On oscillations of a frictional pendulum

Conditions are established under which a standard limit cycle occurs in the system under consideration, or the trajectory closes under the influence of a stagnation domain. It is pointed out that when the solution falls into the stagnation domain it makes no sense to use the asymptotic method because of a large error __________ Translated from Prikladnaya Mekhanika, Vol. 42, No. 2, pp. 104–112, February 2006.     

On the shoreline boundary conditions for Boussinesq‐type models

We propose and illustrate a novel type of shoreline boundary conditions for Boussinesq‐type models. On the basis of characteristic equations of the non‐linear shallow water equations, boundary conditions are developed equations that can suitably model the motion of the instantaneous shoreline. Such boundary conditions are then implemented in a numerical solver for a specific set of Boussinesq‐type equations, which have been proved very effective for near‐shore modelling. Finally, a number of tests are performed to validate and illustrate the behaviour of the new conditions. Copyright © 2001 John Wiley & Sons, Ltd.     

The elastic field near a point of a transition from frictional contact to frictionless contact

The asymptotic nature of the elastic field is studied at the point of transition from frictional contact to frictionless contact between two different elastic bodies. The nature depends on the direction of slip, and the singular stress field appears when the body with smaller /(–1) (: the shear modulus, =3–4, : Poisson's ratio) slips towards the region of frictional contact, while no singularities appear when the direction of slip is opposite. The order of the singularity is smaller than 1/2 regardless of the level of friction.     

On the dynamic vibrations of an elastic beam in frictional contact with a rigid obstacle

Existence and uniqueness results are established for weak formulations of initial-boundary value problems which model the dynamic behavior of an Euler-Bernoulli beam that may come into frictional contact with a stationary obstacle. The beam is assumed to be situated horizontally and may move both horizontally and vertically, as a result of applied loads. One end of the beam is clamped, while the other end is free. However, the horizontal motion of the free end is restricted by the presence of a stationary obstacle and when this end contacts the obstacle, the vertical motion of the end is assumed to be affected by friction. The contact and friction at this end is modelled in two different ways. The first involves the classic Signorini unilateral or nonpenetration conditions and Coulomb's law of dry friction; the second uses a normal compliance contact condition and a corresponding generalization of Coulomb's law. In both cases existence and uniqueness are established when the beam is subject to Kelvin-Voigt damping. In the absence of damping, existence of a solution is established for a problem in which the normal contact stress is regularized.The work of the last two authors was supported in part by Oakland University Research Fellowships.     

On the interaction of frictional formulations with bifurcation phenomena in hyperelastic steady state rolling calculations

A finite element formulation for hyperelastic steady state rolling of inflated tires is analyzed. In particular, numerical difficulties associated with enforcing frictional conditions within such a framework are discussed. We focus in this work on adherent (i.e., no slip) friction formulations, and in addition to analyzing the numerical difficulties associated with such problems, we also study the interaction of frictional conditions with bifurcation phenomena. Such phenomena are observed in the context of multiple solutions (both stable and unstable) of the discretized system, and are also manifested in the behavior of the iterative map used to solve the nonlinear algebraic system of equations.     

Non-uniform frictional sliding under cyclic loading with frictional characteristics changing in the process of sliding

Frictional sliding on a crack with non-uniform frictional characteristics is considered. The present work continues the investigation of Gorbatikh et al. [Int. J. Solids Struct., in press] and focuses on the cyclic loading. The evolution of the sliding process in loading–reloading–unloading cycles is analyzed. We also extend the analysis to the important case when the frictional resistance changes in the process of sliding (such changes may model “degradation” of the sliding surface during sliding, as well as other physical factors, not necessarily related to the sliding itself).     

On the synthesis of acoustic sources with controllable near fields

In this paper we present a strategy for the synthesis of acoustic sources with controllable near fields in free space and constant depth homogeneous ocean environments. We first present the theoretical results at the basis of our discussion and then, to illustrate our findings we focus on the following three particular examples:

• 1.acoustic source approximating a prescribed field pattern in a given bounded sub-region of its near field.
• 2.acoustic source approximating different prescribed field patterns in given disjoint bounded near field sub-regions.
• 3.acoustic source approximating a prescribed back-propagating field in a given bounded near field sub-region while maintaining a very low far field signature.

For each of these three examples, we discuss the optimization scheme used to approximate their solutions and support our claims through relevant numerical simulations.     

On the uncertainty of digital PIV and PTV near walls

The reliable measurement of mean flow properties near walls and interfaces between different fluids or fluid and gas phases is a very important task, as well as a challenging problem, in many fields of science and technology. Due to the decreasing concentration of tracer particles and the strong flow gradients, these velocity measurements are usually biased. To investigate the reason and the effect of the bias errors systematically, a detailed theoretical analysis was performed using window-correlation, singe-pixel ensemble-correlation and particle tracking evaluation methods. The different findings were validated experimentally for microscopic, long-range microscopic and large field imaging conditions. It is shown that for constant flow gradients and homogeneous particle image density, the bias errors are usually averaged out. This legitimates the use of these techniques far away from walls or interfaces. However, for inhomogeneous seeding and/or nonconstant flow gradients, only PTV image analysis techniques give reliable results. This implies that for wall distances below half an interrogation window dimension, the singe-pixel ensemble-correlation or PTV evaluation should always be applied. For distances smaller than the particle image diameter, only PTV yields reliable results.     

On constructing the theory of ductile fracture near friction surfaces

A criterion of ductile fracture is proposed, which takes into account the singular character of theoretical solutions near the maximum friction surfaces and the emergence of a thin layer with intense plastic strains near surfaces with high friction stresses in real processes of metal forming. The equation for the thickness of the layer with intense plastic strains and the fracture criterion include the strain rate intensity factor, apparently, characterizing the intensity of physical processes that occur in a thin material layer near the friction surfaces. Some experimental data are used to determine the thickness of this layer. The ductile fracture criterion is analyzed by solving the problem of strip extrusion under conditions of plane strain deformation.     

关于"多胞材料"和"点阵材料"的一点意见

近年来,新型的结构材料和功能材料层出不穷,有关的新名词术语也极待厘定．