Dynamic analysis of interacting coplanar cracks in a half space with a clamped boundary condition using boundary integral equations

The three-dimensional dynamic problem of coplanar circular cracks in an elastic half-space with a clamped boundary condition is considered. The crack faces are subjected to harmonic loads. The problem is reduced to a system of two-dimensional boundary integral equations of the type of the Helmholtz potential for unknown discontinuities in the displacements of the opposite faces of the cracks. The stress intensity factors at the crack contours are obtained and discussed.Translated from Prikladnaya Mekhanika i Tekhnicheskaya Fizika, Vol. 46, No. 1, pp. 153–159, January–February, 2005     

The method of mixed boundary condition for a kion of linear and nonlinear composite structure

This paper deals with the axisymmetrical deformation of shallow shells in large deflection which are in conjunction with linear elastic structures at the boundary: A method of mixed boundary condition for this problem is introduced, then the problem of a composite structure is transformed into a problem of a single structure and the integral equations are given. The perturbation method is used to obtain the solutions and an example of composite structure consisting of a shallow spherical and a cylindrical shell is presented.Communicated by Yeh Kai-yuan     

THE ELASTIC FIELD INDUCED BY A HEMISPHERICAL INCLUSION IN THE HALF—SPACE

The elastic field induced by a hemispherical inclusion with uniform eigeustralns in asemi-infinite elastic medium is solved by using the Green‘s function method and series expansion tech-nique. The exact solutions axe presented for the displacement and stress fields which can be expressedby complete elliptic integrals of the first, second, and third kinds and hypergeometric functions. Thepresent method can be used to determine the corresponding elastic fields when the shape of the inclusionis a spherical crown or a spherical segment. Finally, numerical results axe given for the displacementand stress fields along the axis of symmetry (x3-axis).     

Two-fluid magnetohydrodynamic model of plasma flows in a quasi-steady-state accelerator with a longitudinal magnetic field

This paper reports the results of numerical studies of axisymmetric flows in a coaxial plasma accelerator in the presence of a longitudinal magnetic field. The calculations were performed using a two-dimensional two-fluid magnetohydrodynamic model taking into account the Hall effect and the conductivity tensor of the medium. The numerical experiments confirmed the main features of the plasmadynamic processes found previously using analytical and one-fluid models and made it possible to study plasma flows near the electrodes. __________ Translated from Prikladnaya Mekhanika i Tekhnicheskaya Fizika, Vol. 50, No. 3, pp. 44–55, May–June, 2009.     

Analysis of electric boundary condition effects on crack propagation in piezoelectric ceramics

There are three types of cracks: impermeable crack, permeable crack and conducting crack, with different electric boundary conditions on faces of cracks in piezoelectric ceramics, which poses difficulties in the analysis of piezoelectric fracture problems. In this paper, in contrast to our previous FEM formulation, the numerical analysis is based on the used of exact electric boundary conditions at the crack faces, thus the common assumption of electric impermeability in the FEM analysis is avoided. The crack behavior and elasto-electric fields near a crack tip in a PZT-5 piezoelectric ceramic under mechanical, electrical and coupled mechanical-electrical loads with different electric boundary conditions on crack faces are investigated. It is found that the dielectric medium between the crack faces will reduce the singularity of stress and electric displacement. Furthermore, when the permittivity of the dielectric medium in the crack gap is of the same order as that of the piezoelectric ceramic, the crack becomes a conducting crack, the applied electric field has no effect on the crack propagation. The project supported by the National Natural Science Foundation of China (19672026, 19891180)     

Non-Newtonian biomagnetic fluid flow through a stenosed bifurcated artery with a slip boundary condition

The effects of a velocity slip and an external magnetic field on the flow of biomagnetic fluid(blood) through a stenosed bifurcated artery are investigated by using ANSYS FLUENT. Blood is regarded as a non-Newtonian power-law fluid, and the magnetization and electrical conductivity are considered in the mathematical model.The no-slip condition is replaced by the first-order slip condition. The slip boundary condition and magnetic force are compiled in the solver by the user-defined function(UDF)...     

Numerical simulation of the flow field in a thermal plasma reactor

A numerical simulation is presented for a thermal plasma reactor with particle-trajectory model in this paper.Turbulance is considered by using simple SGS model.Thegoverning equations are solved by means of the algorithm of SIMPLER.The calculatedresults give the velocity and the temperature fields within plasma reactor,and thetrajectories of the injected particles.     

Effect of electric field modulation on charge propagation in a low-conducting polar liquid

Unsteady processes of current propagation and formation of charge structures in a low-conducting polar liquid in the electric field of a horizontal capacitor are considered. Free charges are assumed to form in the liquid only owing to unipolar injection from the anode, which arises if the field strength on the anode is greater than a threshold value. The charge distribution in time and space and the evolution of the density of the current through the capacitor and the field strength on the anode are analyzed. It is demonstrated that the time intervals between two charge injections in a variable field (injection periods) may vary depending on the external field period. The density of the current through the capacitor is obtained as a function of the frequency and amplitude of the external field. __________ Translated from Prikladnaya Mekhanika i Tekhnicheskaya Fizika, Vol. 49, No. 1, pp. 3–12, January–February, 2008.     

Theory of the temperature relaxation of an electron-ion plasma in a high-frequency electric and constant magnetic field

The effective collision frequency of electrons and ions which leads to temperature equalization in a plasma in a constant magnetic field and a weak high-frequency electric field when the gyroscopic radius of the electrons is less than the Debye screening radius is determined. The corresponding values of the relaxation time are determined over a wide range of values of the ratio between the electron and ion temperatures, over a wide range of values of the magnetic and electric fields, and also as a function of the frequency of the external electric field.Translated from Zhurnal Prikladnoi Mekhaniki i Tekhnicheskoi Fiziki, No. 6, pp. 41–48, November–December, 1970.     

Numerical Simulation of Plasma Dynamics in a Nonuniform Magnetic Field

An efficient algorithm is proposed enabling numerical simulations of plasma dynamics in a nonuniform magnetic field. The present numerical data are in good agreement with experimental data obtained in a GOL-3 setup and with previous simulations. The experimentally observed effect of fast transfer of energy to ions is confirmed. __________ Translated from Prikladnaya Mekhanika i Tekhnicheskaya Fizika, Vol. 47, No. 1, pp. 35–45, January–February, 2006.     

Radiation effects on the thermal boundary layer flow over a moving plate with convective boundary condition

The steady laminar boundary layer flow over a moving plate in a moving fluid with convective surface boundary condition and in the presence of thermal radiation is investigated in this paper. Under certain conditions, the present problem reduces to the classical Blasius and Sakiadis problems. The effects of radiation and convective parameters on the thermal field are thoroughly examined and discussed. Dual solutions are found to exist when the plate and the fluid move in the opposite directions.     

Analysis of guided waves with a nonlinear boundary condition caused by internal resonance using the method of multiple scales

We theoretically investigated the cumulative nonlinear guided waves caused by internal resonance, using the method of multiple scales (MMS), which can construct better approximations to the solutions of perturbation problems. In this study, we consider nonlinearity only on the boundary instead of material nonlinearity or geometric nonlinearity. We showed nonlinear effects on the amplitudes of a lower mode and a higher mode depending on the propagation length. Also, we examined effects of wavenumber detuning from a phase matching condition of the two modes. If the wavenumber detuning is exactly equal to zero, the mechanical energy of the lower mode is transferred through nonlinear coupling to the energy of the higher mode, unilaterally. However, if a wavenumber detuning is not equal to zero, amplitude of the two modes change in a cyclic fashion during wave propagation. The amount of this amplitude variation and its cycle length are determined by the eigenfunctions of the two modes, the nonlinear parameter and the wavenumber detuning.     

The reflected pressure field in the interaction of weak shock waves with a compressible foam

This paper deals with the waves that are reflected from slabs of porous compressible foam attached to a rigid wall when impacted by a weak shock wave. The interest is in establishing possible attenuation of the pressure field after a shock or blast wave has struck the surface. Foam densities from 14 to 38 kg/m³ were tested over a range of shock wave Mach numbers less than 1.4. It is shown that the initial reflected shock wave strength is accurately predicted by the pseudo-gas model of Gelfand et al. (1983), with a pressure ratio of approximately 80% of the value for reflection off a rigid wall. Evidence is presented of gas entering the foam during the early stages of the process. A second wave emerges from the foam at a later stage and is separated from the first by a region of constant velocity and pressure. This second wave is not a shock wave but a compression front of significant thickness, which emerges from the foam earlier than predicted by the pseudo-gas model. Analysis of the origin of this wave points to much more complex flows within the foam than previously assumed, particularly in an apparent decrease in average wave front speed as the foam is compressed. It is shown that the pressure ratio across both these waves taken together is slightly higher than that for reflection off a rigid wall. In some cases this compression wave train is followed by a weak expansion wave.This article was processed using Springer-Verlag T_EX Shock Waves macro package 1990.     

Non-linear Oberbeck-electroconvection in a poorly conducting fluid through a vertical channel in the presence of an electric field

Non-linear Oberbeck-electroconvection (OBEC) in a poorly electrically conducting fluid through a vertical channel, when the walls are held at different temperatures with temperature difference perpendicular to gravity, is studied using the modified Navier stokes equation in the presence of both induced and an applied electric field. Both analytical and numerical solutions for the non-linear coupled equations governing the motion are obtained and found that analytical solutions agree well with numerical solutions for values of the buoyancy parameter N<1. It is shown that OBEC can be controlled by maintaining the temperature difference either in the same direction or opposing the potential difference with a suitable value of electric number W. The effect of W on velocity, temperature, rate of heat transfer, skin friction and mass flow rate are computed and the results are depicted graphically. We found that analytical results agree well with numerical results for small values of N. We also found that an increase in W accelerates the flow and hence increases linearly the skin friction and mass flow rate.     

SPH方法的运动边界条件研究Research on the moving boundary condition in SPH method

提出一种设置运动边界条件的方法,研究边界附近流体粒子积分截断和非物理穿透边界的问题。边界外的虚粒子在每个时间步由边界附近流体粒子对称生成,赋予相应的物理量,并在虚粒子中引入排斥力,利用拉格朗日形式的N‐S方程自编SPH程序,参考一维激波管的精确解验证边界方法的适用性,研究运动边界条件在计算模型中应用。激波管的模拟结果与精确解基本一致,且在运动边界模型中也计算获得合理的结果。文中提出的运动边界条件,避免了边界附近流体粒子积分截断问题,阻止流体粒子在边界处发生非物理穿透的现象。     

Influence of a Longitudinal Magnetic Field on the Hall Effect in the Plasma Accelerator Channel

An analytic model of steady-state two-dimensional flows in coaxial plasma-accelerator channels in the presence of a longitudinal magnetic field is proposed. The solution of the problem is found in the smooth channel approximation for the MHD equations of an ideal two-component plasma. An example of the developing axisymmetric flows is given and the features of the plasma-dynamic processes are investigated. It is found that the Hall effect and the anode flow zone can be reduced using a longitudinal field and plasma rotation.     

Computing Green's function of elasticity in a half-plane with impedance boundary condition

This Note presents an effective and accurate method for numerical calculation of the Green's function G associated with the time harmonic elasticity system in a half-plane, where an impedance boundary condition is considered. The need to compute this function arises when studying wave propagation in underground mining and seismological engineering. To theoretically obtain this Green's function, we have drawn our inspiration from the paper by Durán et al. (2005), where the Green's function for the Helmholtz equation has been computed. The method consists in applying a partial Fourier transform, which allows an explicit calculation of the so-called spectral Green's function. In order to compute its inverse Fourier transform, we separate as a sum of two terms. The first is associated with the whole plane, whereas the second takes into account the half-plane and the boundary conditions. The first term corresponds to the Green's function of the well known time-harmonic elasticity system in (cf. J. Dompierre, Thesis). The second term is separated as a sum of three terms, where two of them contain singularities in the spectral variable (pseudo-poles and poles) and the other is regular and decreasing at infinity. The inverse Fourier transform of the singular terms are analytically computed, whereas the regular one is numerically obtained via an FFT algorithm. We present a numerical result. Moreover, we show that, under some conditions, a fourth additional slowness appears and which could produce a new surface wave. To cite this article: M. Durán et al., C. R. Mecanique 334 (2006).     

Effects of external electric field on pool boiling: Comparison of terrestrial and microgravity data in the ARIEL experiment

Pool boiling in microgravity, in the presence of an electric field or less, was investigated in ARIEL test setup, integrated in Fluidpac facility, on Foton-M2 orbital mission. The nucleate boiling curve with FC-72 was measured in terrestrial and reduced gravity conditions, on a heated surface whose size was relevant from a technical point of view, for various degrees of fluid subcooling and high heat rates. An external electrostatic field was also added to investigate its use as a possible replacement of buoyancy. Counterpart tests were carried out in the same apparatus in normal gravity, before the mission. The present paper deals in particular with the comparison between boiling performance in normal and reduced gravity in the entire experimental range.     

内压对电场下晶内微裂纹演化的影响

基于表面扩散的经典理论及其弱解描述,建立曲率、内压和电场共同作用下的有限单元法,分析了金属材料内部晶内微裂纹的演化过程。对于形态比为β的微裂纹,存在一临界电场值χc,当χ<χc时,微裂纹逐渐圆柱化;当χ>χc时,微裂纹分节为上下或左右两个较小的微裂纹。内压加速有助于微裂纹分节。对于β>1的微裂纹,当β和χ一定时存在一临界内压值qc,当q>qc时,随着电场和内压的增大会率先在裂纹的右端发生裂纹扩展。     

An investigation into the effect of electric field on the performance of Dielectric Barrier Discharge plasma actuators

The influence of the inter-electrode electric field of a single Dielectric Barrier Discharge (DBD) actuator on the performance of the device was investigated. The electric field of the actuator was manipulated through the variation of the angle between the electrodes of the actuators. Response forces generated by the plasma actuators were used as performance indicators for these devices. These forces were measured directly utilizing a highly sensitive balance scale. It was verified that depending on the orientation of the variation of the angle between the electrodes, the performance of the actuator may be decreased or increased when compared to a DBD on a flat dielectric plate more commonly investigated in literature. The manner in which the ionic wind flows over the actuators was also explored in the effort to elucidate the influence of the variation of the angle between the electrodes on the response force generated by the device. Results demonstrated that the response forces generated by the actuators may be improved by up to 50% compared to the actuator configuration on a flat dielectric plate commonly investigated. These results indicate the potential available to advance plasma technology by physically manipulating these devices to increase the performances of the actuators.