On the time decay of solutions in one-dimensional theories of porous materials

In this paper we investigate the temporal asymptotic behavior of the solutions of the one-dimensional porous-elasticity problem when several damping effects are present. We show that viscoelasticity and temperature produce slow decay in time, and the same result is obtained when the porous viscosity is combined with microtemperatures. However, when the viscoelasticity is coupled with porous damping or with microtemperatures the decay is controlled by a negative exponential.     

Time harmonic waves in thermoelastic material with microtemperatures

The present study deals with the propagation of time harmonic waves in an infinite thermoelastic medium with microtemperatures within the context of the theory developed by Iesan and Quintanilla (2000). There exist three sets of coupled dilatational waves and a shear wave propagating at distinct speeds. Each set of coupled dilatational waves consists of displacement, micro and macrotemperature fields, while the lone shear wave is no different from that exist in classical elasticity. The reflection phenomenon of these waves from a plane boundary of a thermoelastic half space has been investigated.     

On the propagation waves in the theory of thermoelasticity with microtemperatures

The present paper studies the propagation of plane time harmonic waves in an infinite space filled by a thermoelastic material with microtemperatures. It is found that there are seven basic waves traveling with distinct speeds: (a) two transverse elastic waves uncoupled, undamped in time and traveling independently with the speed that is unaffected by the thermal effects; (b) two transverse thermal standing waves decaying exponentially to zero when time tends to infinity and they are unaffected by the elastic deformations; (c) three dilatational waves that are coupled due to the presence of thermal properties of the material. The set of dilatational waves consists of a quasi-elastic longitudinal wave and two quasi-thermal standing waves. The two transverse elastic waves are not subjected to the dispersion, while the other two transverse thermal standing waves and the dilatational waves present the dispersive character. Explicit expressions for all these seven waves are presented. The Rayleigh surface wave propagation problem is addressed and the secular equation is obtained in an explicit form. Numerical computations are performed for a specific model, and the results obtained are depicted graphically.     

Thermomagnetic effect with microtemperature in a semiconducting photothermal excitation medium

The main goal of this paper is to focus on the investigation of interaction between a magnetic field and elastic materials with microstructure, whose microelements possess microtemperatures with photothermal excitation. The elastic-photothermal problem in one-dimension is solved by introducing photothermal excitation at the free surface of a semi-infinite semiconducting medium (semiconductor rod). The integral transform technique is used to solve the governing equations of the problem under the effect of the microtemperature field. The analytical expressions for some physical quantities in the physical domain are obtained with the heating boundary surface and free traction. The numerical inversion technique is used to obtain the resulting quantities in the physical domain. The obtained numerical results with some comparisons are discussed and shown graphically.     

Reflection and refraction of plane waves at the interface of an elastic solid and microstretch thermoelastic solid with microtemperatures

The problem of reflection and refraction of waves at the interface of an elastic solid and microstretch thermoelastic solid with microtemperatures has been investigated. It is shown that due to incidence of P-wave or SV-wave at the interface, the waves are reflected and refracted. The amplitude ratios of these various reflected and refracted waves have been computed numerically, and graphical representation of their variations is made with the angle of incidence. Effect of microrotation on these amplitude ratios has been shown graphically. Some particular cases of interest have also been discussed.     

On the Decay Rates of Porous Elastic Systems

In this paper we analyze the porous elastic system. We show that viscoelasticity is not strong enough to make the solutions decay in an exponential way, independently of any relationship between the coefficients of wave propagation speed. However, it decays polynomially with optimal rate. When the porous damping is coupled with microtemperatures, we give an explicit characterization on the decay rate that can be exponential or polynomial type, depending on the relation between the coefficients of wave propagation speed. Numerical experiments using finite differences are given to confirm our analytical results. It is worth noting that the result obtained here is different from all existing in the literature for porous elastic materials, where the sum of the two slow decay processes determine a process that decay exponentially.     

The compliance contact model of cylindrical joints with clearances

This paper is concerned with the determination of the normal force-displacement (NFD) relation for the contact problem of cylindrical joints with clearance. A simple formulation for this contact problem is developed by modeling the pin as a rigid wedge and the elastic plate as a simple Winkler elastic foundation. The numerical results show that the normal displacement relation based on Hertz theory is only valid for the case of large clearance with a small normal load, and the NFD relation based on Persson theory is only effective in the case of very small clearance. The proposed approximate model in this paper gives better results than Hertz theory and Persson theory in a large range of clearances as seen from the comparison with the results of FEM. The project supported by the National Natural Science Foundation of (10272002; 60334030). The English text was polished by Keren Wang.     

An application of theoretical solutions about cylindrical shells with small openings

1　ＯｐｅｎｉｎｇｓｏｆＣｙｌｉｎｄｒｉｃａｌＳｈｅｌｌｓＴｈｅｐｒｏｂｌｅｍｏｆｃｙｌｉｎｄｒｉｃａｌｓｈｅｌｌｓｗｉｔｈｏｐｅｎｉｎｇｓｉｓｏｎｅｏｆｔｈｅｉｍｐｏｒｔａｎｔｑｕｅｓｔｉｏｎｓｔｏａｃａｄｅｍｉａａｎｄｅｎｇｉｎｅｅｒｉｎｇ .Ｉｎｆｉｆｔｙｙｅａｒｓｏｆｉｔｓｄｅｖｅｌｏｐｅｄｈｉｓｔｏｒｙ ,ｇｒｅａｔｅｆｆｏｒｔｓｗｅｒｅｍａｄｅｂｙｍａｎｙａｕｔｈｏｒｓｔｏｏｂｔａｉｎｓｏｌｕｔｉｏｎｓｆｏｒｔｈｉｓｐｒｏｂｌｅｍ[1].Ｔｈｉｓｐｒｏｂｌｅｍｃａｎｂｅｄｉｖｉｄｅｄｉｎｔｏ…     

Minimum principle for mixtures with memory

This work concerns the theory of viscoelastic composites which are modelled as mixtures of two interpenetrating solid continua. First it is given a characterization of the boundary-initial value problem in which the initial conditions are incorporated into the field equations. Then a minimum principle for the dynamic theory is established.     

An analytical theory of heated duct flows in supersonic combustors

One-dimensional analytical theory is developed for supersonic duct flow with variation of cross section, wall friction, heat addition, and relations between the inlet and outlet flow parameters are obtained. By introducing a selfsimilar parameter, effects of heat releasing, wall friction, and change in cross section area on the flow can be normalized and a self-similar solution of the flow equations can be found. Based on the result of self-similar solution, the sufficient and necessary condition for the occurrence of thermal choking is derived. A relation of the maximum heat addition leading to thermal choking of the duct flow is derived as functions of area ratio, wall friction, and mass addition, which is an extension of the classic Rayleigh flow theory, where the effects of wall friction and mass addition are not considered. The present work is expected to provide fundamentals for developing an integral analytical theory for ramjets and scramjets.     

Analysis of shells reinforced by massive stiffening ribs

The paper presents results of applying a heterogeneous mathematical model “elastic body–Timoshenko shell” to design shells with massive ribs. Numerical results are obtained for a cylindrical shell with ribs. They are compared with results obtained using the theory of elasticity and the theory of Timoshenko shells with piecewise-constant thickness Published in Prikladnaya Mekhanika, Vol. 44, No. 11, pp. 132–142, November 2008.     

Impossibility of localization in linear thermoelasticity with voids

In this note we prove the impossibility of the localization in time of the solutions of the linear thermoelasticity with voids. This means that the only solution for this problem that vanishes after a finite time is the null solution. From a thermomechanical point of view, this result says that the combination of the thermal and porous dissipation in the linear theory is not sufficiently strong to guarantee that the thermomechanical deformations will vanish after a finite time. The main idea to prove this result is to show the uniqueness of solutions for the backward in time problem.     

含裂纹的受力试件对超声波传播路径的影响

本从弹性理论及断裂力学理论出发,通过含裂纹试件受力前后形状及折射率的变化,研究了超声波试件受力试件后传播路径的变化,并与光波的变化进行了比较,得到含裂纹的受力试件对于光波来说相当于一“凹”透镜的作用,而对于超声波来说却相当于“凸”透镜的结论。     

求解含缺陷一维周期结构动力响应的高效算法

基于周期结构的动力特性和群理论，建立了一种高效求解含缺陷一维周期结构动力响应的数值方法。在求解结构动力响应时，高效求解结构对应的线性代数方程组最为关键。采用凝聚技术，可减小结构对应线性代数方程组的规模。基于周期结构动力系统中线性代数方程组的特性，通过一个小规模含缺陷结构和一维周期结构的响应分析，可得到含缺陷一维周期结构的动力响应。同理，一维周期结构的动力响应可通过一系列小规模结构的响应分析得到，且小规模结构的动力响应可基于群理论高效求解。数值算例表明，本文算法有较高的求解效率。     

Thermal Stresses in Plane Strain of Porous Elastic Solids

This paper is concerned with the linear theory of thermoelastic materials with voids. We present a method to reduce the thermoelastic problem to an isothermal one with zero body loads and with certain known boundary data. The results are used to study the thermal stresses in a tube and the thermoelastic deformation of a cylinder subjected to a uniform temperature gradient.     

Thrust and slip of a low-pressure tire on compressible ground by the compression-sliding approach

Driving wheels with low-pressure lugged tires are standard propulsion components of wheeled off-road vehicles. Such wheels have been mostly treated in theory as shorter tracks or even as “black boxes”. These procedures, however, appear not to be necessary since an updated theory of thrust generation, based on experiments with double-plate meter, was presented at the 2008 ISTVS Turin conference. This theory is based on the compaction-sliding (CS) concept, which claims that the rearward displacement of soil, a reason for slip, starts as horizontal soil compression by lugs (C-stage at lower thrust), followed by the slide of sheared off soil blocks (S-stage at higher thrust). The thrust in terms of ISTVS Standards equals gross tractive effort minus internal rolling resistance of a tire. The resultant thrust of a tire equals the sum of component thrusts of individual soil segments. The respective technique provides thrust-slip curves, which reflect tire size, loading, inflation pressure and tread pattern design, e.g. tread density, lug angle, pitch, height and tire casing lay-out and thus can be useful notably in assessing the traction properties of new tire designs. Concerning the evaluation of tire traction tests or similar applications, the CS approach offers a simplified version of thrust-slip formula (G-function), which complies with the CS concept and is easy to use.     

Analysis of free vibration of coupled Reissner's plate-liquid-spring system

Based on Reissner's plate theory, the dynamic behaviour of an offshore circular plate with moderate thickness floating on a liquid of finite constant depth and anchored by uniformly distributed springs to the sea bed is investigated. The frequency equation governing the motion of the coupled Reissner's plate-liquid-spring system is analytically obtained by means of the linear potential flow theory and the expansion theorem in modal analysis. Several numerical examples are presented to illustrate the variation in fundamental frequencies of Reissner's floating circular plates with free edge due to the stiffnesses of distributed springs and the depths of liquid.The author is grateful to Mr. W.M. Cheng for his help in completing the numerical calculations.     

线性变厚度矩形薄板自由振动的精确解

基于小挠度薄板理论，采用Ｌｅｒｙ法结合Ｆｒｏｂｅｎｉｕｓ法构造的幂级数解，得到了两对边简支另两对边为ＳＳ、ＣＳ、ＦＦ支承的三种线性变厚度矩形薄板的自振频率随板的边长比及厚度比变化的精确解及其振型函数的解析表达式。     

Two-plane automatic balancing: A symmetry breaking analysis

We present an analysis of a two-plane automatic balancing device for rotating machinery. The mechanism consists of a pair of races that contain balancing balls which move to eliminate imbalance due to rotor eccentricity or principal axis misalignment. A model is developed that includes the effect of support anisotropy and rotor acceleration. The symmetry of the imbalance is considered, and techniques from equivariant bifurcation theory are used to derive a necessary condition for the stability of balanced operation. The unfolding of the solution structure is explored and we investigate mechanical systems in which either the supports or the automatic ball balancer is asymmetric. Here it is shown that, provided the imbalance is small, the balanced state is robust to the considered asymmetries.     

An efficient algorithm for elasto-viscoplastic vibrations of multi-layered composite beams using second-order theory

An efficient time-domain algorithm for plane non-linear flexural vibrations of multi-layered composite beams, which are driven into the inelastic range by severe transverse loadings, is presented. The influence of an axial static preload is considered in the sense of the quasi-linear second-order theory of structures. The inelastic parts of strain are treated as additional sources of selfstress in the linear elastic background-structure, driving the elastic response into the inelastic one. The efficiency of this exact formulation lies in the fact that linear solution techniques can be used in their most powerful form: Rubin's useful formulation for the quasi-static second-order transfer-matrix of linear elastic structures is applied in combination with modal analysis. Having in mind multi-metal beams, the classical lamination theory is assumed to be valid. Beams with overhang composed of ideal elastic-plastic and viscoplastic layers are studied as example structures. The fictitious sources of selfstress are calculated from the different material laws of the layers in a numerical time-stepping procedure, where a generalized midpoint-rule in combination with Crisfield's secant-Newton procedure is used.