Existence theorems in the theory of mixtures

This paper is concerned with boundary-value problems of the linear theory for binary mixtures of elastic bodies. First, a counterpart of the Boussinesq-Somigliana-Galerkin solution in classical elastostatics is established and the fundamental solutions in the equilibrium theory of homogeneous and isotropic mixtures are derived. Then, representations of Somigliana type for the displacement fields are presented. The potentials of single layer and double layer are used to reduce the boundary-value problems to singular integral equations. Existence and uniqueness results are established.     

Free thermoconcentration convection above a localized heat source

Shadowgraph and probe techniques are used to investigate the free convective flow pattern above various localized heat sources (electrolytic cell — point source, short vertical cylinder, sphere) in an exponentially stratified fluid. The characteristic types of structure are classified with respect to the appearance of new forms of instability. The critical values of the global Rayleigh number, at which the flow pattern is restructured, are determined. The dependence of the height of the convection zone and the height of the individual cells on the governing parameters of the problem is investigated and the results are reduced to universal form. Laboratory experiments and oceanic observations are qualitatively compared.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 2, pp. 27–34, March–April, 1989.     

Some new aspects of the slow flow of a viscous fluid through an axisymmetric duct expansion or contraction. II — Experimental part

The flow of a newtonian viscous fluid through a cylindrical duct in the vicinity of a section discontinuity is studied using a visualization technique. The evolution with the Reynolds number of the features of the stationary vortex cell is given, in particular the reversibility of the flow is verified for the very small Reynolds numbers. In the creeping regime a detailed analysis of the velocity and strain-rate fields is performed.     

On the method of indirectly measuring gas and particulate phase velocities in shock induced dusty-gas flows

A method of indirectly measuring the temporally varying velocities of the gas and particulate phases in the nonequilibrium region of a shock wave moving at constant speed in a dusty-gas flow is described, and this method is assessed by using experimental data from shock-induced air flows containing 40-m-diameter glass beads in a dusty-gas shock-tube facility featuring a large horizontal channel (19.7-cm by 7.6-cm in cross-section). Simultaneous measurements of the shock-front speed with time-of-arrival gauges, particle concentration by light extinctiometry and gas-particle mixture density by beta-ray absorption are used in conjunction with two mass conservation laws to obtain the indirect velocity measurements of both phases. A second indirect measurement of the gas-phase velocity is obtained when the gas pressure is simultaneously recorded along with the particle concentration and shock-front speed when used in conjunction with the conservation of mixture momentum. Direct measurements of the particulate-phase velocity by laser-Doppler velocimetry are also presented, as a means of assessing the indirect velocity measurement method.List of symbols a _f frozen speed of sound - D particle diameter - d _f LDV interference fringe spacing - d _m LDV probe-volume diameter - l _m LDV probe-volume length - M _sf frozen shock Mach number - M _se equilibrium shock Mach number - Ñ(D) probability density distribution by number - p pressure - R gas constant - t time - T temperature - S LDV-signal amplitude - v _g gas velocity in laboratory frame of reference - v _p particle velocity in laboratory frame of reference - V _s shock-front velocity - ratio of specific heats of particles and gas - ratio of specific heats of gas - equilibrium specific heats ratio - particle-to-air loading ratio - half-angle between incident laser beams - laser light wavelength - _g gas density - _p particle material density - _g gas concentration - _m mixture concentration - _m ^app apparent mixture concentration - _p particle concentration - particle volume fraction - (D) probability density distribution by volume     

Further studies on dynamic crack branching

The newly derived dynamic-crack-branching criterion with its modifications is verified by the dynamicphotoelastic results of dynamic crack branchings in thinpolycarbonate, single-edged crack-tension specimens. Successful crack branching was observed in four specimens and unsuccessful branching in another. Crack branching consistently occurred when the necessary conditions ofK _I =K _{I b} =3.3 MPa \(\sqrt m\) and the sufficiency condition ofr _o =r _c =0.75 mm were satisfied simultaneously. In the unsuccessful branching test, the necessary condition was not satisfied sinceK _I was always less thanK _{I b} .     

Free vibrations of rectangular orthotropic shallow shells with varying thickness

The paper proposes a numerical-analytic approach to studying the free vibrations of orthotropic shallow shells with double curvature and rectangular planform. The approach is based on the spline-approximation of unknown functions. Calculations are carried out for different types of boundary conditions. The influence of the mid-surface curvature and variable thickness on the behavior of dynamic characteristics is studied __________ Translated from Prikladnaya Mekhanika, Vol. 43, No. 6, pp. 102–115, June 2007.     

Validating a GIS-based multi-criteria method for potential road identification

This paper investigated the validation of a multi-criteria method for identifying potential roads, and demonstrated the capability of analyzing GPS vehicle tracking data for identifying vehicle movement patterns and potential roads. The multi-criteria method was evaluated by comparing the predictions to the site visit results on 34 selected road segments meeting different criteria levels. Results show that locations meeting higher criteria levels have higher possibilities to be roads: an approximately 91% possibility of road existence for the locations meeting all five criteria; 55% for the locations meeting four criteria; and 14% for those meeting criteria level two or three. This approach provides an opportunity for land managers to update existing GIS roads map, or identify newly formed roads that may need either rehabilitation or inclusion into the roads maintenance program.     

Measurements on halogen-quenched counters

Summary Measurements have been made of the gas amplification factor of a cylindrical counter filled with neon-bromine and argon-bromine-mixtures. Information has been obtained as to the mechanism of gas multiplication when the gas amplification is less than 100. The transit time of electrons across a tube of average dimensions operated in the proportional region was found to be less then 0.2 microseconds. The duration and the mechanism of the discharge build-up was found to change with the amount of bromine present in the counter.This work was performed at the Physics Department, Southampton University England.     

Nonlinear problem of flow past a source with the formation of a stagnant zone given different Bernoulli constants

The problem of free flow past a point source is considered for two streams with different Bernoulli constants whose encounter creates a bounded region of constant pressure. The theory and method of solving problems of plane ideal jet flows with different Bernoulli constants in the jets were developed in [1]. Here, in conformity with [1], a nonlinear system of equations is derived, the question of the construction of a high-accuracy numerical solution is considered, and certain calculation results are presented for various values of the Bernoulli and cavitation numbers, which are dimensionless parameters of the problem.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 3, pp. 55–60, May–June, 1986.     

Nonlinear response of a parametrically excited buckled beam

A nonlinear analysis of the response of a simply-supported buckled beam to a harmonic axial load is presented. The method of multiple scales is used to determine to second order the amplitude- and phase-modulation equations. Floquet theory is used to analyze the stability of periodic responses. The perturbation results are verified by integrating the governing equation using both digital and analog computers. For small excitation amplitudes, the analytical results are in good agreement with the numerical solutions. The large-amplitude responses are investigated by using a digital computer and are compared with those obtained via an analog-computer simulation. The complicated dynamic behaviors that were found include period-multiplying and period-demultiplying bifurcations, period-three and period-six motions, jump phenomena, and chaos. In some cases, multiple periodic attractors coexist, and a chaotic attractor coexists with a periodic attractor. Phase portraits, spectra of the responses, and a bifurcation set of the many solutions are presented.