微极热弹性无限板的轴对称自由振动

研究了在应力自由和刚性固定边界条件下,无能量耗散的均匀、各向同性微极热弹性无限板的轴对称自由振动波的传播,导出了相应的对称和斜对称模态波传播的闭合式特征方程和不同区域的特征方程.对短波的情况,应力自由热绝缘和等温板中对称和斜对称模态波传播的特征方程退化为Rayleigh表面波频率方程.根据导出的特征方程得到了热弹性、微极弹性和弹性板的结果.在对称和斜对称运动中计算了板的位移分量幅值、微转动幅值和温度分布,给出了对称和斜对称模式的频散曲线,并示出了位移分量和微转动幅值和温度分布的曲线.能够发现理论分析和数值结论是非常一致的.     

The Structure of Dispersion Relation in Hyperbolic Thermoelasticity

For a system of field equations of hyperbolic thermoelasticity we derive a propagation condition for a thermoelastic disturbance in a form of homogeneous plane wave in deformation and temperature. The corresponding dispersion relation is given in an explicit form, together with the discussion of di.erent types of homogeneous thermoelastic plane waves that may emerge from the resulting system of coupled PDEs.     

On a micro‐macro model for polymeric fluids near equilibrium

In this paper, we study a micro‐macro model for polymeric fluid. The system involves coupling between the macroscopic momentum equation and a microscopic evolution equation describing the combined effects of the microscopic potential and thermofluctuation. We employ an energetic variation procedure to explore the relation between the macroscopic transport of the particles and the induced elastic stress due to the microscopic structure. For the initial data not far from the equilibrium, we prove the global existence and uniqueness of classical solutions to the system. © 2006 Wiley Periodicals, Inc.     

具有立方对称性及两个弛豫时间的微极热弹性介质中调和时间源引起的变形

研究了具有立方对称性及两个弛豫时间的微极热弹性介质在调和时间源中的响应．采用了Fourier变换以及数值逆变换技术．在物理域中,得到了位移、应力、微转动和温度分布的数值结果．将微极立方晶体法向位移、法向力应力、切向耦合应力和温度分布的计算结果,与微极各向同性固体的结果进行比较．绘制了指定材料的数值结果图形．还推断了某些特殊情况的结果．     

格栅夹层梁热弯曲的等效微极热弹性分析

将格栅夹层梁热弯曲等效为微极热弹性梁的受热变形,利用平面微极热弹性理论建立了微极梁受热变形的控制方程组,给出了温度载荷下微极梁的位移表达式.通过胞元能量等效的方法,得到了研究的格栅夹层梁等效微极热弹性梁材料参数.对比了等效微极梁模型和ANSYS有限元软件计算得到的温度载荷下悬臂格栅夹层梁受热弯曲变形的数值结果,两种方法得到的结果非常接近,证明了微极热弹性梁是一种简单有效的模拟格栅夹层梁热变形的等效模型.     

Effect of micro-inertia in the propagation of waves in micropolar thermoelastic materials with voids

The effect of micro-inertia in the propagation of waves in micropolar thermoelastic materials with voids has been investigated. Elastic waves are reflected due to incident coupled longitudinal and coupled shear waves from a plane free boundary of micropolar thermoelastic materials with voids. The amplitude ratios corresponding to the reflected coupled longitudinal and coupled shear waves are derived by using appropriate boundary conditions. Energy partition in the free surface has been presented. The amplitude and energy ratios of the reflected waves are also computed numerically for a particular model.     

热传导的微极固体和流体介质界面上波的传播

研究微极广义热弹性固体半空间和热传导微极流体半空间界面上波的传播.讨论微极广义热弹性固体半空间和热传导微极流体半空间之间平面界面上,斜向入射平面波的反射和透射现象.假设入射波穿过微极广义热弹性固体,射向平面界面后传播.得到了封闭形式的、不同反射和透射波的波幅比,它们是入射角、频率的函数,并为介质的弹性性质所影响.对一些特定的类型,显示出微极和热松弛对波幅比的影响.还从本文的研究中推演出一些早期工作的结果.     

Steady flows of Cosserat–Bingham fluids

The equations describing the steady flow of Cosserat–Bingham fluids are considered, and existence of weak solution is proved for the three‐dimensional boundary‐value problem with the use of the Lipschitz truncation argument. In contrast to the classical Bingham fluid, the micropolar Bingham fluid supports local micro‐rotations and two types of plug zones. Our approach is based on an approximation of the constitutive relation by a generalized Newtonian constitutive relation and a subsequent limiting process. Copyright © 2016 John Wiley & Sons, Ltd.     

Global existence and exponential stability for a nonlinear thermoelastic Kirchhoff–Love plate

We study an initial–boundary-value problem for a quasilinear thermoelastic plate of Kirchhoff & Love-type with parabolic heat conduction due to Fourier, mechanically simply supported and held at the reference temperature on the boundary. For this problem, we show the short-time existence and uniqueness of classical solutions under appropriate regularity and compatibility assumptions on the data. Further, we use barrier techniques to prove the global existence and exponential stability of solutions under a smallness condition on the initial data. It is the first result of this kind established for a quasilinear non-parabolic thermoelastic Kirchhoff & Love plate in multiple dimensions.     

Surface waves in micropolar thermoelasticity

Free surface waves of arbitrary form in a homogeneous and isotropic linear micropolar thermoelastic half-space with stress-free plane boundary are investigated. It is found that all physical quantities associated with the waves are derivable from two scalar functions and that there exist two families of waves in general. One of these is the classical thermoelastic wave modified under the influence of the microelastic field and the other is a new surface wave not encountered in classical elasticity. The waves are not necessarily plane waves and even when these are assumed to propagate in a fixed direction parallel to the boundary, unlike in classical elasticity, the problem is not one of plane strain. Explicit expressions for the displacement vector, microrotation vector and the temperature are obtained and the nature of deformation has been analysed. Several earlier results are deduced as particular cases of the more general results obtained here.     

Wave propagation in a micropolar generalized thermoelastic body with stretch

In the present investigation, we discuss two different problems namely

1. Rayleigh-Lamb problem in micropolar generalized thermoelastic layer with stretch and
2. Rayleigh wave in a micropolar generalized thermoelastic half-space with stretch. The frequency and wave velocity equations for symmetric and anti-symmetric vibrations are obtained for the first problem. The frequency equation has also been derived for the second problem. The special cases of the above said problems of micropolar generalized thermoelasticity with stretch for Green-Lindsay and Lord-Shulman theory have been discussed in detail. Results of these analysis reduce to those without thermal and stretch effects

     

Longitudinal track-bridge interaction due to loading sequences

For continuously welded rails the longitudinal track–bridge interaction plays an important role. The coupling between track and bridge consists of a ballasted interface or a slab track with rail–pads. European codes describe this coupling by means of a bilinear force–displacement relation with making a difference wether the track is loaded or not. This contribution is focussed on an incremental treatment of the long–term loading from seasonal temperature–change followed by several cycles unloaded–loaded–unloaded due to passing trains. As one cycle happens in a rather short time, the mass accelerations are involved, too. The load–character of the coupling–variation will be explained and a comparison between a statical and a dynamical treatment will be presented. (© 2008 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim)     

On the constitutive inequalities and acceleration waves in micropolar media

Acceleration waves in nonlinear thermoelastic micropolar media are considered. We establish the kinematic and dynamic compatibility relations for a singular surface of order 2 in the media. An analogy to the Fresnel–Hadamard–Duhem theorem and an expression for the acoustic tensor are derived. The condition for acceleration wave's propagation is formulated as an algebraic spectral problem. It is shown that the condition coincides with the strong ellipticity of equilibrium equations. (© 2008 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim)     

A Study of Linear Waves Based on Extended Thermodynamics for Rarefied Polyatomic Gases

We study the dispersion relation for sound in rarefied polyatomic gases basing on the recently developed theory of extended thermodynamics (ET) for both dense and rarefied polyatomic gases. For hydrogen and deuterium gases in a wide temperature range where the rotational and vibrational modes in a molecule play a role, we compare the dispersion relations with those obtained in experiments and by the classical Navier–Stokes Fourier theory. From the comparison with experiments, we estimate the bulk viscosity and evaluate its temperature dependence. We study the characteristics of attenuation in a gas which has a larger relaxation time related to the dynamic pressure than the other relaxation times related to the shear stress and the heat flux by adopting the ET theory with 6 fields.     

Exploitation of Configurational Forces in Extended Nonlocal Continua with Microstructure

We investigate aspects of the application of configurational forces in extended nonlocal continua with microstructure. Focussing on multifield approaches to gradient–type inelastic solids, the coupled problem is governed by the macroscopic deformation field, while nonlocal inelastic effects on the microstructure are described by a family of order parameter fields. The dual macro– and micro–field equations are derived within an incremental variational framework. Using an incremental principle, due to the variation with respect to the material position, an additional balance in the material space appears with the dual macro–micro–balances in the physical space. In view of the numerical implementation of this coupled problem by a finite element method, the incremental variational framework is recast into a discrete format in terms of discrete macro– and micro–physical nodal forces and configurational nodal forces. Applying a staggered solution scheme, the configurational branch is used as a postprocessing procedure with all the ingredients known from the solution of the coupled macro–micro–problem. The procedure is implemented for a nonlocal, viscous damage model. The consequences with regard to the configurational nodal forces are assessed by means of a numerical example. (© 2008 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Analytic approximate solutions for heat transfer of a micropolar fluid through a porous medium with radiation

This paper aims to present complete analytic solution to heat transfer of a micropolar fluid through a porous medium with radiation. Homotopy analysis method (HAM) has been used to get accurate and complete analytic solution. The analytic solutions of the system of nonlinear ordinary differential equations are constructed in the series form. The convergence of the obtained series solutions is carefully analyzed. The velocity and temperature profiles are shown and the influence of coupling constant, permeability parameter and the radiation parameter on the heat transfer is discussed in detail. The validity of our solutions is verified by the numerical results (fourth-order Runge–Kutta method and shooting method).     

分数阶热弹理论下重力场对二维纤维增强介质的影响

基于Sherief等提出的分数阶广义热弹性耦合理论,研究了在热冲击作用下二维纤维增强弹性体的热弹性问题.考虑了重力对二维纤维增强线性热弹性各向同性介质的影响,建立了控制方程.运用正则模态法,经过数值计算,对控制方程进行求解,得到了不同分数阶参数和不同重力场下无量纲温度、位移和应力分量的表达式,以图形的方式展示了变量的分布规律并对结果展开了讨论.研究结果为:重力场和分数阶参数对纤维增强介质的位移及应力有着重要的影响,但对温度的影响有限.     

On representations of a general solution in the theory of micropolar thermoelasticity without energy dissipation

In the present paper, the linear theory of micropolar thermoelasticity without energy dissipation is considered. This work is organized as follows: Section 2 is devoted to basic equations for micropolar thermoelastic materials, supposed to be isotropic and homogeneous, and to assumptions on constitutive constants. In Section 3, some theorems related to representations of a general solution are studied. Published in Ukrains’kyi Matematychnyi Zhurnal, Vol. 59, No. 10, pp. 1391–1398, October, 2007.     

Numerical simulation for natural convection of micropolar fluids flow along slender hollow circular cylinder with wall conduction effect

This paper presents a numerical analysis of the flow and heat transfer characteristics of natural convection in a micropolar fluid flowing along a vertical slender hollow circular cylinder with conduction effects. The nonlinear formulation governing equations and their associated boundary conditions are first cast into dimensionless forms by a local non-similar transformation. The resulting equations are then solved using the cubic spline collocation method and the finite difference scheme. This study investigates the effects of the conjugate heat transfer parameter, the micropolar parameter, and the Prandtl number on the flow and the thermal fields. The conjugate heat transfer parameter reduces the solid–liquid interfacial temperature, the skin friction factor and the local heat transfer rate. The effect of wall conduction on the local heat transfer rate, interfacial temperature and skin friction factor is found to be more pronounced in a system with a greater Prandtl number. Moreover, the current results are comparing with Newtonian fluid to obtain the important results of the heat transfer and flow characteristics on micropolar fluids. It shows that an increase in the interfacial temperature, a reduction in the skin friction factor, and a reduction in the local heat transfer rate are identified in the current micropolar fluid case.