Moving load response in micropolar thermoelastic medium without energy dissipation possessing cubic symmetry

The steady state response of a micropolar thermoelastic medium without energy dissipation possessing cubic symmetry due to a moving load has been studied. Fourier transform has been employed and the transform has been inverted by using a numerical inversion technique. The components of displacement, stress, microrotation and temperature distribution in the physical domain are obtained numerically. The results of normal displacement, normal force stress, tangential couple stress and temperature distribution have been compared for micropolar cubic crystal and micropolar isotropic solid. The numerical results are illustrated graphically for a particular material. Some special cases have also been deduced.     

Time harmonic sources at micropolar thermoelastic medium possessing cubic symmetry with one relaxation time

The response of a micropolar thermoelastic medium possessing cubic symmetry with one relaxation time due to time harmonic sources has been investigated. Fourier transform has been employed and the transform has been inverted by using a numerical inversion technique. The components of displacement, stress, microrotation and temperature distribution in the physical domain are obtained numerically. The results of normal displacement, normal force stress, tangential couple stress and temperature distribution have been compared for micropolar cubic crystal and isotropic micropolar solid. The numerical results are illustrated graphically for a particular material. Some special cases have also been deduced.     

Deformation in micropolar cubic crystal due to various sources

The response of a micropolar cubic crystal due to various sources has been studied. The eigenvalue approach using Laplace and Fourier transforms has been employed to solve the problem. The integral transforms have been inverted by using a numerical technique to obtain the displacement, microrotation and stress components in the physical domain. The results of normal displacement, normal force stress and tangential couple stress have been compared for micropolar cubic crystal and micropolar isotropic solid and illustrated graphically.     

Interactions due to mechanical/thermal sources in a micropolar thermoelastic medium possessing cubic symmetry

The present problem is the deformation of micropolar thermoelastic solids with cubic symmetry under the influence of various sources acting on the plane surface. Analytic expressions for displacement components, microrotation, force stress, couple stress, and temperature distribution are obtained in the physical domain for Lord–Shulman (L–S) and Green–Lindsay (G–L) theories of thermoelasticity by applying integral transforms. A numerical inversion technique has been applied to obtain the solution in the physical domain. The numerical results are presented graphically for a particular model.     

Axisymmetric free vibrations of infinite thermoelastic plate

The propagation of axisymmetric free vibrations in an infinite homogeneous isotropic micropolar thermoelastic plate without energy dissipation subjected to stress free and rigidly fixed boundary conditions is investigated. The secular equations for homogeneous isotropic micropolar thermoelastic plate without energy dissipation in closed form for symmetric and skew symmetric wave modes of propagation are derived. The different regions of secular equations are obtained. At short wavelength limits, the secular equations for symmetric and skew symmetric modes of wave propagation in a stress free insulated and isothermal plate reduce to Rayleigh surface wave frequency equation. The results for thermoelastic, micropolar elastic and elastic materials are obtained as particular cases from the derived secular equations. The amplitudes of displacement components, microrotation and temperature distribution are also computed during the symmetric and skew symmetric motion of the plate. The dispersion curves for symmetric and skew symmetric modes and amplitudes of displacement components, microrotation and temperature distribution in case of fundamental symmetric and skew symmetric modes are presented graphically. The analytical and numerical results are found to be in close agreement.     

Axisymmetric free vibrations of infinite micropolar thermoelastic plate

The propagation of axisymmetric free vibrations in an infinite homogeneous isotropic micropolar thermoelastic plate without energy dissipation subjected to stress free and rigidly fixed boundary conditions is investigated. The secular equations for homogeneous isotropic micropolar thermoelastic plate without energy dissipation in closed form for symmetric and skew symmetric wave modes of propagation are derived. The different regions of secular equations are obtained. At short wavelength limits, the secular equations for symmetric and skew symmetric modes of wave propagation in a stress free insulated and isothermal plate reduce to Rayleigh surface wave frequency equation. The results for thermoelastic, micropolar elastic and elastic materials are obtained as particular cases from the derived secular equations. The amplitudes of displacement components, microrotation and temperature distribution are also computed during the symmetric and skew symmetric motion of the plate. The dispersion curves for symmetric and skew symmetric modes and amplitudes of displacement components, microrotation and temperature distribution in case of fundamental symmetric and skew symmetric modes are presented graphically. The analytical and numerical results are found to be in close agreement.     

Effect of the thermal relaxation and magnetic field on generalized micropolar thermoelasticity

The model of generalized micropolar magneto-thermoelasticity for a thermally and perfectly conducting half-space is studied. The initial magnetic field is parallel to the boundary of the half-space. The formulation is applied to the generalized thermo-elasticity theories of Lord and Shulman, Green and Lindsay, as well as to the coupled dynamic theory. The normal mode analysis is used to obtain expressions for the temperature increment, the displacement, and the stress components of the model at the interface. By using potential functions, the governing equations are reduced to two fourth-order differential equations. By numerical calculation, the variation of the considered variables is given and illustrated graphically for a magnesium crystal micropolar elastic material. Comparisons are performed with the results predicted by the three theories in the presence of a magnetic field.     

RESPONSE OF MICROPOLAR THERMOELASTIC SOLID WITH VOIDS DUE TO VARIOUS SOURCES UNDER GREEN NAGHDI THEORY

Green-Naghdi (G-N) theory of thermoelasticity is employed to study the deformation of micropolar thermoelastic solid with voids considering the influence of varions sources acting on the plane surface....     

Moving heat source response in micropolar half-space with two-temperature theory

The present paper deals with the moving heat source response in a homogeneous, isotropic, micropolar semi-infinite medium in the presence of a finite rotation about its axis. In this context, two-temperature generalized thermoelasticity theory has been considered. In order to obtain the physical aspects of displacement, microrotation, stress distribution and temperature changes, a complex quartic equation has been solved by employing Descartes’ algorithm with the help of an irreducible Cardan’s method. To illustrate the analytical developments, the numerical solutions have been carried out for aluminum–epoxy composite, and the variations in displacement, microrotation, stress distribution and temperature changes have been shown graphically. This work may find applications in geophysics.     

Moving inclined load at boundary surface

Introduction Inmanyengineeringphenomenon,includingtheresponseofsolids,geologicalmaterialsand composites,theassumptionsofanisotropicbehaviormaynotcapturesomesignificantfeaturesof thecontinuumresponse.Theformulationandsolutionofanisotropicproblemsarefarmore difficultandcumbersomethanitsisotropiccounterpart.Inrecentyearstheelastodynamicresponse ofanisotropiccontinuumhasreceivedtheattentionofseveralresearchers.Inparticular, transverslyisotropicandorthotropicmaterials,whichmaynotbedistinguishedfrom…     

Free convection on a vertical plate with uniform and constant heat flux in a thermally stratified micropolar fluid

This paper analyzes flow and heat transfer characteristics of the free convection on a vertical plate with uniform and constant heat flux in a thermally stratified micropolar fluid. The dimensionless forms of boundary layer equations and their associated boundary conditions have been derived and the numerical results have been obtained using the method of cubic spline collocation with a finite difference scheme. The effects of the micropolar and stratification parameters on the dimensionless wall temperature, skin friction parameter and wall couple stress are discussed.     

Elastodynamic analysis at an interface of viscous fluid/thermoelastic micropolar honeycomb medium due to inclined load

In this paper, the effect of angle inclination at the interface of a viscous fluid and thermoelastic micropolar honeycomb solid due to inclined load is investigated. The inclined load is assumed to be a linear combination of normal load and tangential load. Laplace transform with respect to time variable and Fourier transform with respect to space variable are applied to solve the problem. Expressions of stresses, temperature distribution, and pressures in the transformed domain are obtained by introducing potential functions. The numerical inversion technique is used to obtain the solution in the physical domain. The frequency domain expressions for steady state are also obtained with appropriate change of variables. Graphic representations due to the response of different sources and changes of angle inclination are shown. Some particular cases are also discussed.     

RESTUDY OF COUPLED FIELD THEORIES FOR MICROPOLAR CONTINUA (Ⅰ)──MICROPOLAR THERMOELASTICITY

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A new micromechanical approach of micropolar continuum modeling for 2-D periodic cellular material

In this paper, we present a new united approach to formulate the equivalent micropolar constitutive relation of two-dimensional (2-D) periodic cellular material to capture its non-local properties and to explain the size effects in its structural analysis. The new united approach takes both the displacement compatibility and the equilibrium of forces and moments into consideration, where Taylor series expansion of the displacement and rotation fields and the extended aver-aging procedure with an explicit enforcement of equilibrium are adopted in the micromechanical analysis of a unit cell. In numerical examples, the effective micropolar constants obtained in this paper and others derived in the literature are used for the equivalent micropolar continuum simulation of cellular solids. The solutions from the equivalent analysis are compared with the discrete simulation solutions of the cellu-lar solids. It is found that the micropolar constants developed in this paper give satisfying results of equivalent analysis for the periodic cellular material.     

Homogenization of microsystem interconnects based on micropolar theory and discontinuous kinematics

In the present paper, the homogenized mechanical response of an interface in a microsystem interconnection is established on the basis of micropolar theory. The interface is treated as a finite RVE (representative volume element), across which macroscopic discontinuities occur as expressed in terms of the regularized discontinuous displacement and rotation fields. For the microstructure within the interfacial RVE, the micro-macro kinematical coupling is introduced as a second-order Taylor series expansion, along with a fluctuation term representing the microscopic displacement variation. In the second-order term of the expansion a restriction for the curvature is made, which motivates the adopted micropolar kinematics. Explicit expressions for the homogenized traction vector and the couple stress traction, associated with displacement and rotational jumps across the interface surface, are derived. A planar elastic interface is subjected to three basic deformation modes, i.e. the standard modes I, II and a non-conventional rotation mode, which are considered in the numerical examples representing a typical interconnect. A comparison to the results from the Taylor assumption is made, which shows that the Taylor assumption method produces an overstiffening of the interface.     

Transient wave analysis of a cantilever Timoshenko beam subjected to impact loading by Laplace transform and normal mode methods

This study applies two analytical approaches, Laplace transform and normal mode methods, to investigate the dynamic transient response of a cantilever Timoshenko beam subjected to impact forces. Explicit solutions for the normal mode method and the Laplace transform method are presented. The Durbin method is used to perform the Laplace inverse transformation, and numerical results based on these two approaches are compared. The comparison indicates that the normal mode method is more efficient than the Laplace transform method in the transient response analysis of a cantilever Timoshenko beam, whereas the Laplace transform method is more appropriate than the normal mode method when analyzing the complicated multi-span Timoshenko beam. Furthermore, a three-dimensional finite element cantilever beam model is implemented. The results are compared with the transient responses for displacement, normal stress, shear stress, and the resonant frequencies of a Timoshenko beam and Bernoulli–Euler beam theories. The transient displacement response for a cantilever beam can be appropriately evaluated using the Timoshenko beam theory if the slender ratio is greater than 10 or using the Bernoulli–Euler beam theory if the slender ratio is greater than 100. Moreover, the resonant frequency of a cantilever beam can be accurately determined by the Timoshenko beam theory if the slender ratio is greater than 100 or by the Bernoulli–Euler beam theory if the slender ratio is greater than 400.     

条形荷载下梯度非均匀非饱和土的动力响应分析

基于多孔介质混合物理论, 建立了梯度非均匀非饱和土地基模型, 研究了条形荷载作用下梯度非均匀非饱和土地基的动力响应问题. 通过傅里叶积分变换和Helmholtz矢量分解原理, 获得频域内非饱和土地基动力响应问题的通解, 结合回传射线矩阵法和边界条件, 求解获得了非均匀非饱和土层中位移、应力以及孔隙压力的计算列式. 假设沿深度方向梯度非均匀非饱和土的物理力学性质按幂函数连续变化, 通过数值傅里叶逆变换得到了非均匀非饱和土地基中的应力、位移以及孔隙压力等物理量的数值解, 分析讨论了土体非均匀性对非饱和土介质动力响应的影响规律. 结果表明: 土体非均匀性显著改变了非饱和土中竖向位移、正应力和孔隙压力在其深度方向上的振动模态, 其中孔隙气压在其深度方向的振动频率随着梯度因子的增加而不断增大, 波峰值不断靠近地表处附近; 竖向位移随着梯度因子的增大不断减小; 正应力和孔隙水压随着梯度因子的增大先增大后减小, 并且土体非均匀程度越高, 正应力与孔隙水压的幅值越大.      

Interfacial imperfection on reflection and transmission of plane waves in anisotropic micropolar media

This study is concerned with the reflection and transmission of plane waves at an imperfectly bonded interface between two orthotropic micropolar elastic half-spaces with different elastic and micropolar properties. There exist three types of coupled waves in xy-plane. The reflection and transmission coefficients of quasi-longitudinal (QLD) wave, quasi-coupled transverse microrotational (QCTM) wave and quasi-coupled transverse displacement (QCTD) wave have been derived for different incidence waves and deduced for normal force stiffness, transverse force stiffness, transverse couple stiffness and perfect bonding. The numerical values of modules of the reflection and transmission coefficients are presented graphically with the angle of incidence for orthotropic micropolar medium (MOS) and isotropic micrpolar medium (MIS). Some particular cases of interest have been deduced from the present investigation.     

Restudy of coupled field theories for micropolar continua (I)—Micropolar thermoelasticity

Problems of micropolar thermoelasticity have been presented and discussed by some authors in the traditional framework of micropolar continuum field theory. In this paper the theory of micropolar thermoelasticity is restudied. The reason why it was restricted to a linear one is analyzed. The rather general principle of virtual work and the new formulation for the virtual work of internal forces as well as the rather complete Hamilton principle in micropolar thermoelasticity are established. From this new Hamilton principle not only the equations of motion, the balance equation of entropy, the boundary conditions of stress, couple stress and heat, but also the boundary conditions of displacement, microrotation and temperature are simultaneously derived. Contributed by DAI Tian-min Foundation item: the National Natural Science Foundation of China (10072024); the International Cooperation Project of the NSFC (10011130235) and the DFG (51520001); the Research Foundation of Liaoning Education Committee (990111001) Biography: DAI Tian-min (1931-)     

圆柱外表面受热冲击问题的广义热弹性分析

基于 L-S 广义热弹性理论, 针对实心圆柱体在外表面受均匀热冲击作用下的一维广义热弹性问题进行研究分析. 利用热冲击的瞬时特征, 借助于 Laplace 正、反变换技术及柱函数的渐近性质, 推导了热冲击作用周期内温度场、位移场和应力场的渐近表达式. 通过计算, 得到了热冲击条件下各物理场的分布规律以及延迟效应和耦合效应对热弹性响应的影响规律. 结果表明: 当考虑延迟效应和耦合效应时, 热扰动将以两组速度不同的波的形式向前传播, 延迟效应和耦合效应对各物理场的建立时间, 阶跃间隔和阶跃峰值均产生影响, 且延迟效应和耦合效应均在一定程度上削弱了热冲击的作用效果.