Gradient surface ply model of SH wave propagation in SAW sensors

Investigation of the propagation of the wave in SAW sensors is a basis for the research and design of the sensors. With the advance of the sensor, both the effect of environment on the surface ply and the geometry of waveguide are complicated. To consider the complication, a model with gradient surface ply and multilayer waveguide of SH wave propagation in sensor is proposed. The equation of wave velocity is derived by a transfer matrix method. Through the equation, the function of wave velocity increment via the change of parameters in the surface ply is obtained. The effect of the inhomogeneity on the function is also studied. Finally, some influencing factors of the behavior of the sensor are discussed. This study was supported by the National Natural Science Foundation of China (No. 59635140), the Doctoral Education Foundation of the Ministry of Education of China and Aeronautics Foundation of China.     

Nonisothermal deformation of a viscoelastic medium

One of the current problems of the mechanics of viscoelastic media is the question of the effect of temperature. This problem was first raised in the work of A. A. Aleksandrov and Yu. S. Lazurkin who set forth the basic ideas of the principle of temperature-time superposition for isothermal loading at different temperatures. A similar approach was adopted by Leaderman, Ferry, and others. Subsequently, in the work of Morland and Lee [1] the principle was formally extended to the case of variable temperatures.In this paper the problem of the nonisothermal deformation of a viscoelastic medium is examined on the basis of the thermodynamics of irreversible processes. Given sufficiently well justified assumptions about the construction of the basic thermodynamic potential, this approach inescapably leads to the conclusion that the state of the viscoelastic medium depends not only on the current value of the temperature field but also on its history of variation. The relations obtained are similar to those proposed in [1], thus providing a theoretico-physical basis for the above-mentioned principle and its extension to the case of nonisothermal processes.     

Hypersonic viscous shock layer in a swirling gas flow on a permeable surface

A hypersonic swirling flow of viscous compressible gas past rotating axisymmetric blunt bodies is considered, its velocity vector being parallel to the axis of rotation of the body. The body surface is assumed permeable, while, in the general case, the gas is not injected (drawn off) along the normal to the body surface. An analytic solution of the problem, valid at small Reynolds numbers, is found in the first approximation of the integral method of successive approximations. On the basis of the results of the numerical solution, obtained in a wide range of variation of the determining parameters of the problem, we investigate the influence of the swirling of the free-stream flow, the angular velocity of rotation of the body, the Reynolds number and the injection (suction) parameter on the structure of the compressed layer, and the coefficients of friction and heat transfer on the body surface. The influence of the swirling of the flow on the nature of the asymptotic behavior of the viscous shock layer equations at large Reynolds numbers is studied. It is shown that the presence of a nonzero peripheral component for the velocity vector of the gas in the shock layer can lead to a qualitative change in the nature of the flow. Deceased Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 6, pp. 27–37, November–December, 1986. The authors thank G. G. Chernyi for his useful discussion of the results of the work.     

非球形固体颗粒对弯管内壁的磨损机制

为研究弯管内固体颗粒在液相夹带条件下的运动特性及颗粒对弯管内壁的磨损,采用计算流体动力学与离散元耦合的方法,建立数值模型,考虑固液两相之间的作用,对弯管内的固液两相流动进行数值模拟;通过软件的应用程序编程接口嵌入自编译磨损模型;借助试验结果,验证数值模型的有效性. 结果表明,所建立的数值模拟方案可以准确地模拟颗粒在管内的运动特征并能够预测弯管内壁的磨损位置以及磨损程度. 弯管内的二次流对颗粒运动有重要影响,弯管外侧壁面中心线附近的磨损较严重,磨损的形式以小角度划擦切削为主. 弯管磨损主要与颗粒对壁面的碰撞速度、碰撞角度及碰撞频率有关. 运动中的颗粒与壁面发生多次碰撞,碰撞角度逐渐减小. 随着颗粒球形度的增大,在相同碰撞条件下引起的磨损量变小,但是会降低颗粒的随流性. 颗粒形状影响颗粒在流场中的运动速度以及颗粒与壁面的碰撞. 随着颗粒球形度增大,严重磨损区域向弯管进口方向移动,壁面平均磨损量先减小后增大;当输送颗粒的球形度为0.91时,壁面磨损量最小.      

Reflection of shock waves from a solid boundary in a mixture of condensed materials. 1. Equilibrium approximation

The process of reflection of shock waves (SW) from a solid wall in a two-component mixture of condensed materials is studied within the framework of mechanics of heterogeneous media. The velocity of a reflected SW and the values of the parameters behind its front are analytically determined as functions of the velocity of the incident wave and the initial parameters of the mixture. It is shown that the absolute value of the velocity of the reflected SW can be greater than the velocity of the incident SW in mixtures with a small content of the light component and at low velocities of the incident shock wave. The nonmonotonic character of the dependence of pressure in the final equilibrium state behind the incident SW on the initial volume concentration of particles is demonstrated. The velocity of the incident SW is estimated for the case where a similar effect is also observed behind a reflected SW. It is established that, for weak shock waves, the dependence of the amplification factor of the reflected SW on the initial volume concentration of the light component is nonmonotonic and has a local maximum. It is noted that, as the velocity of the incident SW increases, the effect of compacting of the mixture (increase in concentration of the heavy component) behind the reflected SW becomes much less pronounced than in a passing SW. Institute of Theoretical and Applied Mechanics, Siberian Division, Russian Academy of Sciences. Novosibirsk 630090. Translated from Prikladnaya Mekhanika i Tekhnicheskaya Fizika, Vol. 40, No. 5, pp. 73–78, September–October, 1999.     

Inverse approach and sensitivity analysis for identification of ingot-mould thermal resistance in continuous casting of metals

The problem of appropriate location of the sensors for identification of ingot – mould thermal resistance during continuous casting of metals is the subject of the paper. Analysed problem belongs to the group of inverse problems. The present work shows also the method of identification of unknown thermal resistance using the temperature measurements at the number of sensors located in the wall of the mould. The influence of the location of the sensors on the results of identification is analysed. The best location of the sensors results from the sensitivity analysis for the steady-state inverse heat conduction problem. Validation of the proposed inverse method is realized by comparison of the results taken from solution of inverse and direct problems. Several numerical examples are presented and analysed.     

Dynamic contact angle for etting of a surface by a van der waals fluid

We consider the creeping motion of a thin layer of a nonvolatile viscous fluid spreading due to capillary forces over a rigid surface covered by a thin homogeneous film (microfilm). The influence of van der Waals forces on the asymptotic slope of the free boundary of the layer is studied in the region of large thickness, where capillary forces dominate. A solution of the problem of the slope angle is obtained for the entire possible range of the microfilm thickness. In the limit of small thickness of the microfilm, this solution is in agreement with the well-known solution of the problem of the dynamics of wetting of a dry surface in the presence of a precursory film and van der Waals forces. The role of the condition at the end of the precursory film is studied. Institute of Mechanics of Multiphase Systems, Siberian Division, Russian Academy of Sciences. Tyumen' 625000. Translated from Prikladnaya Mekhanika i Tekhnicheskaya Fizika. Vol. 41, No. 4, pp. 101–105, July–August. 2000.     

Influence of polymer additives in a flow on the hydrodynamic characteristics of two-dimensional profiles

The problem of separationless flow of homogeneous dilute polymer solutions over two-dimensional profiles is considered. The complete flow is divided by the outer edge of the boundary layer and the wake into two regions: a region of irrotational flow and a region of viscous flow — the boundary layer and wake. The characteristics of the two regions are matched at their boundary. The problem is solved by successive approximation with allowance for the mutual influence of the two regions on each other. The influence of the irrotational region on the viscous region is taken into account through the distribution of the pressure on the boundary of the wake and the boundary layer. The influence of the viscous part of the flow is taken into account by the introduction of an associated vortex whose intensity is equal to the integral of the vorticity in the complete viscous region, and also by the introduction of additional velocities on the boundary of the wake and the boundary layer. These deform the streamlines in the irrotational part of the flow and ensure that they match the flow pattern in the real fluid. The results of the calculations of the hydrodynamic characteristics of a Zhukovskii profile are compared with experimental data. The influence of the introduction into the flow of polymer additives on the distributed and total characteristics of the flow at a number of Reynolds numbers is analyzed for the example of the modified profile NACA66.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 6, pp. 35–41, October–December, 1981.     

The stability of vortex filaments

The article discusses the problem of the nonlinear oscillations of concentrated vortexes, For a vortical annulus and a spiral vortical filament, the article demonstrates the character of the change in the form and the frequency of the oscillations with an increase in the amplitude. In the case of standing waves, the solution is obtained in the form of a series with respect to the amplitude of the perturbations, with an accuracy up to terms of the third order of smallness, inclusive. For running waves, the solution is constructed using a method analogous to the Stewart method. The same problem is solved using direct numerical integration of the starting equations of motion. The values of the critical amplitudes which bring about the breakdown of a vortical annulus are obtained. It is shown that as a result of the nonlinearity of the equations in solution of the problem with the starting data higher harmonics can separate out intensively. For a spiral vortical filament, a study was made of the nonlinear interaction of the perturbations; it is shown, in particular, that a perturbation which is stable according to the linear theory may become unstable as a result of nonlinear interaction with neighboring perturbations along the length of the wave and of perturbations of the frequency.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 3, pp. 42–49, May–June, 1973.The authors thank G. I. Petrov for his direction of the work, as well as V. Ya. Shkadov for his interest in the work.     

Transient dynamic behavior of a closed gas-filled shell subjected to internal blast loading

The paper concerns the numerical solution of a problem on the forced vibration of a shell system under a blast load. The mathematical model of the transient dynamic process in the given multicomponent system is based on the use of a system of hydrodynamic equations to describe the motion of the detonation products and air and equations from shell theory to determine the stress-strain state of the shell system. The hydrodynamic equations are integrated in moving grids by the method developed by S. K. Godunov. The shell-theory equations are integrated by the integro-interpolation method. The distribution of the loads on the shells, the distribution of the maximum strains along the generatrix of the shell system, and the transformations of the detonation products at characteristic points are presented. S. P. Timoshenko Institute of Mechanics, National Academy of Sciences of Ukraine, Kiev, Ukraine. Translated from Prikladnaya Mekhanika, Vol. 34, No. 3, pp. 76–82, March, 1999.     

Investigation of field of dynamic stresses with impulse loading

An analytic solution of the problem of determining the dynamic stresses for the region of plasto-elastic deformations of cylindrically shaped bodies subjected to impulse loading is obtained. On the basis of this solution, laws governing the dependence of the energy parameters of a source of disturbances on the characteristics of the field of dynamic stresses are determined. It is established that the amplitude and sign of these disturbances are defined by the magnitude of the pressure, and the duration of the action of these disturbances by the duration of the impulse. Mining Academy of Ukraine, Dnepropetrovsk, Ukraine. Translated from Prikladnaya Mekhanika, Vol. 35, No. 2, pp. 65–69, February, 1999.     

EFFECT OF STRESS-STRAIN CURVE OF MATERIAL ON SOLUTION OF PLANE-STRESS PROBLEMS WITH LARGE PLSTIC DEFORMATION

本文首先将以前所得到的关于两个轴对称塑性平面应力问题(薄圆环和旋转盘)的有关方程和计算结果作了一个简单的叙述.这些计算结果是根据两种不同硬化特性的材料和一种理想塑性材料的应力应变曲线在不同负荷下计算得到的.这些结果指出这三种不同材料的应力应变曲线和负荷对于这两个问题的主应力比值和比例应变的影响很小,而对于比例应力的影响则很大.之后,分析了二维的塑性平面应力问题的方程;这些方程考虑了大应变,但不包括体积力(body force).分析这些方程中的包括材料应力应变曲线项和载荷数项的结果,认为假若在边界上的主应力的比值和比例应变不变,则材料的应力应变曲线和载荷对于主应力比值和比例应变的分布的影响可能不大,而对于比例应力的影响则很大.这种边界条件在实际问题中的普通加减下,满足的可能想是很大的.薄圆环和旋转盘的边界条件及所得的结果和这分析的结果是完全一致的.从这些结果并可提出一个简单而相当准确的近似解,最后并将本文所得的结果和依留辛(Ильюшии)的理论——关于小应变下三维问题形变理论的应用条件——作了比较.     

Subcritical growth of high-cycle fatigue cracks in finite thin isotropic plates

The problem of constructing a two-stage model of the motion of a fatigue crack in finite thin isotropic plates under symmetric tension-compression is formulated, and a method for its solution is considered. The two-stage nature is regarded as the presence of the incubation and propagation stages. The model is constructed by jointly considering the resolving equations of the theory of elasticity and the evolutionary equations of the mechanics of continuous damage. The damage function's attaining the critical value is considered as a criterion of initiation of local fracture and movement of a fatigue crack. Plates containing central and lateral cracks are considered. The effect of the level of stresses, the finiteness of the plate, the initial length of the crack, and the behavior of the length of the plastic zone on fracture kinetics is evaluated. The present work was carried out with financial support from the European Community in accordance with the INTAS-UA 95-0202 International Project. S. P. Timoshenko Institute of Mechanics, National Academy of Sciences of Ukraine, Kiev. Translated from Prikladnaya Mekhanika, Vol. 36, No. 7, pp. 106–116, July, 2000.     

Hydrostatics in weak force fields. Equilibrium shapes of a rotating weightless liquid

We examine the problem of axisymmetric equilibrium forms of the surface of a rotating liquid which has surface tension in the absence of an external force field. We do not assume a priori closure of the equilibrium surface or that it intersects the axis of rotation [1, 2]. We study the properties of the two-parameter family of solutions of the equilibrium equation. Typical forms of the integral curves are constructed from the results of numerical computation on a computer. The methods of boundary layer theory are used to find the approximate expression for the form of the equilibrium surface for large angular rates of rotation.The author wishes to thank L. V. Babenko for writing the program for the numerical calculation and also A. D. Myshkis and A. D. Tyuptsov for discussions of the results and for their valuable advice.     

Anomalous readings of Pitot tubes in suspensions of solid particles and in solutions of polymers,lowering the turbulent friction

An anomalous lowering of the readings of Pitot tubes in flows of suspensions of solid particles of equal densities has been observed in a liquid. A universal dependence has been obtained, connecting the defect in the readings of Pitot tubes with their diameter, with the diameter of the particles of the suspensions, with the velocity of the flow, and with the volumetric concentration of the particles. The article presents new data on anomalous readings of Pitot tubes in polymer solutions, lowering the turbulent friction resistance. The character of this phenomenon is analogous to the lowering of the readings in suspensions. It is postulated that the anomalous readings of Pitot tubes in polymer solutions are connected with elasticoviscous associates of macromolecules of the polymer and molecules of the solvent. Experimental data are used to calculate the effective dimensions and volumetric concentration of the associates in the solutions.Moscow. Translated from Izvestiya Akademii Nauk SSSR. Mekhanika Zhidkosti i Gaza, No. 2, pp. 48–54, March–April, 1972.     

Approximate kinetic equations in rarefied gas theory

The fundamental kinetic equation of gas theory, the Boltzniann equation, is a complex integrodiffcrential equation. The difficulties associated with its solution are the result not only of the large number of independent variables, seven in the general case, but also of the very complicated structure of the collision integral. However, for the mechanics of rarefied gases the primary interest lies not in the distribution function itself, which satisfies the Boltzmann equation, but rather in its first few moments, i.e., the averaged characteristics. This circumstance suggests the possibility of obtaining the averaged quantities by a simpler way than the direct method of direct solution of the Boltzmann equation with subsequent calculation of the integrals.It is well known that if a distribution function satisfies the Boltzmann equation, then its moments satisfy an infinite system of moment equations. Consequently, if we wish to obtain with satisfactory accuracy some number of first moments, then we must require that these moments satisfy the exact system of moment equations. However, this does not mean that to determine the moments of interest to us we must solve this system, particularly since the system of moment equations is not closed. The closure of the system by specifying the form of the distribution function (method of moments) can be considered only as a rough approximate method of solving problems. First, in this case it is not possible to satisfy all the equations and we must limit ourselves to certain of the equations; second, generally speaking, we do not know which equation the selected distribution function satisfies, and, consequently, we do not know to what degree it has the properties of the distribution function which satisfies the Boltzmann equation.A more reliable technique for solving the problems of rarefied gasdynamics is that based on the approximation of the Boltzmann equation, more precisely, the approximation of the collision integral. The idea of replacing the collision integral by a simpler expression is not new [1–4]. The kinetic equations obtained as a result of this replacement are usually termed model equations, since their derivation is usually based on physical arguments and not on the direct use of the properties of the Boltzmann collision integral. In this connection we do not know to what degree the solutions of the Boltzmann equation and the model equations are close, particularly since the latter do not yield the possibility of refining the solution. Exceptions are the kinetic model for the linearized Boltzmann equation [5] and the sequence of model equations of [6], constructed by a method which is to some degree analogous with that of [5].In the present paper we suggest for the simplification of the solution of rarefied gas mechanics problems a technique for constructing a sequence of approximate kinetic equations which is based on an approximation of the collision integral. For each approximate equation (i.e., equation with an approximate collision operator) the first few moment equations coincide with the exact moment equations. It is assumed that the accuracy of the approximate equation increases with increase of the number of exact moment equations. Concretely, the approximation for the collision integral consists of a suitable approximation of the reverse collision integral and the collision frequency. The reverse collision integral is represented in the form of the product of the collision frequency and a function which characterizes the molecular velocity distribution resulting from the collisions, where the latter is selected in the form of a locally Maxwellian function multiplied by a polynomial in terms of the components of the molecular proper velocities. The collision frequency is approximated by a suitable expression which depends on the problem conditions. For the majority of problems it may obviously be taken equal to the collision frequency calculated from the locally Maxwellian distribution function; if necessary the error resulting from the inexact calculation of the collision frequency may be reduced by iterations.To illustrate the method, we solve the simplest problem of rarefied gas theory-the problem on the relaxation of an initially homogeneous and isotropic distribution in an unbounded space to an equilibrium distribution.The author wishes to thank A. A. Nikol'skii for discussions of the study and V. A. Rykov for the numerical results presented for the exact solution.     

Nonequilibrium homogeneous condensation of gases in high-velocity flows

This paper discusses questions of the homogeneous condensation of water vapors in high-velocity flows. Special attention is paid to agreement between the results of calculations and experimental data in a wide range of temperatures and pressures in the condensation zone and of the gradients of the gasdynamic parameters. The article proposes a relationship enabling a sufficiently exact determination of the value of the maximal supercooling. A parametric investigation is made, showing that the value of the maximal supercooling of the flow, as well as the drop size, are determined above all by the saturation temperature of the flow and the rate of change of the temperature along the line of flow in the condensation zone. The isentropic index of a mixture of gases and the concentration of the condensing component have a relatively weak effect on the value of the maximal supercooling, but the presence of other gases can appreciably affect the drop size. The Mach number of the flow with M > 1.5 has no effect on the value of the maximal supercooling and the drop size.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 6, pp. 81–88, November–December, 1978.     

Delayed fracture of a transversally isotropic viscoelastic material with a crack under a cyclic load

The delayed fracture of a transversally isotropic viscoelastic material due to slow subcritical growth of a flat circular macrocrack of normal separation under a cyclic load is investigated. The analysis is based on the modified δC of fracture and the hypothesis of the constancy of the prefracture zone. The study is made within the framework of the Boltzmann-Volterra theory for bounded resolvent operators of difference type, which describe the transversal isotropy of the strain properties of the material. To determine the analytic form of the kernel for the irrational function of a linear combination of the above-mentioned integral operators, the method of continued fractions is used. Analytical and numerical calculations are carried out for the bounded resolvent operators of difference type with the kernel in the form of Rabotnov's fractional exponential function. S. P. Timoshenko Institute of Mechanics, National Academy of Sciences of Ukraine, Kiev. Translated from Prikladnaya Mekhanika, Vol. 36, No. 1, pp. 123–129, January, 2000.     

Experimental analysis of displacements and shears at surfaces of contact

The displacements which exist at the contact between two loaded bodies depend on the geometry of the surface of contact, the type of the loading and the property of the materials. A method has been developed to determine these displacements experimentally. A grid has been photographically printed on an interior plane of a transparent model of low modulus of elasticity. The displacements were recorded photographically and the analysis was conducted on the photographs of the deformed grids. Shears were determined from the change in angles. The precision of the measurements at the interface is estimated to be plus or minus 0.05 mm. Examples of application are given for the cases of loads applied normally and tangentially to a rigid cylindrical punch resting on a semi-infinite soft plate. Important observations can be made on the zones of friction and of slip. The proposed method is three dimensional and the distributions can be obtained at several interior planes by changing the position of the plane of the grid. The limitations of the method are pointed out. The possibility of using gratings (12 to 40 lpmm) is considered, as well as the advantages of using moiré to analyze the displacements.