Existence of Solutions with the Prescribed Flux of the Navier–Stokes System in an Infinite Cylinder

The existence and uniqueness of a solution to the nonstationary Navier–Stokes system having a prescribed flux in an infinite cylinder is proved. We assume that the initial data and the external forces do not depend on x₃ and find the solution (u, p) having the following form

Heat transfer in tube assemblies under conditions of laminar axial,transverse and inclined flow

This paper considers laminar flow heat transfer in tube assemblies. The main interest is focused on the virtually unexplored cases of heat transfer under conditions of fully-developed flow inclined to the axes of the tubes and of purely transverse developing flow. The limiting cases of purely axial or purely transverse fully-developed flow are also examined. In all cases, the thermal boundary condition on the tubes is constant heat flux. Governing differential equations are expressed in terms of curvilinear-orthogonal coordinates and solved using finite-differences. Results are compared with available theoretical and experimental data. The effect of the transverse component of the flow on the temperature distribution is found to remain very strong even in nearly-axial flows and therefore considerably higher heat transfer coefficients are exhibited by a nearly-axial flow than a purely axial one.     

Whirling of a forced cantilevered beam with static deflection. III: Passage through resonance

Nonstationary excitations of slender, elastic, cantilevered beams with equal principal moments of inertia are considered. The excitation frequency is slowly increased or decreased through a resonance of the first mode at a constant rate. Three resonances are investigated: primary resonance, superharmonic resonance of order two and subharmonic resonance of order two. After application of Galerkin's method with three modes, the nonlinear, nonstationary response of the first mode of the beam is determined by two methods: integration of the modulation equations obtained from the method of multiple scales, and direct numerical integration of the temporal equations of motion. Time histories are presented and the effects of excitation amplitude, rate of acceleration or deceleration through resonance, damping and initial conditions of the disturbance on the maximum response are studied. The effect of a persistent random disturbance is also examined. Although the excitation acts in the vertical plane, whirling occurs if the beam is subjected to out-of-plane disturbances.     

Analytical simulation as a support tool in the decision process “wheels or tracks”

In the development of a weapon system, the maximization of demands concerning features like fire power, armor and mobility often leads to incompatibilities within the overall systems, to an imbalanced design and excessively high cost. The consequence is a decrease in mission availability. Therefore, system analysis utilizing simulation techniques is being used more and more in the early stages of the development process. This paper describes the application of such simulation techniques to practical cases. First, the development of a system is described by which to select wheeled or tracked running gears for combat vehicles considering the compatibility of fire power, armor, mobility and cost. Secondly, the possible upper weight ranges for wheeled combat vehicles are discussed, using analytical modeling of vehicle mobility as a basis. The methods used in these cases can also be applied to non-military problems.     

The two-dimensional velocity shift caused by the use of a rotating mirror in PIV flow field measurements

A theoretical analysis of the two-dimensional velocity shift by the use of a rotating mirror in PIV flow field measurements has been carried out by the application of ray optics. The velocity shift has been calculated directly in the flow field co-ordinates. In dimensionless form the results are also available in the image plane. It is shown that the distribution of the velocity shift over the entire observation field may not usually be assumed to be uniform (and may vary by up to 20%). The effect of the layout and arrangement of the rotating mirror on the velocity shift and its distribution has been analysed. In addition, the sensitivity of the velocity shift to the design tolerances and imperfections of the rotating mirror is given.     

Influence of load amplitude and uniaxial tensile properties on fatigue crack growth

The rate at which energy is accumulated within a unit volume of material in fatigue is assumed to depend not only on load-time history but also on the specimen size and geometry in addition to material type. A threshold level for the hysteresis strain energy density function accumulated in the material is used for predicting macrocrack growth. This is accomplished by application of the incremental theory of plasticity for each increment of crack growth. The accumulated hysteresis strain energy density factor ΔS to crack growth increment Δa ratio is found to be constant for fixed specimen size and loading, i.e., . Results are obtained for the cylindrical bar specimens with a penny-shaped defect at the center subjected to a constant amplitude and frequency loading. The resistance curves in the ΔS versus Δa plot are parallel lines as specimen size is altered. This information provides a rational means for predicting the influence of specimen size on fatigue lifetime.The results are also compared with those found for geometrically similar plate specimens with line cracks. Cylinder bar specimens of the same material are found to sustain more load cycles prior to catastrophic failure.     

Finite-amplitude convection in mixtures with heat sources proportional to the concentration of one of the components

A numerical investigation has been made into the equilibrium stability with respect to finite perturbations of a mixture with heat sources proportional to the concentration of an active component. The convective motions that develop after the loss of stability were also studied. The equations of thermoconcentration convection were solved by the grid method for a planar region of rectangular shape simulating a convective cell in the horizontal layer. Neutral curves for finite-amplitude perturbations are constructed, the regions of existence of subcritical motions are found, and a comparison with the results of linear theory is made.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 6, pp. 10–16, November–December, 1982.We thank E. M. Zhukovitskii for discussing the results of the paper.     

Nonlinear analysis of the forced response of a beam with three mode interaction

An analysis is presented for the primary resonance of a clamped-hinged beam, which occurs when the frequency of excitation is near one of the natural frequencies,_n . Three mode interaction (₂ 3₁ and _{3 1} + 2₂) is considered and its influence on the response is studied. The case of two mode interaction (₂ 3₁) is also considered to compare it with the case of three mode interaction. The straight beam experiencing mid-plane stretching is governed by a nonlinear partial differential equation. By using Galerkin's method the governing equation is reduced to a system of nonautonomous ordinary differential equations. The method of multiple scales is applied to solve the system. Steady-state responses and their stability are examined. Results of numerical investigations show that there exists no significant difference between both modal interactions' influences on the responses.     

Separation of a three-dimensional boundary layer

The line of separation of the three-dimensional boundary layer on an arbitrary curvilinear surface is a singular streamline on the body surface which separates the detachment region and which is a line of confluence for the limiting streamlines. Expressions are derived for the three-dimensional separation criteria on the basis of the condition of zero frictional force in the projection on the normal to the line of separation. The position of the line of separation is determined from the solution of an ordinary differential equation. An analysis is made of various cases of separation on the surface of a yawed cylinder and on the surface of sharp cones at an angle of attack in a supersonic stream. The position of the lines of separation is determined experimentally from the confluence of thin liquid films applied to the surface. It is shown that separation occurs on the sharp cone on the line z=π for values of the parameter K=?0.85.