On the dynamics of the vortex structures generated by plasma DBD actuator

The plasma actuator is used to generate pseudo-periodical vortices moving almost parallel to the wall under various settings of high-voltage high-frequency power AC. Low-frequency amplitude modulation is desired to generate vortices, otherwise wall-jet-like flow is present. It will be shown how the dynamics of generated coherent vortices alternates depending on generator setting, frequency spectrum will be introduced in dependency on frequency of amplitude modulation and duty cycle. Measurements will be performed using TR-PIV technique or HW anemometry across wall-jet flow. The generated flow patterns are to be applied for control of boundary layers. (© 2013 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Two-dimensional steady-state oscillation problems of anisotropic elasticity

The paper deals with the two-dimensional exterior boundary value problems of the steady-state oscillation theory for anisotropic elastic bodies. By means of the limiting absorption principle the fundamental matrix of the oscillation equations is constructed and the generalized radiation conditions of Sommerfeld-Kupradze type are established. Uniqueness theorems of the basic and mixed type boundary value problems are proved.     

Two-dimensional stressed state of an anisotropic body with holes, elastic inclusions, and cracks

Generadized complex potentials are used to solve a problem for the elastic stressed state of a body with a general rectilinear anisotropy in a two-dimensional stressed-deformed state. The body has longitudinal cavities, inclusions, planar cracks, or rigid lamellar inclusions. A least-squares methods is used to reduce the problem to a system of linear algebraic equations which is solved for the unknown constants in the complex potentials. Donetsk State University. Translated from Teoreticheskaya i Prikladnaya Mekhanika, No. 29, pp. 63–70, 1999.     

Two-dimensional almost-Riemannian structures with tangency points

Two-dimensional almost-Riemannian structures are generalized Riemannian structures on surfaces for which a local orthonormal frame is given by a Lie bracket generating pair of vector fields that can become collinear. We study the relation between the topological invariants of an almost-Riemannian structure on a compact oriented surface and the rank-two vector bundle over the surface which defines the structure. We analyse the generic case including the presence of tangency points, i.e. points where two generators of the distribution and their Lie bracket are linearly dependent. The main result of the paper provides a classification of oriented almost-Riemannian structures on compact oriented surfaces in terms of the Euler number of the vector bundle corresponding to the structure. Moreover, we present a Gauss–Bonnet formula for almost-Riemannian structures with tangency points.     

Influence of vortex structures on the controlled motion of an above-water screwless robot

This paper is devoted to an experimental investigation of the motion of a rigid body set in motion by rotating two unbalanced internal masses. The results of experiments confirming the possibility of motion by this method are presented. The dependence of the parameters of motion on the rotational velocity of internal masses is analyzed. The velocity field of the fluid around the moving body is examined.     

Two-dimensional vortex sheets for the nonisentropic Euler equations: Nonlinear stability

We show the short-time existence and nonlinear stability of vortex sheets for the nonisentropic compressible Euler equations in two spatial dimensions, based on the weakly linear stability result of Morando and Trebeschi (2008) [20]. The missing normal derivatives are compensated through the equations of the linearized vorticity and entropy when deriving higher-order energy estimates. The proof of the resolution for this nonlinear problem follows from certain a priori tame estimates on the effective linear problem in the usual Sobolev spaces and a suitable Nash–Moser iteration scheme.     

Modeling anisotropic conducting surfaces by strip structures

Translated from Metody Matematicheskogo Modelirovaniya i Vychislitel'noi Diagnostika, pp. 193–199, Izd. Moskovskogo Universiteta, Moscow, 1990.     

Stresses in an anisotropic cylinder

The present article considers the use of the random anisotropy potential to investigate the stress field in an anisotropic cylinder. The mechanical properties of the body are considered to be determined and the displacements at the boundary to be random. The general solution to the elasticity-theory problem for the displacements in an anisotropic body is expressed in the form of the sum of the general solution of a homogeneous equation system and the special solution of an inhomogeneous system. Determination of the latter reduces to solution of a system of integral equations with a common kernel in the form of Green functions of the Laplacian. The first- and second-order moments for the displacements and stresses are given, a numerical example is examined, and the convergence of the approximation-calculation procedure is investigated.S. M. Kirov Ural Polytechnic Institute, Sverdlovsk. Translated from Mekhanika Polimerov, No. 2, pp. 315–320, March–April, 1972.     

Surfaces of discontinuity and waves in an anisotropic plasma with generalized polytropic equations of state

Summary In this paper, using the theory of the surfaces of discontinuity, we study the non-linear, three-dimensional wave propagation in an anisotropic plasma with generalized polytropic equations of state. A detailed account of the surfaces of weak discontinuity is given, whether they are wavefronts or material surfaces. The specific subjects treated in the paper are indicated by the titles of the Sections. Entrata in Redazione il 28 settembre 1978.     

Nonlinear analysis and elastic-plastic behavior of anisotropic structures

An elastic-plastic analysis of anisotropic work-hardening materials based on a quadratic approximation of the Tsai-Wu criterion is presented. General expressions for the anisotropic parameters in the yield condition are derived for initial and subsequent yielding. Particularly, the plastic constitutive relations are expressed by means of both the flow theory as well as the deformation theory extended to anisotropic plasticity. The numerical algorithms are based upon the notion of a return mapping procedure and a consistent tangent operator valid for anisotropic elastic-plastic materials including work-hardening effects is developed. The solution equations are evaluated by consistent linearization of a nonlinear variational principle and a Newton-Raphson scheme is adopted for the iterative solution of the nonlinear problems. Numerical examples exhibit the reliable performance of the proposed algorithm in some practical calculations. The effects of anisotropy and the differences between flow and deformation theories in the obtained solutions are discussed and compared with available numerical results.     

Thermoelastic stresses in an anisotropic slab

This paper deals with the thermoelastic stresses in an infinite slab of an anisotropic material of constant finite thickness, which arise due to temperature field varying along the thickness and length of the slab. One face of the slab is rigidly fixed and held at a constant temperature while on the other face, which is held stress-free, a continuous temperature field is applied. The differential equations involved are solved by the general operator method and the stress, displacement and temperature distributions in the slab are numerically evaluated for zinc. Results are represented in graphs.     

Theoretical and experimental investigation of anisotropic damage in textile-reinforced composite structures

In the present work, a phenomenological plane-stress damage-mechanics-based model for textile-reinforced composites is presented and its predictive capability is evaluated by carrying out a series of experimental tests. Damage variables are introduced to describe the evolution of the damage state and, as a subsequence, the degradation of material stiffness. For calculating the nonlinear stress and strain distribution of complexly loaded composites with a textile reinforcement, a special emphasis has to be placed on the interaction between the fiber failure due to the stress in the fiber direction and the matrix failure due to the transverse and shear stresses. This demands the formulation of realistic failure criteria taking into account the microstructural material behavior and different fracture modes. The new failure criteria, like the fracture mode concepts, consider these fracture modes, as well as further fracture types, in the reinforcement plane. The failure criteria are based on equations for failure surfaces in the stress space and damage thresholds in determining the stiffness degradation of the composite. The model proposed was used to characterize the strength and the failure behavior of carbon-fiber-reinforced composites. For this purpose, several unidirectional and bidirectional tests were performed to determine the specific properties of the material. The specimens were investigated by using acoustic emission techniques and strain-controlled tension and torsion tests.Russian translated published in Mekhanika Kompozitnykh Materialov, Vol. 40, No. 6, pp. 791–810, November–December, 2004.     

Generation of the vortex train using plasma barrier discharge actuator

The plasma actuator is used to generate periodical train of vortices moving along the surface. For generation the high-frequency high-voltage AC is used forming more-or-less steady wall-jet-like flow by the dielectric barrier discharge or corona discharge. Low-frequency modulation of the supply voltage is applied to generate vortices. Parameters of the vortex train are studied as function of the generator setting using TR-PIV technique. The generated flow patterns are to be applied for control of a boundary layer. (© 2011 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Dispersed failure of an anisotropic flywheel

Based on a hereditary damage model of solids, the strength of a cylindrically anisotropic flywheel is calculated. By using a failure criterion, the location and time of initial failure is determined in relation to an anisotropy parameter, for which the ratio of rigidities in the tangential and radial directions is taken. The process of dispersed failure depends on the expansion intensity of the damaged zone. The boundary of the zone is the failure front, whose equations of motion are obtained in the cases of absence and presence of a residual strength for the material behind the failure front. In the second case, the damaged material is modeled by an isotropic elastic medium with considerably reduced values of strength and rigidity characteristics, and variations in the pressure on the failure front are also determined. Graphs of the radial coordinate of failure front as a function of time are constructed and analyzed for different values of the anisotropy parameter, the degree of residual strength and density behind the failure front, and proportions of geometrical sizes of the flywheel. The critical failure times are found. A system of restrictions on the values of mechanical and geometrical parameters is revealed which makes possible the realization of the process of dispersed failure investigated.Translated from Mekhanika Kompozitnykh Materialov, Vol. 41, No. 1, pp. 93–108, January–February, 2005.     

Inference for an anisotropic diffusion model

The vector sum of a white noise in an unknown hyperspace and an Ornstein-Uhlenbeck process in an unknown line is observed through sharp linear test functions over a finite time span. The parameters associated with the white noise (including the hyperplane) are determinable with precision and index the measure-equivalence classes in the relevant sample space. An intraclass relative density provides a basis for Bayesian inference of the remaining parameters.     

Design of anisotropic structures: Calculation,optimization, and tests

Conclusions A computational procedure based on a limiting state has been worked out which proposes the performance of tests of samples, small-scale models, and full-scale structures and a statistical analysis of the experimental data. Advantages of the method are shown in comparison with the computational method based on fracturing loads which pertain to estimating the accuracy of the computational scheme of structures and determining their safety coefficients. An optimality criterion is formulated within the framework of the method which is related to ensuring a maximum of the limiting (fracturing or critical) load with a constant mass of the structure.Applications of the method are given to estimation of the strength and stability of structures made out of polymeric and metal CM with the use of the Gol'denblat-Kopnov criterion and solutions based on linear shell theory. The conditions for realization of the optimality criterion of structures are determined. Recommendations are made for the rational reinforcement of structures made out of filamentary CM, and a procedure is proposed for the rational design of reinforced structures.As an example of the tests for stability of cylindrical shells made out of aluminum-magnesium alloy under external pressure, the legitimacy of the cause of the disagreement between the calculated and experimental critical loads, which consists of a discrepancy in the nature of wave formation at the instant of stability loss and initial imperfections, and the effectiveness of the computational method based on a limiting state are confirmed. Refined computational formulas for the critical loads of cylindrical shells made out of fiberglass, carbon fiber, and boraluminum under typical kinds of loading are proposed within the framework of the method and on the basis of an analysis of the results of tests, and a comparison is made of the effectiveness of the reinforcement of shells made out of aluminum-magnesium alloy and carbon fiber. The values of the safety coefficients of structures which guarantee their reliability are determined.Translated from Mekhanika Kompozitnykh Materialov, No. 2, pp. 262–271, March–April, 1980.