Existence of a new type of irregular shock-wave interaction

Several types of plane shock-wave interactions [1–5], realized in various cases of practical importance, are now known. In [7] the possibility of the existence of a new type of shock-wave interaction was demonstrated by numerically solving the axisymmetric boundary-value problem. Here, the corresponding two-dimensional boundary-value problem of the interaction between a shock wave and a plane shock is numerically studied, a theoretical basis is obtained for the region of existence of the shock-wave interaction detected, and its principal properties are investigated. Moscow, Dnepropetovsk. Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 5, pp. 181–183, September–October, 1988.     

Aeroelastic stability of a wing with bracing struts (Keldysh problem)

The problem of the influence of bracing struts of two types on the aeroelastic stability of a wing is studied. The formulation of the problem follows that considered by M. V. Keldysh [1]. The behavior of the eigenvalues is studied in the complex plane and the stability, flutter, and divergence domains are constructed. Moscow. Translated from Izvestiya Rossiiskoi Akademii Nauk, Mekhanika Zhidkosti i Gaza, No. 1, pp. 151–162, January–February, 1998.     

Wave processes in solids with defects

The propagation of plane harmonic waves in viscoelastic and elastoviscoplastic materials are studied using the equations of the field theory of defects, the kinematic identities for an elastic continuum with defects, and the dynamic equations of gauge theory. Wave propagation velocities and refraction and absorption coefficients are determined. The structure of the waves and the correlation between the displacement waves and the defect-field waves determining plastic deformation are analyzed. __________ Translated from Prikladnaya Mekhanika i Tekhnicheskaya Fizika, Vol. 49, No. 6, pp. 190–197, November–December, 2008.     

Contact problem for a plane crack under a normally incident antiplane shear wave

The contact-interaction problem for a stationary plane crack with friction between its edges under the action of a normal (to the crack plane) harmonic shear wave is addressed. Antiplane deformation conditions are considered. The distribution of contact forces and displacement discontinuity of crack edges are studied Published in Prikladnaya Mekhanika, Vol. 43, No. 5, pp. 138–142, May 2007.     

Evolution of perturbations on the surface of a viscoelastic liquid

The stability of a layer of a viscoelastic liquid on an inclined plane is studied within the framework of the model with a time-dependent “memory” in the presence of surface tension. It is shown analytically and numerically that these flows can be stable or unstable depending on the Reynolds number. Profiles of the free surface are found as functions of the Reynolds and Weber numbers. Translated from Prikladnaya Mekhanika i Tekhnicheskaya Fizika, Vol. 41, No. 3, pp. 86–91, May–June, 2000.     

Invariant Solutions of the Thermal-Diffusion Equations for a Binary Mixture in the Case of Plane Motion

The group properties of the thermal-diffusion equations for a binary mixture in plane flow are studied. Optimal systems of first-and second-order subalgebras are constructed for the admissible Lie operator algebra, which is infinite-dimensional. Examples of the exact invariant solutions are given, which are found by solving ordinary differential equations. Exact solutions are found that describe thermal diffusion in an inclined layer with a free boundary and in a vertical layer in the presence of longitudinal temperature and concentration gradients. The effect of the thermal-diffusion parameter on the flow regime is studied. __________ Translated from Prikladnaya Mekhanika i Tekhnicheskaya Fizika, Vol. 47, No. 1, pp. 95–108, January–February, 2006.     

Harmonic thickness vibrations of inhomogeneous elastic layers with curved boundaries

The thickness vibrations of elastic inhomogeneous bodies of different geometry under dynamic harmonic loading are studied. The dependence of the amplitude–frequency characteristics of homogeneous and inhomogeneous bodies on excitation frequency is analyzed in detail. The frequency spectra for plane, cylindrical, and spherical layers are determined     

Rheostructural studies of a discotic mesophase pitch at processing flow conditions

The flow-induced microstructure of a mesophase pitch was studied within custom-made dies for changing wall shear rates from 20 to 1,100 s^− 1, a flow scenario that is typically encountered during fiber spinning. The apparent viscosity values, measured at the nominal wall shear rates ranging from 500 to 2,500 s^− 1 using these dies, remain fairly constant. The microstructure was studied in two orthogonal sections: r–θ (cross section) and r–z (longitudinal mid plane). In these dies, the size of the microstructure gradually decreases toward the wall (to as low as a few micrometers), where shear rate is highest. Furthermore, as observed in the r–θ plane of the capillary, for a significant fraction of the cross section, discotic mesophase has a radial orientation. Thus, the directors of disc-like molecules were aligned in the vorticity (θ) direction. As confirmed from the microstructure in the r–z plane, most of the discotic molecules remain nominally in the flow plane. Orientation of the pitch molecules in the shear flow conditions is consistent with that observed in controlled low-shear rheometric experiments reported earlier. Microstructral investigation suggests that the radial orientation of carbon fibers obtained from a mesophase pitch originates during flow of pitch through the die.     

Thermovibrational convective instability of mechanical equilibrium of an inclined fluid layer

The convective instability of mechanical equilibrium of an inclined plane layer of fluid developing under the action of a static gravity field and high-frequency vibration is studied. Configurations corresponding to four directions of the equilibrium temperature gradient — vertical, longitudinal, horizontal, and transverse — are considered for an arbitrary orientation of the vibration axis. The stability limits and the characteristics of the critical perturbations are determined. Perm’. Translated from Izvestiya Rossiiskoi Akademii Nauk, Mekhanika Zhidkosti i Gaza, No. 1, pp. 8–15, January–February, 1998. This investigation was carried out with partial support form RSA-NASA (contract No. 920/18 — 5208/96).     

Explosive projection of liquid from a thick-walled cylindrical container

The process of projection of a layer of an ideal liquid enclosed into a cylindrical elastoplastic shell by products of instantaneous detonation of a high explosive charge is studied numerically in a two-dimensional plane formulation. The processes of shell fracture and liquid exhaustion through the resultant slots are considered. Numerical results are analyzed, and analytical relations for angular distributions of radial velocity and mass of the liquid escaping through the slots are derived. __________ Translated from Prikladnaya Mekhanika i Tekhnicheskaya Fizika, Vol. 50, No. 3, pp. 56–63, May–June, 2009.     

Crosslinking of a polyester resin in the heated plain sheet copper mould

The crosslinking of the unsaturated polyester was studied by using experiments and a model of the process. The kinetic parameters were calculated from the heat flux–time curves obtained by differential scanning calorimetry (DSC, Netzsch–Simultaneous Thermal Analyser DSC 200), working in DSC (dynamic) mode. The temperature–time histories were studied in plain sheet copper mould. The mathematical model was constructed by taking into account the heat transferred by conduction through the resin, as well as the kinetics of heat generated by the crosslinking reaction. The contributions to the rise in temperature from heat conduction and chemical reaction are different in different parts of the composite, and can explain the temperature-, or degree of crosslinking (DOC)–time histories. By considering temperature–time histories developed within the sample, more extensive knowledge of the process can be obtained. The effect of the heat transfer by conduction through the composite as well as the internal heat generated by the cure reaction is clearly shown, despite the complexity of the process. Finally, good agreement between experimental data and predicted mathematical model of the crosslinking process in plane sheet mould was shown.     

Plane strain problem for an incompressible nonlinearly elastic solid

The plane strain of an incompressible body is studied with geometrical and physical nonlinearity and potential forces taken into account. A nonlinear system of equations for strains is obtained in actual variables, and conditions of its ellipticity are derived in terms of the elastic potential. Boundary conditions for strains are found from specified loads. Analytical solutions of the boundary problem in strains and their corresponding stress fields are found for the case of identical elongations. __________ Translated from Prikladnaya Mekhanika i Tekhnicheskaya Fizika, Vol. 50, No. 2, pp. 217–225, March–April, 2009     

Averaged rotations at finite plane strain

The averaged rotations and other mechanical parameters at finite plane strains of an elastic material, which are characterized by a linear relation between the Cauchy stresses and the Almansi strains, are studied. The form of the elastic potential is determined. The displacement problem is reduced to a boundary-value problem for complex potentials, which is solved in terms of Cauchy-type integrals for the specified boundarys displacements. The results obtained are compared with the linear solution. Novosibirsk State University, Novosibirsk 630090. Translated from Prikladnaya Mekhanika i Tekhnicheskaya Fizika, Vol. 41, No. 3, pp. 187–196, May–June, 2000.     

Domain decomposition method with hybrid approximations applied to solve problems of elasticity

To solve two-dimensional boundary-value problems of elasticity, two iteration algorithms of the domain decomposition method are proposed: parallel Neumann–Neumann and sequential Dirichlet–Neumann. They are based on the hybrid boundary–finite-element approximations. The algorithms are proved to converge. The optimal parameters are selected using the minimum-residual and steepest-descent methods. Some plane problems of elasticity are solved as examples, and stationary and nonstationary iteration algorithms in these examples are analyzed for efficiency Translated from Prikladnaya Mekhanika, Vol. 44, No. 11, pp. 18–29, November 2008.     

On the types and number of plane waves in hypoelastic materials

General principles are formulated for modeling the elastic deformation of materials and analyzing plane waves in nonlinearly elastic materials such as hyperelastic, hypoelastic, and those governed by the general law of elasticity. The results of studying the propagation of plane waves in hypoelastic materials are further outlined. The influence of initial stresses and initial velocities on the types and number of plane waves is studied. Wave effects characteristic of hypoelastic materials are predicted theoretically. One of such effects is blocking of certain types of plane waves by initial stresses __________ Translated from Prikladnaya Mekhanika, Vol. 41, No. 11, pp. 96–107, November 2005.     

Analysis of plane and cylindrical nonlinear hyperelastic waves in materials with internal structure

A comparative analysis of two types of hyperelastic waves—plane waves (with plane front) and cylindrical waves (with curved front)—is offered. The propagation of the waves is studied theoretically for quadratically nonlinear hyperelastic media and numerically for a class of unidirectional fibrous composite materials. Hyperelasticity is described using the classical Murnaghan potential and a structural model of the first order—the model of effective constants. The internal structure of materials is described by this model and is at the micro-or nanolevels in numerical analysis. Particular attention is given to the evolution of the wave profile. It is studied in three stages: (i) derivation of nonlinear wave equations, (ii) construction of solutions in the form of plane and cylindrical waves, and (iii) numerical analysis of the evolution of these waves in composites with microlevel (Thornel) or nanolevel (Z-CNT) fibers. The main similarities and differences between plane longitudinal and cylindrical waves are shown. The most unexpected result is the striking difference between the evolution patterns numerically observed for plane and cylindrical wave profiles __________ Translated from Prikladnaya Mekhanika, Vol. 42, No. 10, pp. 21–46, October 2006.     

Experimental study of the instability of convective boundary layers under the action of vibration

The wave instability of convective boundary layers in a horizontal cylindrical layer of ethanol under the action of vertical hamonic high-frequency vibration is studied. A strong destabilizing effect of the vibration on the stability of the convective boundary layers is detected. In the plane of the gravity and vibration Rayleigh numbers (Ra and R _V ), the excitation limit of the wave instability is determined. The periods of the temperature oscillations caused by the waves in the boundary layers near the inner and outer cavity boundaries are studied as functions of the Rayleigh numbers. Perm’. Translated from Izvestiya Rossiiskoi Akademii Nauk, Mekhanika Zhidkosti i Gaza, No. 3, pp. 32–40, May–June, 1998.     

Spherical particle sedimentation along an inclined plane at small reynolds numbers

At small Reynolds numbers, the gravity-driven motion of a solid spherical particle along an inclined plane in a Newtonian liquid initially at rest was studied experimentally. A comparison of the experiment with the calculations showed that motions both with and without particle-plane contact may occur. The latter cannot be explained within the Stokes approximation. Moscow. Translated from Izvestiya Rossiiskoi Akademii Nauk, Mekhanika Zhidkosti i Gaza, No. 4, pp. 129–136, July–August, 1998.     

Stability of a thin panel with added elements in a supersonic gas flow

Thin elastic panels subjected to compression in the median plane and to supersonic gas flow are considered. An element is attached to the panel by an elastic spring and linear dashpot. The stability of the initial planar state of the panel is studied as a function of the main control parameters—such as the gas velocity and membrane force—and the parameters of the attached element. The evolution of the stability regions in the control-parameter plane is considered. Special attention is paid to compound bifurcation points and stabilization islets. Institute of Machine Science, Russian Academy of Sciences, Moscow, Russia. Translated from Prikladnaya Mekhanika, Vol. 35, No. 12, pp. 3–10, December, 1999.     

Stability of Poiseuille flow in the presence of a longitudinal magnetic field

The stability of the plane flow of an electrically conducting fluid with respect to small perturbations was studied at large Reynolds numbers in the presence of a longitudinal magnetic field. The dependence of the critical Reynolds number on the electrical conductivity is investigated. At large Reynolds numbers, a new branch of instability and a sudden change in the critical Reynolds numbers is found. __________ Translated from Prikladnaya Mekhanika i Tekhnicheskaya Fizika, Vol. 49, No. 3, pp. 45–53, May–June, 2008.