Stresses in an elastic body under nonlinear antiplane deformation

The stress field in a cylindrical elastic body under antiplane deformation and certain constraints imposed on volume and surface forces is studied in a nonlinear formulation in actualstate variables. A boundaryvalue problem for independent stress components is formulated in Cartesian and complex variables, sufficient ellipticity conditions for this problem are indicated, and constraints on surface loading are imposed. Analytical solutions are given for linear and weak nonlinear elastic potentials. Similarity to a plane subsonic idealgas flow is established. An approximate method for the solution of the problem is developed.     

Effect of high-frequency vibrations on the stability of advective flow

The stability of plane convective flow in a horizontal layer with a longitudinal temperature gradient under the action of longitudinal vibrations is considered. The behavior of small normal plane and spiral perturbations is investigated. It is shown that the vibrations enhance the stability with respect to almost all types of perturbations. The sole exception is plane thermal waves whose existence domain extends toward low Prandtl numbers. Perm’. Translated from Izvestiya Rossiiskoi Akademii Nauk, Mekhanika Zhidkosti i Gaza, No. 1, pp. 16–22, January–February, 1998. The work was supported by the Russian Foundation for Fundamental Research (project No. 94-01-01730).     

Breaking of gravity waves in a neighborhood of their second critical propagation speed

Experimental data on gravity shallow-water waves generated by a vertical plate moving in a predetermined manner are given. The plate completely covers the cross section of the channel. It is found that with when the wave speed exceeds the first critical value known in hydraulics, the wave retains smoothness. Breaking of the waves begins at the second critical speed (which is about 1.3 times as high), whose value coincides with the limiting propagation speed of a solitary wave. Lavrent'ev Institute of Hydrodynamics, Siberian Division, Russian Academy of Sciences, Novosibirsk 630090. Translated from Prikladnaya Mekhanika i Tekhnicheskaya Fizika, Vol. 39, No. 2, pp. 52–58, March–April, 1998.     

Analysis of nonlinear solutions with many singular points in problems of spatial deformation of rods

We consider an algorithm for obtaining numerical solutions of the geometrically nonlinear problems of spatial deformation of elastic rods in the presence of many singular points. The questions of the construction of bifurcation solutions and the stability of the found states of equilibrium are discussed. The results of a study of the nonlinear deformation and stability of a ring in the spatial formulation, which are supported by experimental data, are given. Chaplygin Siberian Aviation Institute, Novosibirsk 630051. Translated from Prikladnaya Mekhanika i Tekhnicheskaya Fizika, Vol. 39, No. 6, pp. 148–153, November–December, 1998.     

Stability of a spanwise nonuniform boundary layer flow

The linear stability of a boundary layer flow with a spanwise-periodic nonuniformity in the velocity profile is investigated. This flow can be considered as a model of a streaky structure occurring in the boundary layer at a high freestream turbulence level. It is shown that for a small nonuniformity amplitude symmetric modes similar to Tollmien-Schlichting waves are the most unstable. At higher nonuniformity amplitudes, antisymmetric modes, qualitatively different from Tollmien-Schlichting waves and having a larger phase velocity, are the most amplified. Moscow. Translated from Izvestiya Rossiiskoi Akademii Nauk, Mekhanika Zhidkosti i Gaza, No. 6, pp. 54–63, November–December, 1998. The study was carried out with the support of the International Scientific and Technical Center (project No. 199-95) and the Russian Foundation for Basic Research (project No. 95-01-01201a).     

Parametric study of the Hartmann–Sprenger tube

Experiments were conducted with a Hartmann–Sprenger tube (H–S) to study the effect of different parameters on the frequency and amplitude of acoustic fluctuations excited when the H–S underexpanded jet impinges on an in-line cavity. Time averaged shadowgraphs were acquired to study the flow field between the underexpanded jet and the cavity for varying parameters of the H–S tube. It was observed that the H–S tube primarily excited two different modes. The first mode corresponds to the jet regurgitant mode (JRG) where the frequency of oscillations scales as a function of the cavity depth. The other mode is screech where an oscillating shock is formed in front of the cavity. The screech mode excites a higher acoustic frequency than the JRG and it is observed to be a strong function of the pressure ratio R, and distance between the jet and the cavity X. At a fixed cavity length, varying standoff distance X could excite either the JRG or screech. At very low standoff distances (X/D_j<0.8), the current study indicates that there is a mode switch from screech to JRG. A cavity to jet diameter, D_c/D_j>1 was found to sustain JRG over a wide range of X. Diameter ratios D_c/D_j<1 sustained high frequency screech modes in a wide range of H–S tube parameters.     

Measurement of mean rotation and strain-rate tensors by using stereoscopic PIV

A technique is described for measuring the mean velocity gradient (rate-of-displacement) tensor by using a conventional stereoscopic particle image velocimetry (SPIV) system. Planar measurement of the mean vorticity vector, rate-of-rotation and rate-of-strain tensors and the production of turbulent kinetic energy can be accomplished. Parameters of the Q criterion and negative λ₂ techniques used for vortex identification can be evaluated in the mean flow field. Experimental data obtained for a circular turbulent jet issuing normal to a crossflow in a low speed wind tunnel for a jet-to-crossflow velocity ratio of 3.3 are presented to show the applicability of the proposed technique. The results reveal the presence of a secondary counter-rotating vortex pair (SCVP) which is located within the jet core and has a sense of rotation opposite to that of the primary one (PCVP). Consistency of the measurements is verified by the agreement of data obtained in two perpendicular planes. Accuracy of the data is discussed and algebraic relations for some measurement uncertainties are presented.     

Vortex structure generation on the frontal surface of a cylinder set transversely in a hypersonic flow

The problem of formation of spatially periodic structures on the frontal surface of a cylindrically blunted body set transversely in a hypersonic flow is studied. Within the framework of the model adopted, a possible mechanism of vortex structure generation on the frontal surface of the blunt body is proposed and confirmed by calculations; in this mechanism, the curved bow shock produces a vortex flow, while in its turn the vortex, which persists under weak dissipation, acts on the shock thus maintaining its curved shape. It is shown that the spatially periodic mode of hypersonic flow past a cylinder can exist in the case of a uniform incident flow and under homogeneous boundary conditions on the body surface.     

On the spectrum of natural frequencies of circular cylindrical shells completely filled with a fluid

The natural frequencies of cylindrical shells filled with a fluid and having the ends either simply supported or clamped are determined. Conditions are studied under which the natural frequencies of the shell are close or multiple __________ Translated from Prikladnaya Mekhanika, Vol. 42, No. 5, pp. 42–49, May 2006.     

External shock loading on a submerged fluid-filled cylindrical shell

The interaction between a submerged fluid-filled elastic circular cylindrical shell and an external shock wave is considered. The study focuses on the internal acoustic field. A linear formulation of the problem is considered. A semi-analytical solution is obtained and used to simulate the interaction. A variety of phenomena are observed in the internal fluid, including the reflection and focusing of the internal acoustic wave as well as the radiation into the fluid of elastic waves propagating in the shell. Throughout the paper, the results of numerical simulations are compared with available experimental data, and a good agreement is observed. The solution developed appears to be suitable for use as a benchmark. Engineering relevance of the phenomena observed is discussed.