On the role of the Chezy frictional term near the shoreline

The behavior of the Chezy frictional term near the shoreline has been studied in detail. An asymptotic analysis valid for water depths going to zero clearly shows that the use of such a term implies a non-receding motion of the shoreline. This phenomenon is induced by a thin layer of water which, because of frictional forces, remains on the beach and keeps it wet seaward of the largest run-up. However, the influence of such a frictional layer of water on the global wave motion is very weak and practically negligible for most of the swash zone flow dynamics. The existence of a non-receding shoreline has led to some clarifications on the role of some ad-hoc tools used in numerical models for the prediction of the wet/dry interface.     

On the receptivity of the by-pass transition to the length scale of the outer stream turbulence

The effect of length scale on flat-plate by-pass boundary layer transition under free stream turbulence conditions has been investigated. Plane grids generated a constant value of 3 percent intensity turbulent fluctuations and five values of the dissipation length parameter in the range of 2.2 mm to 33.3 mm at 5 m/s flow velocity in the plane of the leading edge of the flat plate. The investigated boundary layer corresponds to the ERCOFTAC Test Case T3A+. Distributions of integral parameters as well as the statistical characteristics of the turbulent fluctuations were measured. They document a significant effect of turbulence length scale on the onset and the end of by-pass transition. It was found that the onset of the final stage of transition comes on later in `fine-grained' turbulence than in the case of large free stream turbulence length scale. At the same time, the extent of the transition region shortens with decreasing length scale. Nevertheless, the transition process terminates sooner in a flow with a large turbulence length scale than in a flow with a small one. An attempt has been made to describe these observations quantitatively.     

Reevaluation of the adhesive relationship between the tire and the soil

The author proved in an earlier article that the shear diagram is not in accord with its mechanical definition. The shear stress cannot be zero at the beginning of the initial rising portion of the curve. Shearing is not an increasing loading process, rather it is a limiting case to which a finite shear stress belongs. On the other hand the sheared surface varies under the tire. There are kinematic reasons for this. Points on the tire surface describe a looped cycloid and they slip in a backward direction (opposite to the direction of travel) while contacting the soil. Thus the driving force, which points in the direction of travel, is the product of the shear stress of finite magnitude and the sheared area. The latter increases proportionally with slip. The author describes his equation which is based on the principles discussed above. He supports his theory with a numerical example.     

Contribution to the improvement of the QUICK scheme for the resolution of the convection–diffusion problems

The present paper deals with the improvement of a QUICK scheme for the resolution of convection–diffusion problems. In order to avoid any unstability problems and to increase the convergence speed a new deferred correction is suggested. Checking the required stability criteria, benefits are taken from the accuracy of the central difference scheme when it is possible. Otherwise, a upwind scheme is introduced in the deferred correction term warranting the stability of the whole scheme. Tests have been carried out on a wall driven square cavity and on a buoyancy driven cavity. Comparisons have been achieved with reference data in order to assess the accuracy of the present scheme. Further comparison with other differentiation scheme demonstrate that the present formulation is fast and accurate.     

不可压缩粘性流动的CBS有限元解法

对于二维不可压缩粘性流动,首先通过坐标变换的方式得到了的不含对流项的NS方程,并给出了CBS有限元方法求解的一般过程。结合一类同时含有压力和速度的出口边界条件,对方腔顶盖驱动流、后向台阶绕流和圆柱绕流进行了计算。所得结果与基准解符合良好,验证了CBS算法对于定常、非定常粘性不可压缩流动问题的可行性和所用出口边界条件的无反射特性。特别的,对于圆柱绕流,Re=100时非定常升、阻力系数及漩涡脱落等非定常都得到了较好地模拟,为一进步研究自激振动等更加复杂的非定常流动问题奠定了基础。     

On the interaction between the input signal and the singularity expansion method

For transient excitation, it is well known that the Singularity Expansion Method (SEM) is a late time technique that is not in general suitable for early time. Lossy dielectric slab studies, with bounded integrable finite-duration input signal, have shown that the SEM representation for early time requires an additional branch cut contribution and a modification of the SEM series for completeness. Other researchers indicated that the SEM representation is not complete for most cases of practical interest and that it may not converge for early time. In this paper, we present an approach, using the input signal, to obtain a convergent SEM series that is valid for early as well as for late time. In this approach the branch cut contribution is not needed and instead we have pole contributions form the input signal and a modified SEM series. In addition, two forms of SEM representations will be presented, the traditional form and the time varying coupling coefficient form. Furthermore, the interaction and the effect of the input signal choice on the SEM representation will be clarified. This will be done for a dielectric slab backed by a perfect conductor.     

光测力学技术：连接虚拟空间和现实世界的纽带

在轿车的整个开发过程中，零部件、总成和整车产品都必须根据试验结果验证和优化，在轿车开发的过程中测试技术是连接设计师思维空间和现实空间的纽带，现代光学测试技术以数字图象数据处理技术为基础，融汇贯通高速宽带数字采样、数据库和数据自动分析以及计算机智能工程及专家系统等最新技术，巧妙应用于轿车开发过程，在满足计算机虚拟开发工程对测试技术新要求的同时，还可以优化轿车开发程序，提高开发质量，本文以作者多年来在德国轿车开发部门主持的现代测试技术项目的实例介绍采用光测技术解决开发程序中的问题的构想，方法和手段。     

On the criterion for the absolute stability of the control system

In this paper, firstly we give the criterion for the absolute stability of the second canonical form for the control system, including the equation of the longitudinal motions of a plane as a particular example. The corresponding result in [8], [9] is a particular example given in this paper. Secondly, we give the criteria for the absolute stability of the first canonical form in the usual case and in the critical case. Finally, we give some criteria for the absolute stability of the general form for the direct control system.All the results in this paper merely depend upon the relations between the parameters of the system itself to give an explicit algebraic discriminant.     

On the size of the hysteresis in pseudoelasticity

Pseudoelasticity is a phenomenon that occurs in alloys with shape memory: In a loading-unloading cycle a body will return to its original configuration, but its path in a load-deformation diagram will run through a hysteresis loop.Pseudoelastic behaviour can be modelled by statistical mechanics which produces a non-monotone load-deformation isotherm. Once such a nonmonotone curve has been calculated there is the possibility of a phase transition that is connected with a hysteresis loop.The paper describes a method for the calculation of the width of the hysteresis. It comes to the conclusion that this width is determined by the interfacial energy associated with domain boundaries between the phases. The bigger that energy is the bigger is the hysteresis loop.     

Singularities of the boundary layer equations and the structure of the flow in the vicinity of the convergence plane on conical bodies

The singularities of the boundary layer equations and the laminar viscous gas flow structure in the vicinity of the convergence plane on sharp conical bodies at incidence are analyzed. In the outer part of the boundary layer the singularities are obtained in explicit form. It is shown that in the vicinity of a singularity a boundary domain, in which the flow is governed by the shortened Navier-Stokes equations, is formed; their regular solutions are obtained. The viscous-inviscid interaction effect predominates in a region whose extent is of the order of the square root of the boundary layer thickness, in which the flow is described by a two-layer model, namely, the Euler equations in the slender-body approximation for the outer region and the three-dimensional boundary layer equations; the pressure is determined from the interaction conditions. On the basis of an analysis of the solutions for the outer part of the boundary layer it is shown that interaction leads to attenuation of the singularities and the dependence of the nature of the flow on the longitudinal coordinate, but does not make it possible to eliminate the singularities completely.     

On the dynamics of the fluid balancer

This paper is concerned with the dynamics of a so-called fluid balancer; a hula hoop ring-like structure containing a small amount of liquid which, during rotation, is spun out to form a thin liquid layer on the outermost inner surface of the ring. The liquid is able to counteract unbalanced mass in an elastically mounted rotor. The paper derives the equations of motion for the coupled fluid–structure system, with the fluid equations based on shallow water theory. An approximate analytical solution is obtained via the method of multiple scales. For a rotor with an unbalance mass, and without fluid, it is well known that the unbalance mass is in the direction of the rotor deflection at sub-critical rotation speeds, and opposite to the direction of the rotor deflection at super-critical rotation speeds (when seen from a rotating coordinate system, attached to the rotor). The perturbation analysis of the problem involving fluid shows that the mass center of the fluid layer is in the direction of the rotor deflection for any rotation speed. In this way a surface wave on the fluid layer can counterbalance an unbalanced mass.     

An attempt to localize the sound sources in a turbulent jet using the results of the measurements of the acoustic field and the velocity fluctuation correlations

A model of noise generation in the mixing layer of a jet is proposed on the basis of the measurements of the acoustic radiation of a free jet by means of a microphone system, which makes it possible to determine the location of sources of sound at a given frequency, and hot-wire measurements of the velocity of the motion of vortices of given dimensions in the mixing layer. It is shown that the acoustic wave generation can be attributed to turbulence intermittence in the jet, that is, an unsteady motion of a region occupied by a “turbulent fluid”. As a result, an unsteady motion of the air ejected by the jet produces acoustic waves.     

On the structure of the theory of viscoplasticity

In various formulations of plasticity, there is evident a structure embracing several features, including inviscidity, a yield condition, and a constitutive inequality. By means of these features the constitutive equations of plasticity are derived. In the present paper we introduce a viscoplastic counterpart of the constitutive inequality of plasticity, and we consider its physical significance. We also present a theory of viscoplasticity having a structure similar to that of plasticity and its relation with the Hohenemser-Prager prototype of viscoplastic constitutive relations is considered.     

On a Fluid-Structure Model in Which the Dynamics of the Structure Involves the Shear Stress Due to the Fluid

In this paper we consider a model for fluid-structure interaction. The hybrid system describes the interaction between an incompressible fluid in a three-dimensional container with interior a fixed domain and a thin elastic plate, the interface, which coincides with a flexible flat part of the surface of the vessel containing the fluid. The motion of the fluid is described by the linearized Navier–Stokes equations and the deformation of the plate by the classical plate equations for in-plane motions, modified to include the viscous shear stress which the fluid exerts on the plate as well as damping of Kelvin–Voigt type. We establish the existence of a unique weak solution of the interactive system of partial differential equations by considering an appropriate variational formulation. Uniform stability of the energy associated with the model is shown under the assumption that the potential plate energy is dominated by the dissipation induced by the viscosity of the fluid. The retention of the physical parameters in the problem is an a priori requirement in this physical condition.      

Nonlinear oscillations of a pendulum cable with the effects of the friction and the radius of the support

Nonlinear Dynamics - The dynamics of a pendulum cable with a special constitutive law subjected to a time-dependent velocity is investigated. The Coulomb friction between the cable of pendulum and...     

On the Control of the Friction Force

This paper tackles the problem of controlling the Coulomb friction force in order to achieve damping characteristics which can be advantageous in engineering applications, particularly in the area of vibration control, for example, vehicle suspensions, rotating machinery foundations or earthquake protection systems. The control schemes employed belong to the family of variable structure controllers (VSC), a class of robust control algorithms, namely sliding mode control (SMC) and switched state feedback (SSF). The schemes perform force tracking control, aiming at making the friction force track a reference force in order to reduce the acceleration experienced by a suspended mass. The plant investigated is a 2-degree of freedom system and in this study represents a quarter car. The controller performances are investigated both numerically and experimentally.     

On the theory of the vibropump

The problem of vibratory lifting of a fluid was considered in [1] on the assumption of incompressibility of the pump tubing. In the present paper account is taken of the elasticity of the tubing materal. This leads to the consideration of forced oscillation regimes in two elastic media coupled by nonlinear conditions on one of the boundaries. In this case there is an ambiguity in the relations between the unknowns and governing quantities which leads to a hysteresis effect.     

On the singularity index and the unfolding of the diffraction catastrophes

The caustics of high-frequency wave propagation may be classified using catastrophe theory. The wavefield in the vicinity of any caustic is described by the corresponding diffraction catastrophe. The singularity index, β, is a measure of the rate at which such a wavefield diverges as ω→∞ at the point where all control parameters and moduli are set equal to zero. It is shown that away from this point β also describes a balance between two different measures of the unfolding of the wavefield in each control direction, β = σ_nϱ_n. The indices σ_n and ϱ_n describe, respectively, the rate at which individual ray arrivals separate in time and decay as a function of control parameter.     

Spectral Properties of the Linearization at the Burgers Vortex in the High Rotation Limit

We study a linearized operator of the equation for the axisymmetric Burgers vortex which gives a stationary solution to the three dimensional Navier–Stokes equations with an axisymmetric background straining flow. It is numerically known that the Burgers vortex obtains better stabilities as the circulation number (or the vortex Reynolds number) is increasing. Although the global stability of the axisymmetric Burgers vortex is already proved rigorously, mathematical understanding of this numerical observation has been lacking. In this paper we study a linearized operator that includes the circulation number as a parameter, and prove that if the operator is restricted on a suitable invariant subspace, then its spectrum moves to the left as the circulation number goes to infinity. As an application, we show that the axisymmetric Burgers vortex with a high rotation has a better stability, in the sense that the non-radially symmetric part of solutions to the associated evolution equation decays faster in time if the circulation number is sufficiently large.