Showing papers in "Journal of Applied Mechanics and Technical Physics in 2012"

Generalized equivalence transformations and group classification of systems of differential equations

Abstract: The notion of generalized equivalence transformations for which the equivalence transformations considered by Ovsyannikov are universal equivalence transformations is introduced for a system of differential equations. An algorithm of the group classification of the system of differential equations with the help of these generalized equivalence transformations is proposed. The efficiency and advantages of this algorithm are demonstrated by examples of equations of gas dynamics and equations of nonlinear longitudinal oscillations of a viscoelastic bar in the Kelvin model.

High-rate deformation and fracture of fiber reinforced concrete

Abstract: This paper presents the results of dynamic compression and splitting-tensile tests of cardiff fiber reinforced concrete (CARDIFRC) composite using the Kolsky technique and its modification. The strength and deformation characteristics of fiber-reinforced concrete were determined experimentally at high strain rates. The mechanical characteristics were found to depend on the strain rate and stress rate. A uniform interpretation of the rate effects of fracture of the tested fiber-reinforced concrete is given on the basis of a structural-temporal approach. It is shown that the time dependences of both the compressive and tensile strengths of fiber reinforced concrete are well calculated using the incubation time criterion.

Effect of the contact-line dynamics on the oscillations of a compressed droplet

Abstract: This paper studies the natural and forced oscillations of a deformed droplet of an inviscid liquid surrounded by a different liquid and bounded in the axial direction by solid planes. In equilibrium, the droplet is a figure of revolution and the ratio of its radius to height is significant. The equilibrium contact angle between the side surface of the droplet and the solid surface is different from a right angle. The motion of the contact line is taken into account by setting an effective boundary condition. It is shown that three characteristic ranges of natural frequencies exist.

Numerical simulation of wave formation in an oblique impact of plates by the method of molecular dynamics

Abstract: Results of numerical simulations of wave formation in an oblique symmetric impact of metal plates by the method of molecular dynamics are presented. In this case, the impacting plates experience the same loading conditions as in explosive welding. It is demonstrated that the evolution of waves on the interface between the welded plates is caused by self-induced oscillations in the vicinity of the contact point. A mechanism of building-up and sustaining of self-induced oscillations is proposed on the basis of numerical calculations performed.

Mathematical model of micropolar elastic thin plates and their strength and stiffness characteristics

Abstract: A number of hypotheses were formulated using the properties of an asymptotic solution of boundary-value problems of the three-dimensional micropolar (moment asymmetric) theory of elasticity for areas with one geometrical parameter being substantially smaller than the other two (plates and shells). A general theory of bending deformation of micropolar elastic thin plates with independent fields of displacements and rotations is constructed. In the constructed model of a micropolar elastic plate, transverse shear strains are fully taken into account. A problem of determining the stress-strain state in bending deformation of micropolar elastic thin rectangular plates is considered. The numerical analysis reveals that plates made of a micropolar elastic material have high strength and stiffness characteristics.

Effect of sound-absorbing materials on intensity of disturbances in the shock layer on a flat plate aligned at an angle of attack

Abstract: Results of a numerical and experimental study of characteristics of disturbances in a hypersonic shock layer on a flat plate covered by a sound-absorbing coating and aligned at an angle of attack are presented. Experiments and computations are performed for the free-stream Mach number M∞ = 21 and Reynolds number ReL = 6 · 104. A possibility of suppressing pressure fluctuations in the shock layer at frequencies of 20–40 kHz with the use of tubular and porous materials incorporated into the plate surface is demonstrated. Results of numerical simulations are found to be in good agreement with experimental data.

Motion of a slender body in a fluid under a floating plate

Abstract: This paper studies the three-dimensional unsteady problem of the hydroelastic behavior of a floating infinite plate under the impact of waves generated by horizontal rectilinear motion of a slender solid in a fluid of infinite depth. An analytic solution of the problem is found based on the known solutions for the unsteady motion of a point source of mass in a fluid of infinite depth under a floating plate. Asymptotic formulas are obtained which model the motion of a solid slender body in a fluid by replacing the body with a source-sink system. These formulas are used to numerically analyze the effect of plate thickness, depth of the body, its dimensions and the velocity of rectilinear motion on the amplitude of deflection of the floating plate. The motion of a submarine under a nonbreakable plate was modeled experimentally. Theoretical and experimental data are in good agreement.

Effect of micro-blowing of a gas from the surface of a flat plate on its drag

Abstract: Low-velocity gas flows past a flat plate are numerically simulated. The influence of gas micro-blowing from some part of the surface and its distribution on the local and integral friction coefficients is studied. It is demonstrated that the integral value of friction is almost independent of the distribution of blowing domains over the plate surface if the total blowing intensity stays unchanged. The calculated decrease in the friction drag is in both qualitative and quantitative agreement with experimental results.

Laboratory observation of slow movements in rocks

Abstract: It is established that the development of a localized plastic strain during compression of samples of rocks (sylvinite, marble, and sandstone) deformed by different micromechanisms has an autowave character. It is shown that the velocity of propagation of autowaves arising in the samples under compression is 10−5 to 10−4 m/s (0.3 to 3.0 km/g) and is close to the velocity of slow waves observed in the Earth’s crust after earthquakes or rockbursts.

Nonlinear model of a pipeline in a gravity field with an ideal fluid moving through it

Abstract: A nonlinear model describing the movement of a pipeline with fluid moving through it and allowing consideration of a number of applications that do not have solutions within the linear model is proposed. The problem of equilibrium of a pipe with fluid moving through it in the gravity field is solved. An exact solution for the simplified non-stationary model equation is constructed.

Nucleation and growth of a gas bubble in magma

Abstract: The dynamics of a “collective” gas bubble in the magma melt during its decompression was numerically studied on the basis of a complete mathematical models of an explosive volcanic eruption. It is shown that the bubble size distribution obtained for the nucleation process has one peak, which allows considering a “collective” bubble. The main stages of bubble growth due to gas diffusion and changes in the viscosity of the medium are determined. It is shown that the high viscosity of the melt makes possible the transition from the Rayleigh equation to a simpler relation for the radial velocity of the bubble.

Exact solution of the navier-stokes equations in a fluid layer between the moving parallel plates

Abstract: This paper studies exact solutions of the Navier-Stokes equations for a layer between par- allel plates the distance between which increases proportionally to the square root of time. A count- able set of exact solutions and their derived countable set of continuous families of exact solutions are obtained. It is shown that certain intervals of the Reynolds parameter have two solutions and some of them one solution.

Dam-break flows at a jump in the width of a rectangular channel

Abstract: The problem of dam-break flow at a jump in the width of a rectangular channel is studied in the first shallow-water approximation. Two cases where the upstream channel width is greater or smaller than the downstream channel width are considered. It is shown that in the first case, the problem is uniquely solvable under the assumption that the total energy of the flow is conserved at the jump in the channel width, and in the second case, a solution of the problem for some initial data exists only provided that the total energy of the flow is lost at this jump.

Supersonic flow of a rarefied gas around a wire grid

Abstract: The direct simulation Monte Carlo method is used to study a plane-parallel supersonic gas flow through a grid formed by a number of infinite parallel wires. Characteristic features of the shock disturbance formation of in the interaction of a supersonic flow with a permeable grid are revealed. Particular attention is paid to studying the influence of geometrical parameters of the wire target on the number of particles colliding with the surface of the wires.

Experimental verification of the method of calculating the flow parameters in the test section of the hotshot wind tunnel

Abstract: Calculated parameters of the gas flow in the test section of a high-enthalpy short-duration wind tunnel (IT-302M hotshot wind tunnel) are compared with experimentally determined values. It is demonstrated that the differences in flow characteristics in the test section measured by two methods [flow rate determined by the method of flask filling and physical velocity determined by particle image velocimetry (PIV)] and the calculated values is within several percent. The experimental results show that the assumptions taken for calculating the flow parameters in the test section ensure a fairly accurate description of the processes in the gas-dynamic duct of the hotshot wind tunnel. The most significant differences between the calculated and experimental values are found to be induced by two factors: neglect of heat losses from the test gas (gas flow) to the walls of the first settling chamber and uncertainty in reconstructing the pressure level in the first chamber at the time t = 0.

Construction of constitutive equations of creep in orthotropic materials with different properties under tension and compression

Abstract: Constitutive equations of steady creep are proposed for structural aluminum alloys that possess significant anisotropy at elevated temperatures in addition to different resistances to tension and compression.

Chaotic phase synchronization of vibrations of multilayer beam structures

Abstract: Complex deterministic vibrations of a multilayer stack of beams linked only by boundary conditions are considered. A mathematical model of the stack is constructed taking into account the geometric and physical nonlinearities of the beams and the contact interaction of their layers. A method for the study of phase synchronization of vibrations based on wavelet analysis is developed. The influence of boundary conditions for the lower beam and different types of nonlinearity (physical, geometrical, and contact) and their combinations on the character and phase synchronization of vibrations of the multilayer stack of beams is studied.

Formation of a cavity in the initial stage of motion of a circular cylinder in a fluid with a constant acceleration

Abstract: This paper considers the joint motion of an ideal fluid and a circular cylinder completely immersed in it at small times. It is assumed that the cylinder, which was initially at rest, moves in a horizontal direction with a constant acceleration. The dynamics of the internal and external free boundaries of the fluid at small times is studied. An asymptotic analysis of the form of the internal free surface near the separation points is performed. It is shown that at high acceleration of the circular cylinder, a large cavity is formed behind, with a strong perturbation of the external free surface of the fluid over the surface of the cylinder.

Oil recovery in the presence of microbubbles in the filtration flow

Abstract: This paper presents mathematical models for oil-gas flow taking into account the various processes due to the formation of gas micronuclei (microbubbles) in oil: slip of oil relative to the walls of the pore channels (gas lubrication), changes in oil viscosity, and motion of microbubles with respect to oil. We consider examples of oil flow in the near-wellbore zone for the case where a reduction in pressure to the saturation pressure leads to the formation of gas microbubbles and micronuclei and examples of the action of a water-gas mixture in the case where oil foams in the contact area with the injected gas, i.e., a finely dispersed mixture of oil and microbubbles is formed. The behavior of indicator curves for an oil well with the formation of microbubbles is simulated, and the effect of microbubbles on the oil recovery factor in a water-alternating-gas injection process is studied.

Stability analysis of cylindrical shells containing a fluid with axial and circumferential velocity components

Abstract: The stability of an elastic circular cylindrical shell of revolution interacting with a compressible liquid (gas) flow having both axial and tangential components is analyzed. The behavior of the fluid is studied within the framework of potential theory. The elastic shell is described in terms of the classical theory of shells. Numerical solution of the problem is performed using a semianalytical finite element method. Results of numerical experiments for shells with different boundary conditions and geometric dimensions are presented. The effects of fluid rotation on the critical flow velocity and the effect of axial fluid flow on the critical angular velocity of fluid rotation were estimated.

Finite-difference solution of unsteady natural convection flow past a nonisothermal vertical cone under the influence of a magnetic field and thermal radiation

Abstract: An analysis is performed to study the heat transfer characteristics of natural convection over a vertical cone under the combined effects of a magnetic field and thermal radiation. The cone surface is subjected to a variable surface temperature. The fluid considered is a gray absorbing/emitting, but non-scattering medium. The boundary layer equations governing the flow are reduced to non-dimensional equations using non-dimensional quantities valid in the free-convection regime. The resulting non-dimensional governing equations are solved by an implicit finite-difference method of the Crank-Nicolson type, which is rapidly convergent and unconditionally stable. Numerical results are obtained for velocity, temperature, local and average skin friction, and local and average Nusselt numbers for various values of parameters occurring in the problem and are presented in the graphical form. Excellent agreement of the results obtained with available data is demonstrated.

Differentiation of the energy functional in the equilibrium problem for a Timoshenko plate containing a crack

Abstract: The variational formulation of the equilibrium problem for a Timoshenko plate containing a vertical plane crack is considered. Nonpenetration conditions in the form of inequalities (Signorini type conditions) are specified on the crack faces. The behavior of the solution and the corresponding energy functional of the plate with variation in the crack length is analyzed. A formula for the derivative of the energy functional along the crack length is obtained. The solutions are found to continuously depend on the parameter characterizing the crack length.

Heat and mass transfer analysis in unsteady boundary layer flow through porous media with variable viscosity and thermal diffusivity

Abstract: In this paper, a comprehensive mathematical analysis is carried out on an unsteady boundary-layer flow with heat and mass transfer characteristics of a viscous fluid through porous media. Fluid suction or blowing is assumed to take place at the surface. The governing coupled nonlinear partial differential equations are transformed into coupled nonlinear ordinary differential equations by using a similarity transformation and are solved analytically and numerically by using the homotopy analysis method and the Runge-Kutta and shooting technique, respectively. A comparison between analytical and numerical results is conducted, which shows excellent agreement.

Effect of the recoil pressure induced by evaporation on motion of powder particles in the light field during laser cladding

Abstract: A model is proposed, which takes into account acceleration of powder particles by a force induced by recoil of material vapors from the irradiated region of the particle surface. Results of a numerical analysis of heat and mass transfer in the case of motion of individual stainless steel powder particles in a gas flow and in a light field of laser radiation under conditions of laser cladding are presented. Acceleration of particles is found to depend on their diameter, carrier gas velocity, powder material properties, laser radiation power, and degree of attenuation of the power density in the laser beam in the direction of its action on the substrate. The calculated results are compared with experimental data on light-propulsion acceleration of individual particles (of aluminum, aluminum oxide, and graphite) under the action of pulsed laser radiation.

Finding the elastic strain limit at the tip region of a physical cut with arbitrarily loaded faces

Abstract: A model describing the stress-strain state in the neighborhood of a physical cut with an arbitrary distribution of external load along its faces is presented. The stress-strain state of a material layer bounded by the continuations of the cut faces is considered. The interaction between the layer and the external half-planes leads to a closed system of integrodifferential equations for the mean stress components in the layer, which splits into two equations for the mean normal stresses and an equation for the mean shear stress. Numerical solutions of the system for the cases of symmetric and antisymmetric loading of the faces by concentrated forces are given. Conditions for the transition of the tip region of the cut to the state of plasticity and fracture are considered.

Numerical modeling of the air flow in the human nasal cavity with simulation of application of the clinical method of active anterior rhinomanometry

Abstract: The air flow in the human nasal cavity is numerically modeled with the use of the clinical method of measuring of the nasal cavity capacity. Results obtained in this study offer an explanation for the contradiction between the computed data and data obtained during clinical measurements.

Evolution of strain localization autowaves in a zirconium alloy and evaluation of plasticity margin in a rolling area

Abstract: The stress-strain state of a zirconium alloy in a cold rolling area is studied by considering the evolution of strain localization autowaves and changes in the ultrasound velocity. It is found that in the region of transition from the upsetting zone to the reduction zone, there is a significant exhaustion of the plasticity reserve of the material, so that fracture is most likely in exactly this region. It is shown that the traditional methods of estimating the plasticity margin from mechanical characteristics cannot reveal this region; an integrated analysis of plastic deformation macrolocalization patterns and acoustic measurement results is required.

Short-duration wind tunnel with combined heating and stabilization of parameters

Abstract: A high-enthalpy short-duration wind tunnel (hotshot wind tunnel) is designed for different operation modes ensured by combining various methods of test gas heating [by an electric arc, chemical energy, adiabatic compression, and heating in an external source of heat (with respect to the settling chamber)]. The wind tunnel is designed for the following ranges of parameters: stagnation pressure p0 = 1–200 MPa, stagnation temperature T0 = 600–4000 K, Mach number M = 4–20, and test time t < 1 s. The wind tunnel can operate both in the regime of the classical hotshot facility with decreasing parameters of the test gas and in the regime with stabilization of parameters owing to synchronized motion of the opposite pistons of the pressure multiplier toward each other.

Quasi-static compression and spreading of an asymptotically thin nonlinear viscoplastic layer

Abstract: The problem of quasi-static compression and spreading (squeezing) of a thin viscoplastic layer between approaching absolutely rigid parallel-arranged plates is solved using asymptotic integration methods rapidly developed in recent years in the mechanics of deformable thin bodies. A solution symmetric about the coordinate axes is sought in the same region of the layer as in the classical Prandtl problem. The layer material is characterized by a yield point and a hardening function relating the intensities of the stress and strain rate tensors. The conditions of no-flow and reaching certain values by tangential stresses are imposed on the plate surfaces. The coefficients at the terms of the asymptotic expansions corresponding to the minus first and zero powers of the small geometrical parameter are obtained. An approximate analytical solution in the case of power hardening and large Saint-Venant numbers is given. The physical meaning of the roughness coefficient characterizing the cohesion between the plates and viscoplastic material is discussed.

Variational principles and optimal solutions of the inverse problems of creep bending of plates

Abstract: It is shown that inverse problems of steady-state creep bending of plates in both the geometrically linear and nonlinear formulations can be represented in a variational formulation. Steady-state values of the obtained functionals corresponding to the solutions of the problems of inelastic deformation and elastic unloading are determined by applying a finite element procedure to the functionals. Optimal laws of creep deformation are formulated using the criterion of minimizing damage in the functionals of the inverse problems. The formulated problems are reduced to the problems solved by the finite element method using MSC.Marc software.