Arbitrary body,close to a wedge,in a supersonic flow

The problem of supersonic flow around bodies close to a wedge was first discussed in the two-dimensional case in [1]. The shock wave was assumed to be attached, and the flow behind it to be supersonic; taking this into account, the angle of the wedge was assumed to be arbitrary. The surface of the body was also arbitrary, provided that it was close to the surface of the wedge. In solution of the three-dimensional problem, there was first considered flow around two supporting surfaces with only slightly different angles of attack [2], and then around a delta wing [3, 4]. In all these articles, the Lighthill method was used to solve the Hilbert boundary-value problem [5, 6]. A whole class of surfaces of bodies with arbitrary edges, under the assumption that the surface of the body was cylindrical, with generatrices directed along the flow lines of the unperturbed flow behind an oblique shock wave, was discussed in [7]. In the present work, the problem is regarded for a broad class of surfaces of bodies, using a new method which generalizes the results of [8].Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 4, pp. 109–117, July–August, 1974.The author thanks G. G. Chernyi for his direction of the work.     

Quasistatic periodic contact problem for a viscoelastic layer,a cylinder,and a space with a cylindrical cavity

This paper considers the contact problem of interaction of a rigid die, a rigid band, and a rigid insert with a viscoelastic layer, a viscoelastic cylinder, and viscoelastic space with a cylindrical cavity, respectively. It is assumed that the die, band, and insert move at a constant velocity along the boundaries of the viscoelastic bodies. In the first stage, the displacement of the boundaries of the above-mentioned bodies is determined as a function of the applied normal loads ignoring friction in the contact area. In the second stage, integral equations are derived to determine contact pressure in the contact problems. In the third stage, approximate solutions of the integral equations are constructed using a modified Multhopp-Kalandia method.     

Mechanics of a thin,tensioned shell,wrapped helically around a turn-bar

The fluid–structure interactions between a flexible web and an externally pressurized air cushion are modeled allowing for the possibility of contact. The web is wrapped around a porous, cylindrical turn-bar at an oblique angle (helically). The turn-bar supplies pressurized air into the web/turn-bar clearance to float the web. The shell model, developed to represent the mechanics of the web, allows it to be wrapped around the cylinder in a helical fashion. The fluid mechanics of the air in the web/turn-bar clearance is a two-dimensional form of the incompressible Navier–Stokes equations averaged in the clearance direction and augmented by nonlinear source terms. Contact between the web and the reverser, which is undesirable in a turn-bar application, is included in the model in order to enable the analysis of the limiting cases. The coupled equilibrium between fluid mechanics, shell deflections and contact is found numerically. This paper describes the theory. Case studies are conducted in order to understand the mechanics of the coupled system, and to make design recommendations. It is shown that the helix angle has a strong influence on the equilibrium configurations: increasing helix-angle results in increased web-reverser separation, while the air pressure settles to a lower value. This behavior is due to the reduced shell stiffness and belt-wrap pressure for the helically wrapped webs. Conditions that render a nearly uniform web/turn-bar clearance in the circumferential direction are identified. The supply pressure and airflow rates necessary to prevent web-scratches are calculated.     

Reflection and transmission of a transient,elastic, line-source excited SH wave by a planar,elastic bonding surface in a solid

Closed-form time-domain expressions are obtained for the particle displacement of the elastic wave motion generated by a two-dimensional SH-wave line source and reflected and transmitted by a planar, elastic bonding interface of two homogeneous, isotropic, semi-infinite, perfectly elastic solids. The properties of the elastic bonding interface are characterized by a matrix of ‘spring coefficients’ through which the traction on each of the two faces is linearly related to the particle displacement of either of the two faces. The solution is constructed with the aid of (an extension of) the modified Cagniard method. The obtained solution of the forward model is believed to be of importance to the inverse problem that aims at reconstructing the elements of the matrix of ‘spring coefficients’ from measured values of the reflected and/or the transmitted wavefield quantities at a number of positions.     

Unsteady outflow of a warm dense Van der Vaals medium from a plane layer,a cylinder,and a sphere

The unsteady outflow of a warm dense boiling compressiblemedium, initially at rest, from a plane layer, a cylinder, and a sphere into a vacuumis investigated in the approximation of an inviscid and non-heat-conducting two-parameter “gas-liquid”, whose thermodynamic properties are determined by the Van der Vaals equation of state. The expansion, the boiling, and the two-phase medium generation are assumed to be thermodynamically equilibrium, while the transition is instantaneous. The speed of sound suffers a discontinuity across the phase transition line of the second kind (binodal), whereas the pressure, the temperature, the density, the entropy, and the enthalpy remain continuous. The main issue in the thermodynamic calculations, which are the same for all the problems, is the construction of the binodal and, at the same time, an isentrope in an equilibrium two-phase mixture, reduced to the numerical integration of two ordinary differential equations. The one-dimensional problems of unsteady outflow are solved by means of the method of characteristics using the isentropes obtained in the thermodynamic calculations. As distinct from the plane problem, in the cylindrically and spherically symmetric problems there are no regions of homogeneous boiling liquid, which would be finite in space and time.     

Does a charge,falling freely in a static gravitational field,radiate?

Summary The Poynting vector flux from a charge at rest in an inertial frame is calculated, on the basis of the standard classical Maxwell-Lorentz theory, in a uniformly accelerated frame, through a suitable set of spherical 2-surfaces. The results are also interpreted in the framework of general relativity, and critically discussed in connection with the equivalence principle. In particular, we introduce a ?quasi-local? definition of radiation, and conclude that a charge, falling freely in a gravitational field locally approximated by a static homogeneous gravitational field (SHGF), does not radiate in its rest frame, but does radiate in a frame supported in the SHGF. Such a radiation appears as ?fictitious?, i.e. a coordinate transformation eliminating the gravitational field eliminates at the same time also the radiation.

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Sommario Data una carica in quiete in un riferimento inerziale, si calcola, nell'ambito dell'elettrodinamica di Maxwell-Lorentz, il flusso del vettore di Poynting in un riferimento uniformemente accelerato, attraverso una opportuna classe di 2-superfici sferiche. I risultati ottenuti sono interpretati anche nello schema della relatività generale e discussi criticamente in relazione al principio di equivalenza. In particolare, introducendo una definizione ?quasi-locale? di irraggiamento, si conclude che una carica in caduta libera in un campo gravitazionale localmente approssimabile da un campo statico e omogeneo (SHGF) non irraggia nel suo riferimento di riposo, ma irraggia nel riferimento solidale con il campo. Tale irraggiamento risulta un fenomeno ?apparente?, nel senso che una trasformazione di coordinate che elimina il campo gravitazionale elimina al tempo stesso anche l'irraggiamento.

     

Axisymmetric waves in a fluid-filled,hollow, elastic cylinder surrounded by a fluid

The laws of propagation of axisymmetric normal modes in a hollow cylinder filled with and surrounded by fluid media are investigated. Dispersion curves are plotted, exhibiting functional relations between the complex propagation constant and the dimensionless frequency. Distinctive attributes of the dispersion curves and the energy characteristics of the investigated waveguide structure are analyzed.Institute of Hydromechanics, National Academy of Sciences of Ukraine, Kiev. S. P. Timoshenko Institute of Mechanics, National Academy of Sciences of Ukraine, Kiev. Translated from Prikladnaya Mekhanika, Vol. 30, No. 9, pp. 15–23, September, 1994.     

Filter Feeding, Chaotic Filtration, and a Blinking Stokeslet

The filtering mechanisms in bivalve molluscs, such as the mussel Mytilus edulis, and in sessile organisms, such as Vorticella or Stentor, involve complex fluid mechanical phenomena. In the former example, three different sets of cilia serving different functions are involved in the process whereas in the sessile organisms the flexibility and contractile nature of the stalk may play an important role in increasing the filtering efficiency of the organisms. In both cases, beating microscopic cilia are the “engines” driving the fluid motion, so the fluid mechanics will be dominated entirely by viscous forces. A fluid mechanical model is developed for the filtering mechanism in mussels that enables estimates to be made of the pressure drop through the gill filaments due to (i) latero-frontal filtering cilia, (ii) the lateral (pumping) cilia, and (iii) through the non-ciliated zone of the ventral end of the filament. The velocity profile across the filaments indicates that a backflow can occur in the centre of the channel leading to the formation of two “standing” eddies which may drive particles towards the mucus-laden short cilia, the third set of cilia. Filter feeding in the sessile organisms is modelled by a point force above a rigid boundary. The point force periodically changes its point of application according to a given protocol (a blinking stokeslet). The resulting fluid field is illustrated via Poincaré sections and particle dispersion—showing the potential for a much improved filtering efficiency. Returning to filter feeding in bivalve molluscs, this concept is extended to a pair of blinking stokeslets above a rigid boundary to give insight into possible mechanisms for movement of food particles onto the short mucus-bearing cilia. The appendix contains a Latin and English version of an “Ode of Achievement” in celebration of Sir James Lighthill's contributions to mathematics and fluid mechanics. Received 20 December 1996 and accepted 22 April 1997     

Soot formation in a steady, nonpremixed, recirculating flame

An inverted step burner has been designed in which a steady ethylene, recirculating flame is established. The burner was housed within a vertical wind tunnel. Laser extinction was used to determine the soot volume fraction in the recirculation zone. Temperatures were determined by a thermocouple. One-dimensional laser-Doppler velocity (LDV) measurements were obtained with a frequency shift system to measure the flow field in the recirculating flame. All the measurements were obtained for a fixed ethylene flow rate; a low and a high velocity in the approach flow were investigated.

Variation in air velocity changed the structure of the flame. At low flow conditions, the soot loading has two distinct peaks at the lower and upper edge of the flame. At the higher air velocity, the upper part of the flame has a much lower relative soot loading as a result of the shorter residence time. The location of the peak values of the soot also changed with the residence time. The peak temperature was of the order of 1600°C. The soot loading was low in the regions of high temperature and relatively high in regions of low temperatures, reflecting the important role of thermal radiation in these luminous flames. The LDV measurements were used to reveal the nature of the flow field. The local soot loading in the flame increased as the approach flow velocity increased; this result suggests the possibility that soot may continue to grow when it is recirculated to regions of growth in a flame.     

Innovation, imitation, and problem-solving in a networked group

We implemented a problem-solving task in which groups of participants simultaneously played a simple innovation game in a complex problem space, with score feedback provided after each of a number of rounds. Each participant in a group was allowed to view and imitate the guesses of others during the game. The results showed the use of social learning strategies previously studied in other species, and demonstrated benefits of social learning and nonlinear effects of group size on strategy and performance. Rather than simply encouraging conformity, groups provided information to each individual about the distribution of useful innovations in the problem space. Imitation facilitated innovation rather than displacing it, because the former allowed good solutions to be propagated and preserved for further cumulative innovations in the group. Participants generally improved their solutions through the use of fairly conservative strategies, such as changing only a small portion of one's solution at a time, and tending to imitate solutions similar to one's own. Changes in these strategies over time had the effect of making solutions increasingly entrenched, both at individual and group levels. These results showed evidence of nonlinear dynamics in the decentralization of innovation, the emergence of group phenomena from complex interactions of individual efforts, stigmergy in the use of social information, and dynamic tradeoffs between exploration and exploitation of solutions. These results also support the idea that innovation and creativity can be recognized at the group level even when group members are generally cautious and imitative.     

Velocity measurements in a turbulent,dilute, two-phase jet

The results of an experimental investigation into the behavior of unconfined, steady, fully turbulent, two-phase jets are described. A round jet of 25.4 mm in diameter, exit velocity of 20 m/s and containing 80 m beads with a mass density of loading of 1.5% was examined. Mean velocity profiles at several stations, as well as the rms values and velocity cross-correlations for both phases were measured by laser-Doppler velocimetry. It was found that the particles lagged the fluid by 8% near the exit, but later, at 9 jet diameters downstream led it by about 7%. Also, the velocity profiles of the particles were flatter than those of the fluid.     

Excitation,inertia, and drag forces on a cylinder vibrating transversely to a steady flow

We present a computational study of the forces on a cylinder oscillating harmonically in the direction perpendicular to a uniform flow. The two-dimensional Navier–Stokes equations are solved on a coordinate system fixed on the cylinder. The Reynolds number is equal to 400. Several oscillation frequencies are considered: (a) resonant forcing, (b) forcing at frequency below the natural frequency of the wake, and (c) forcing at frequency above the natural frequency of the wake. Once the flow has reached a statistical steady state, the lift and drag forces on the cylinder are computed. The lift force in particular is decomposed into one component that is in phase with the velocity (excitation force), and one component that is ${180}^{\circ }$ out of phase with the acceleration (inertia or added mass force). The variation of the forces as a function of the amplitude-over-diameter-ratio is studied in detail. It is found that the scaling of the so-called inertia component of the force with the acceleration of the cylinder can lead to serious problems at small amplitudes of oscillation, and that it is overall preferable to scale both components of the force with the dynamic pressure of the fluid. Through extensive flow visualization, it is shown that changes in the state of the flow are related to the abrupt changes of the forces with the amplitude-over-diameter-ratio. Moreover, qualitative differences are found between the results for the below resonance and the resonant or above resonance forcing. The former are characterized by smooth variation of the hydrodynamic force coefficients and spatially ordered vortex streets. The latter are characterized by continuous and sharp, even jump-like, changes of the forces, and a variety of vortex patterns in the wake, resulting for some combinations of frequency and amplitude of oscillation to spatially disordered vortex streets.     

Forced Oscillations of a System,Containing a Snap-Through Truss,Close to Its Equilibrium Position

The nonlinear dynamics of a two-degree-of-freedom mechanical system is considered. This system consists of a linear oscillator under the action of a time-periodic force and a snap-through truss, which acts as an absorber of the forced oscillations of the linear main system. The forced oscillations of the snap-through truss close to its equilibrium position are analyzed by the multiple scales method.     

Free non-axisymmetric oscillations of a thick-walled,nonhomogeneous, transversally isotropic,hollow sphere

Institute of Mechanics, Academy of Sciences of the Ukrainian SSR, Kiev. Translated from Prikladnaya Mekhanika, Vol. 24, No. 5, pp. 12–17, May, 1988     

Periodic solution of a second order, autonomous, nonlinear system

There exist a sufficient condition for the existence of at least one periodic solution for a type of second order autonomous ordinary differential equations. The correctness of the condition has been pointed out by Schauder's fixed point theorem. In order to indicate the validity of the assumptions made, two illustrative examples, showing its application in the nonlinear vibration and relaxation oscillation are presented.     

Automatic locking of a parametrically resonating,base-excited,nonlinear beam

Nonlinear Dynamics - Described is a closed-loop control scheme capable of stabilizing a parametrically excited nonlinear structure in several vibration modes. By setting the relative phase between...     

Formation, evolution, and decay of a vortex street in the wake of a streamlined body

The decay of a Kármán vortex street and the formation of a secondary vortex structure in the far wake of a streamlined cylinder are studied. The dynamics of spatially evolving vortex structures is examined in the free flow and in the following ways of external influence on this flow: rotation with a constant velocity and translational and rotational oscillations of the cylinder. The results are obtained by numerically solving the Navier-Stokes equations with two different methods. The corresponding boundary value problems are formulated in the domains extended up to 500 radii of the cylinder.     

Simultaneous extension, inflation, and shear of a cylindrical tube

Summary Rivlin's solution [1] of the title problem for Mooney materials is generalized by dropping the assumption that the hydrostatic pressure is a function of the radial distance only. Due to this generalization the normal tractions over the cylindrical surfaces are not constant as in the previous solution but vary linearly along the axis of the tube. Further, the longitudinal forces per unit length of the deformed tube, over the cylindrical surfaces, are no longer equal. Solutions for a solid cylinder are then deduced from the general solution. The effect of self-weight on the solutions is briefly dealt with.