the hydrodynamic force due to heaving radiation motion are presented in terms of the added mass and damping coefficients for a polynomial cap and for a rough disc, modelled by a superposition of sinusoidal surfaces defined by randomly generated parameters. The solution exhibits larger maxima associated with smaller volume of submergence of the body. A slight shift of the damping coefficient maxima to lower frequencies is noticed for the caps. Rough discs with similar statistical properties exhibit different behaviours. Thus, it is the exact specific form of the rough disc that dictates the hydrodynamic force.     

Impactless biped walking on a slope

Walking without impacts has been considered in dynamics as a motion/force control problem. In order to avoid impacts, an approach for both the specified motion of the biped and its ground reaction forces was presented yielding a combined motion and force control problem. As an application, a walker on a horizontal plane has been considered. In this paper, it is shown how the control of the ground reaction forces and the energy consumption depend on the gradient of a slope. The biped dynamics and the constraints within the biped system and on the ground are discussed. A motion control synthesis is developed using the inverse dynamics principle proven to be most efficient for human walking research, too. The impactless walking with controlled legs is illustrated by a seven-link biped. The “flying” biped has nine degrees of freedom, with six control inputs. During locomotion, the standing leg has three scleronomic constraints, and the trunk has three rheonomic constraints. However, there are three rheonomic constraints for the prescribed leg motion or three scleronomic constraints for reaction forces of the trailing leg, respectively. The nominal control action for impactless walking can be precomputed and stored. The model proposed allows the investigation of several problems: uphill and downhill walking, optimization of step length, stiction of the feet on the slope and many more. All these findings are also of interest in biomechanics.     

Investigation of vortex development on accelerating spanwise-flexible wings

The effect of spanwise flexibility on the development of leading-edge vortices for impulsively started flat plates at low Reynolds numbers has been investigated. A theoretical model is proposed, based on the Euler–Bernoulli beam theory, coupled with a vortex growth model based on vorticity flux through a leading-edge shear layer. The model was validated for rigid and flexible flat plates undergoing a towing motion at an angle-of-attack of 45°. It is shown that a phase-delay in lift and drag generation occurs between rigid and flexible cases. The model indicates decreasing vorticity along the span as the wing is accelerated and begins to bend. Particle image velocimetry measurements conducted at three different spanwise planes showed a delay in vortex growth along the span, despite a uniform spanwise circulation. This uniform spanwise distribution of circulation is in contrast to the quasi-two-dimensional model, which predicted a reduced circulation near the profile tip where plate motion was delayed. It is therefore concluded that circulation must be dynamically redistributed through vorticity convection during the impulsive motion.     

基于序列图像的鱼游运动机理分析

自上世纪60年代起,鱼游运动机理分析一直是研究的热点之一。本文提出了一种基于序列图像的鱼游运动机理分析方法,从图像处理的角度来分析鱼游运动机理问题。该方法首先通过图像差分得到鱼体的轮廓,然后利用能量函数自动抽取游动鱼体的体干曲线。在此基础上,通过样条曲线参数拟合进一步得到鱼体游动时体干曲线形变的准确数据和各种运动学参数。以黑鳍鲨稳态游动为例,本文还建立了鲹科模式游动的运动学参数模型并讨论了模型中参数对鱼体游动的影响。实验表明,相比于传统方法,本文所提出的方法无需对实验环境和对象加以限制,可以自动获得鱼类游动时的体干曲线形变的准确数据,从而据此建立更加真实有效的鱼游运动学参数模型。     

Dynamical behavior of a mobile system with two degrees of freedom near the resonance

The design of mobile robots that can move without wheels or legs is an important engineering and technological problem.Self-propelling mechanisms consisting of a body that has contact with a rough surface and moveable internal masses are considered.Mathematical models of such systems are presented in this paper.First,a model of a vibration driven robot that moves along a rough horizontal plane with isotropic dry friction is studied.It is shown that by changing the off-resonance frequency detuning in sign,one can control the direction of motion of the system.In addition,a locomotion system which moves in an environment with anisotropic viscous friction is considered.For all models,the method of averaging to obtain an algebraic equation for the steady-state"average"velocity of the system is used. Prototypes were constructed to compare the theoretical results with experimental ones.     

A viscous vortex particle method for deforming bodies with application to biolocomotion

Bio‐inspired mechanics of locomotion generally consist of the interaction of flexible structures with the surrounding fluid to generate propulsive forces. In this work, we extend, for the first time, the viscous vortex particle method (VVPM) to continuously deforming two‐dimensional bodies. The VVPM is a high‐fidelity Navier–Stokes computational method that captures the fluid motion through evolution of vorticity‐bearing computational particles. The kinematics of the deforming body surface are accounted for via a surface integral in the Biot–Savart velocity. The spurious slip velocity in each time step is removed by computing an equivalent vortex sheet and allowing it to flux to adjacent particles; hence, no‐slip boundary conditions are enforced. Particles of both uniform and variable size are utilized, and their relative merits are considered. The placement of this method in the larger class of immersed boundary methods is explored. Validation of the method is carried out on the problem of a periodically deforming circular cylinder immersed in a stagnant fluid, for which an analytical solution exists when the deformations are small. We show that the computed vorticity and velocity of this motion are both in excellent agreement with the analytical solution. Finally, we explore the fluid dynamics of a simple fish‐like shape undergoing undulatory motion when immersed in a uniform free stream, to demonstrate the application of the method to investigations of biomorphic locomotion. Copyright © 2008 John Wiley & Sons, Ltd.     

Swimming in an inviscid fluid

We present a set of equations governing the motion of a body due to prescribed shape changes in an inviscid, planar fluid with nonzero vorticity. The derived equations, when neglecting vorticity, reduce to the model developed in Kanso et al. (J Nonlinear Sci 15:255–289, 2005) for swimming in potential flow, and are also consistent with the models developed in Borisov et al. (J Math Phys 48:1–9, 2007), Kanso and Oskouei (J Fluid Mech 800:77–94, 2008), Shasikanth et al. (Phys Fluids 14(3):1214–1227, 2002) for a rigid body interacting dynamically with point vortices. The effects of cyclic shape changes and the presence of vorticity on the locomotion of a submerged body are discussed through examples.     

Features of Movement of a Rotational Body

Vertical motion of a rotational body in an air environment as a mechanical model of a rotochute is considered. It is assumed that, in the process of motion, the symmetry axis of the rotational body remains vertical and the rotational body itself rotates relative to this axis. The aerodynamic impact model is based on a quasistatic approach. Steady regimes of motion are identified, their stability is analyzed, and certain features of transition regimes are explored, including those related to the exchange between the energy of rotational motion and the energy of translational motion.     

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分析人体双足步行的动态稳定性以及跳跃运动的动力学过程. 讨论与竞走和跑步运动有关的 力学问题.     

振动驱动移动系统平面避障运动分析

近年来,工业机器人的应用领域日益广泛,可移动机器人的发展备受关注,为了在一些复杂环境中准确地完成作业,学者们提出并研究了振动驱动移动系统.本文研究了在各向异性黏性摩擦环境中一类有两个在平行轨道内做正弦运动的内部质量块的振动驱动移动系统的运动规律,提出了使系统完成包括避障等规定作业的驱动设计方法.首先利用第二类拉格朗日方程,建立了系统的动力学方程;然后,利用速度Verlet积分法分析了系统的运动规律,得到了内部驱动参数与系统运动轨迹、运动速度的关系;最后,结合振动驱动移动系统的运动规律,提出了使系统沿预设路径运动和实现避障运动的驱动设计方法.通过曲线离散得到了系统沿预设路径运动的移动轨迹,进而通过改变内部质量块的驱动参数,使系统沿预设路径运动.为了使移动系统在障碍物环境中达到目标位置,提出了结合栅格法,Floyd算法及最小顶点圆法的优化的路径规划计算方法,得到了振动驱动移动系统在障碍物环境中运动的最优路径,并通过改变内部质量块的驱动参数实现了移动系统的避障运动.     

HYDRODYNAMIC RESISTANCE EFFECT OF FLUID LAYER BETWEEN TWO IMMERSED APPROACHING PARTICLES

1. Introduction The mechanisms of impact and rebound of solid parti- cles in particulate flow systems are of interest over a wide range of application areas such as fluidized beds, pneu- matic transport, filtration processes, erosion and pollution control of suspended particles. In many cases, the colli- sions of particles against themselves and against walls may affect the properties of the mixture. Efforts have been made to describe the fundamental mechanics of particle collisions. The conta…