The approximate determination of the hunting movement of a railway vehicle by aid of the method of Krylov and Bogoljubov

Summary The author deals with the problem of the lateral oscillations of a railway vehicle moving on a straight track. Because of the possibility that the flange of each of the wheels temporarily contacts the rail belonging to it, the problem lies in the field of the self-sustained vibrations of non-linear mechanical systems with more than one degree of freedom. In the case under consideration, in which the vehicle and the track had been strongly simplified, the limit-cycle for the motion as well as its stability were determined approximately by the method of Krylov and Bogoljubov. This method is described in §§ 2 and 3. § 3 is more specially devoted to the so-called method of the equivalent linear equations. The latter equations are considered valid not only in the case in which the motion is purely periodic (in which a limit-cycle has been reached), but also in the neighbouring case, in which the motion slightly damps out or increases. This enables us to determine not only the limit-cycle but also its stability. In § 4 the method is applied to the problem of the hunting movement of the railway vehicle. The number of degrees of freedom is equal to 2, and we chose for the two generalised coordinates the lateral displacements of the leading wheel set and the trailing wheel set respectively. The linear creep law is assumed to be valid for the relation between the so-called slip coefficients and the tangential forces which the rails exert on the tyres and conversely. The limit-cycle obtained by applying Krylov and Bogoljubov's method corresponds to the limit-cycle previously found by means of Ritz' method. As to the stability it appears that the limit-cycle is always stable.Paper delivered at the Xth International Congress of Applied Mechanics at Stresa Aug. 31st to Sept. 7th, 1960.     

Complexification phenomenon in an example of sensitive singular perturbationPhénomène de complexification dans un exemple de perturbation singulière sensitive

We consider singular perturbation problems depending on a parameter ε?0 such that for ε>0 the solution u^ε belongs to a Sobolev space on a domain $\text{Ω}$, but the limit u⁰ is not a distribution on $\text{Ω}$. A very simple model problem, solvable by Fourier transform allows us to study the complexification process of u^ε as $\text{ε↘0}$. The limit holds in the topology of a space of analytical functionals. To cite this article: C.A. De Souza, É. Sanchez-Palencia, C. R. Mecanique 332 (2004).     

The computation of three-dimensional systems with various turbulence model variations

The standardk-? equations and other turbulence corrections are evaluated and reported with respect to their applicability in three-dimensional flows. The turbulence models are formulated on the assumption that an isotropic eddy viscosity and the modified Boussinesq hypothesis adequately describe the stress distributions, and that the source of predictive error is a consequence of the modelled terms in thek-? equations. Turbulence model corrections are incorporated to investigate their impact on these errors. Predictions from various turbulence models are compared with experimental data from an isothermal 3-D configuration. The data comparisons delineate the relative advantages and disadvantages of various modifications. Thek-? model performs competitively with other model corrections and in some instances is judged to be superior than the modified treatments. However, given the additional computational time and the marginal superiority of the investigated models, it is recommended that present 3-D computational code calculations retain the standardk-? model.     

Transient compressible boundary layer on a wedge impulsively set into motion

Summary The development of a compressible boundary layer over a wedge impulsively set into motion is studied in this paper. The initial motion is independent of the leading edge effect and the solutions are those of a Rayleigh-type problem. The motion tends to an ultimate steady state of Falkner-Skan type. The equations governing the transient boundary layer from the initial steady state to the terminal steady-state change their character after certain time due to the leading edge effect and thereafter solution depends on both the end conditions. Numerical solutions are obtained through the second-order accuracy upwind scheme. The effects of the Falkner-Skan parameter and the surface temperature on the transient flow and heat transfer are also studied. It has been found that the flow separation does not occur form–0.0707 when _w = 1.5 (hot wall), andm–0.118 when _0.5 (cold wall).     

Flow-induced structure in a system of nuclear waste simulant slurries

Thixotropy and antithixotropy were characterized in nuclear waste simulant slurries. For the neutralized current acid nuclear waste (NCAW) simulant slurries, NCAW with glycolic acid (NCAW+GA), and NCAW with nitric acid (NCAW+NA) (pH 4), a pre-shear flow at constant shear rate destroys the aggregates in the suspension and reduces viscosity. For the NCAW+NA (pH7–9), a pre-shear enhances the aggregates in the suspension and increases viscosity. With the addition of silica to the NCAW+GA and NCAW+NA slurries, the pre-shear effect tends to promote aggregation due to the formation of a network in the suspension, and hence, the viscosity increases. The macroscopic rheological property variation due to the microstructural aspects of the suspensions associated with the shear-induced effect are addressed.     

Procedure for describing the deformation of materials to fracture under conditions of near-superplasticity

Novosibirsk. Translated from Prikladnaya Mekhanika i Tekhnicheskaya Fizika, No. 1, pp. 149–157, January–February, 1995.     

Asymptotic analysis of convective flows in a rotating spheroid for vanishing viscosity and thermal conductivity

The six-dimensional model of viscous fluid thermal convection in a uniformly rotating ellipsoid [1] is studied. The limiting case in which the viscosity and thermal conductivity approach zero while the Prandtl number Pr remains finite is considered. Using both asymptotic and numerical methods, it is shown that for Pr > 2 the attractor is a two-dimensional invariant torus or a limit cycle; the corresponding convective flows are either quasiperiodic, with two basic frequencies, or periodic. It is also shown that resonances on the torus play a dominant role in the breakdown of two-dimensional toruses with increasing viscosity and thermal conductivity.Rostov-on-Don. Translated from Izvestiya Rossiiskoi Akademii Nauk, Mekhanika Zhidkosti i Gaza, No. 5, pp. 35–38, September–October, 1995.     

Geometrically nonlinear analysis of the stressstrain state of toroidal shells under pure bending

Novosibirsk. Translated from Prikladnaya Mekhanika i Tekhnicheskaya Fizika, No. 1, pp. 139–145, January–February, 1995.     

Phase-stepped ESPI and moiré interferometry for measuring stress-intensity factor andJ integral

Electronic-speckle-pattern interferometry and moiré interferometry have been used to calculateK ₁ andJ for compact tension specimens. Automated-fringe-pattern analysis enables the full-field of data to be used with the minimum of operator intervention. Measurements are shown to be accurate to within 10 percent. TheJ-measurement procedure employed could form the basis of an automatic-fault detection system.     

Modeling of the dynamics of the change in the index of refraction during resonance interaction of radiation with vibrational-rotational transitions

Moscow. Translated from Prikladnaya Mekhanika i Tekhnicheskaya Fizika, No. 1, pp. 21–29, January–February, 1994.