Damping by dry friction of dynamic loads in a fiber-reinforced composite

Conclusions The accurate analytical solutions of a number of nonlinear problems of impacts on semiinfinite and finite fibers, interacting with the matrix in accordance with the dry friction law, were obtained. We examined the cases of both unidirectional motions and reversed motions caused by unloading, and also oscillatory motions. The results can be used to calculate the energy dissipated in the separating sections of the composite in shock effects. It was shown that the amount of energy dissipated in the dynamic effect is considerably greater than in the quasistatic effect. Thus, dissipation in the system with friction depends strongly on the nature of load application with time.Translated from Mekhanika Kompozitnykh Materialov, No. 1, pp. 28–37, January–February, 1986.     

The Small Deborah Number Limit of the Doi‐Onsager Equation to the Ericksen‐Leslie Equation

We present a rigorous derivation of the Ericksen‐Leslie equation starting from the Doi‐Onsager equation by the Hilbert expansion method. The existence of the Hilbert expansion is related to an open question of whether the energy of the Ericksen‐Leslie equation is dissipated. On this point, we show that the energy is dissipated for the Ericksen‐Leslie equation derived from the Doi‐Onsager equation. The most difficult step is to prove a uniform bound for the remainder of the Hilbert expansion. This step is connected to the spectral stability of the linearized Doi‐Onsager operator around a critical point and the lower bound estimate for a bilinear form associated with the linearized operator. By introducing two important auxiliary operators, we can obtain the detailed spectral information for the linearized operator around all the critical points. We establish a precise lower bound of the bilinear form by introducing a five‐dimensional space called the Maier‐Saupe space.© 2015 Wiley Periodicals, Inc.     

Dissipated compacta

The dissipated spaces form a class of compacta which contains both the scattered compacta and the compact LOTSes (linearly ordered topological spaces), and a number of theorems true for these latter two classes are true more generally for the dissipated spaces. For example, every regular Borel measure on a dissipated space is separable.The standard Fedor?uk S-space (constructed under ?) is dissipated. A dissipated compact L-space exists iff there is a Suslin line.A product of two compact LOTSes is usually not dissipated, but it may satisfy a weakening of that property. In fact, the degree of dissipation of a space can be used to distinguish topologically a product of n LOTSes from a product of m LOTSes.     

Global existence and decay of smooth solution for the 2-D MHD equations without magnetic diffusion

We prove the global existence and the decay estimates of small smooth solution for the 2-D MHD equations without magnetic diffusion. This confirms the numerical observation that the energy of the MHD equations is dissipated at a rate independent of the ohmic resistivity.     

A mathematical study of energy dissipation due to atrioventricular valve vibration

A mathematical model of the dynamic response of atrioventricular valve leaflets to the systolic pressure pulse is used to calculate the resultant energy dissipation under the action of viscous damping. The energy dissipated from mitral and tricuspid leaflets is compared, and the effects of leaflet size, closing velocity, the magnitude of the damping force, and the rate of change of the atrioventricular pressure gradient are investigated. The results are interpreted in relation to experimentally documented first heart sound determinants.     

Energy Dissipated Across Shocks in Weak Solutions of Conservation Laws

Manipulation of conservation laws through multiplication by mappings of the unknown function result in singular terms that are densities supported on the discontinuity locus. We derive an expression for these singular terms which have been interpreted as the energy dissipated at the shocks. As an application, the expression for these singular terms is obtained from the transport equation governing the propagation of small amplitude high frequency waves in hyperbolic conservation laws. Analogous formulas are obtained for rich systems in several space dimensions.     

Mixed integer formulations for the probabilistic minimum energy broadcast problem in wireless networks

In this paper we study a new variant of the minimum energy broadcast (MEB) problem, namely the probabilistic MEB (PMEB). The objective of the classic MEB problem is to assign transmission powers to the nodes of a wireless network is such a way that the total energy dissipated on the network is minimized, while a connected broadcasting structure is guaranteed by the assigned transmission powers. In the new variant of the problem treated in this paper, node failure is taken into account, aiming at providing solutions with a chosen reliability level for the broadcasting structure. Three mixed integer linear programming formulations for the new problem are presented, together with efficient formulation-dependent methods for their solution. Computational results are proposed and discussed. One method emerges as the most promising one under realistic settings. It is able to handle problems with up to fifty nodes.     

Nonequilibrium Statistical Thermodynamics of Two Dissipative Processes in Solids: Energy Losses of Channeled Particles at Low Velocities and Ultrasound Absorption by Conduction Electrons

We use methods of nonequilibrium statistical thermodynamics to investigate two dissipative processes in solids. We find the electron energy losses of a particle moving in a planar channeling regime and the sound absorption coefficient in metals under electron impurity scattering. The oscillator model is used to analyze the contribution from the effect of electron entrainment by a moving scattering center to the total dissipated energy. We investigate the frequency and temperature dependence of energy losses and also the dependence of the absorption coefficient on the sound wave vector.     

Inverse analysis of a non-linear viscous fluid based on dissipated energy measured with a simple-shear rheometer

Oscillatory rheometer measurements are used to determine the material parameters of a NEWTONian fluid model, which can be expressed by a linear constitutive relation. However, rheological materials, such as polymer melts, mixture of oils, or food paste, can only be modeled as non-NEWTONian fluids by using non-linear constitutive relations. Since the rheometer measures the energy loss in the induction motor due to shear loading of the viscous material, this can be used as the objective function for a regression analysis. The dissipated energy will be obtained as outlined in [1]. The goal of this work is to explain how to determine the parameters of a non-linear material model by using the energy loss that is measured in a rheometer. (© 2013 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Numerical Analysis of a Cyclical Loaded Construction under Corrosion Degradation

A contribution for analytical and numerical tools that permits of a deterministic evaluation of structure behavior in external conditions, under multiparameter and/or cyclic mechanical, thermal and chemical loads, is the aim of this paper. Particular structure elements undergo the plastic and corrosion degradation and they dissipate energy, which consists of irreversible contributions, like a work on the inelastic strains. The construction and its unit lifetime are estimated according to a dissipated energy criterion. The paper emphasizes the modeling and numerical implementation of degradation effects, such as cyclic plasticity, generated by mechanical and thermal loads, stress corrosion, electrochemical corrosion and low-cyclic corrosion. (© 2005 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim)     

The optimal shape of a pipe

In shape optimization, recently the question arose, whether or not the cylindrical pipe has the optimal shape for the transport of an incompressible fluid. In this short note, a proof will be presented that a cylindrical pipe with Poiseuille’s flow inside indeed is optimal for the transportation of an incompressible fluid under the criterion “energy dissipated by the fluid.” The proof reduces the problem to the minimization of a two-dimensional Dirichlet’s integral. This simpler problem can be solved with a symmetrization argument.     

Numerical inaccuracies across the interface of a nested grid

This article addresses and discusses the inaccuracies in finite differencing across the interface of a nested grid. Explicit schemes for the advection and diffusion equations are analyzed on the fine and coarse grids and reformulated at the interface to guarantee that the evolving solution is unaffected by the abrupt change of the spatial grid resolution. The associated errors are expressed as a function of the wavelength of the initial field distribution and the ratio between the coarse and fine grid resolution. It is found that large-scale features of the coarse grid must supply energy to sustain the small-scale features of the fine grid. To not deplete the large-scale motion, a source of energy must be given at the interface in the form of a computational diffusive term with negative viscosity coefficient. On the other hand, not all the energy of the small-scale features of the fine grid has to be transferred to the large-scale motion, but some of it needs to be computationally dissipated at the interface. © 1994 John Wiley & Sons, Inc.     

圆形硐室岩爆机制及其突变理论分析

硐室岩爆机制是围岩中处于极限状态的塑性变形集中区承载能力下降时,其中完好岩体部分以弹性方式卸载,当后者释放的弹性能超过前者形变耗散的能量时便发生岩爆．以岩体等效应变为状态变量,建立了硐室岩爆的突变模型,给出岩爆释放地震能计算式．分析表明: 岩爆发生条件与岩体的升降模量比及岩体裂隙发育程度有关;对于特定冲击倾向的岩体,存在相应的临界软化区深度,当满足岩爆发生条件,且软化区深度达到临界深度时会发生岩爆．     

Finite element analysis of laminar and turbulent flows using LES and subgrid-scale models

Numerical simulations of laminar and turbulent flows in a lid driven cavity and over a backward-facing step are presented in this work. The main objectives of this research are to know more about the structure of turbulent flows, to identify their three-dimensional characteristic and to study physical effects due to heat transfer. The filtered Navier–Stokes equations are used to simulate large scales, however they are supplemented by subgrid-scale (SGS) models to simulate the energy transfer from large scales toward subgrid-scales, where this energy will be dissipated by molecular viscosity. Two SGS models are applied: the classical Smagorinsky’s model and the Dynamic model for large eddy simulation (LES). Both models are implemented in a three-dimensional finite element code using linear tetrahedral elements. Qualitative and quantitative aspects of two and three-dimensional flows in a lid-driven cavity and over a backward-facing step, using LES, are analyzed comparing numerical and experimental results obtained by other authors.     

Fractional Variational Approach for Dissipative Mechanical Systems

More recently, a variational approach has been proposed by Lin and Wang for damping motion with a Lagrangian holding the energy term dissipated by a friction force. However, the modified Euler-Lagrange equation obtained within their for- malism leads to an incorrect Newtonian equation of motion due to the nonlocality of the Lagrangian. In this communication, we generalize this approach based on the fractional actionlike variational approach and we show that under some simple restric- tions connected to the fractional parameters introduced in the fractional formalism, this problem may be solved.     

On the problem of dynamic contact angle

Plane motion of a viscous incompressible fluid bounded by a rectangular rigid wall and a free boundary of constant form is investigated. The free boundary is in contact with the rigid wall at a point which moves along the wall, coming into contact with it at a constant rate. The asymptotics of the velocity field near the point of contact is computed under the assumption that the motion is stationary in the coordinate system attached to the moving free boundary and, that the energy is dissipated as a finite rate.     

On the dissipation due to wave ringing in nonelliptic elastic materials

Summary Initial-boundary value problems describing the mechanics of nonelliptic elastic materials give rise to solutions that involve phase boundaries, the motion of which can dissipate mechanical energy. We investigate whether this dissipation, acting alone, can drive such a system toward equilibrium. Moving phase boundaries are regarded as a localized dissipative mechanism, and we consider a model which specifically excludes dissipation away from a phase boundary (such as that due to viscoelastic damping). In the problem under consideration, wave packets reverberate between the fixed external boundary and a single internal phase boundary. The phase boundary remains stationary unless it is acted upon by one of these wave packets, and each such interaction dissipates a finite amount of energy while causing the initiating wave packet to split into a reflected wave packet and a transmitted wave packet. Consequently, the number of wave packets increases in a geometric fashion. Each individual interaction of a wave packet with the phase boundary is, in a certain sense, mechanically underdetermined, and we augment the mechanical theory with two alternative energy criteria, each of which determines a different interaction dynamics. These alternative energy criteria are motivated by considerations of maximizing the energy dissipation in the system. We treat a system that is perturbed out of an initial minimum energy equilibrium state by a disturbance at the external boundary. A framework is developed for treating the resulting wave reverberations and calculating the energy dissipation for large time. Numerical computation indicates that the total energy dissipated in both versions of the dynamical problem is that which is necessary to settle into a new energy-minimal equilibrium state. We then establish the same result analytically for a meaningful limit involving a vanishingly small dynamical perturbation.     

Stability of critical shapes for the drag minimization problem in Stokes flow

We study the stability of some critical (or equilibrium) shapes in the minimization problem of the energy dissipated by a fluid (i.e. the drag minimization problem) governed by the Stokes equations. We first compute the shape derivative up to the second order, then provide a sufficient condition for the shape Hessian of the energy functional to be coercive at a critical shape. Under this condition, the existence of such a local strict minimum is then proved using a precise upper bound for the variations of the second order shape derivative of the functional with respect to the coercivity and differentiability norms. Finally, for smooth domains, a lower bound of the variations of the drag is obtained in terms of the measure of the symmetric difference of domains.     

A two-scale simulation method accounting for thermal effects during turning

During chip formation in turning processes, mechanical work is dissipated into thermal energy by plastic deformations and frictional processes. In case of dry cutting, the generated heat is in part removed with the chips while the rest flows into the tool and the workpiece. Within the latter, the temperature increases due to this heat flow, which in turn causes thermal expansions that increase the cutting depth and thus induce deviations from the nominal workpiece geometry. These effects are treated separately by a local model for the chip formation and a global model for the whole workpiece in order to determine the temperature distribution inside the workpiece and the dependent thermal expansion. (© 2014 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)     

电流变液中粒子成链机理的理论模型

建立了一理论模型用来解释在电场作用下电流变液中粒子集束成链的机理。通过假设在成链过程中释放的电磁能等于由于粘性流体而导致的能量耗散,建立了控制链长大的微分方程。基于这样的能量方程,可以预报成链的速度及电流变液的响应时间。该模型也预报了电场强度温度,以及诸如微粒的含量,介电常数等微结构参数对电流变液响应的影响。