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.     

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.     

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.     

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.     

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...     

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.     

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     

Vibrations of a Semiinfinite,Orthotropic, Cylindrical Shell of Open Profile

Natural vibrations localized at the free edge of a semiinfinite, elastic, orthotropic, circular cylindrical shell of open profile are studied. The cylinder is hinged along the bounding generatrices. Dispersion equations are derived from the classical equations describing the dynamic equilibrium for orthotropic cylindrical shells. It is established that these dispersion equations and the dispersion equations for a semiinfinite orthotropic plate strip are in an asymptotic relationship. A procedure for analysis of the possible types of vibrations at the free edge of the cylinder is described. Approximate values of the dimensionless natural frequency and damping factor are determined for shells of different radii     

Initial stage of reflection of a plane shock wave from a cylinder,sphere, and ellipsoid of revolution

The stage of regular reflection of a plane shock wave from a blunt body (cylinder, sphere, and ellipsoid of revolution) is considered. At the point of intersection of the reflected shock wave and the surface of the body, analytic expressions are found for the derivative of the Mach number of the wave with respect to the time, the curvature of the wave, the normal derivatives of the density and the pressure, and the derivative of the Mach number along the wave front. It is shown that the flow has a singularity at = _* < _** (s** is the limiting angle [1] of regular reflection of a shock wave from a rigid surface). The distribution of the parameters in the region between the reflected shock wave and the surface of the body is found up to terms of third order in the time. The density distribution behind the reflected shock wave was measured experimentally, and also the shape of the reflected wave at different instants of time.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 2, pp. 94–100, March–April, 1980.     

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.     

Transmission of a screw dislocation across a coherent, non-slipping interface

Current research on nanocrystalline metals and nanoscale multilayer thin films suggests extraordinary plastic strength is due to confinement of slip to individual grains or layers. To assess the magnitude of confinement, a Peierls model of slip transmission of a screw dislocation across a coherent, non-slipping interface is presented. The results reflect that large interfacial barriers to transmission are generated by rapid fluctuations in dislocation line energy near the interface due to elastic modulus mismatch, stacking fault energy mismatch, and antiphase boundary energy for transmission into an ordered phase. Coherency stress is predicted to dramatically alter the dislocation core configuration and impart additional strength regardless of the sign. Contributions to strength are not additive due to nonlinear coupling via the dislocation core configuration. The predicted barrier strength for a coherent (0 0 1) Cu/Ni interface is comparable to atomistic (EAM) results but larger than estimates from hardness data.     

Interaction of a crack with a pair of thin, elastic inclusions

The influence of a pair of thin, elastic inclusions on the stress intensity at a crack tip is considered. The interaction problem is formulated as a set of coupled singular integral equations and the solution is obtained by the Gauss-Chebyshev numerical technique. The stress intensity is computed as a function of certain geometric and elastic parameters of the inclusions, and the toughening effect of these parameters is evaluated.