Coaxial Shells Research Articles

Hrem Lattice Image Simulations of Circular Cross-Sectional Multishell Carbon Nanotubes

In recent years there has been much interest in a newly found member of the fullerene family, carbon nanotubes. As a result of the small dimensions of these structures much of the structural investigation has involved the use of HREM images of the tubes1−3. From these images it has been proposed that the idealised structure of a carbon nanotube comprises closed cylindrical coaxial shells of graphite in which each shell may have its own unique helical pitch due to the numerous ways in which a sheet of graphite may be rolled to form a cylinder. We have previously discussed HREM image simulations of the {100} fringes at the centre of nanotubes which assumed that the top and bottom faces of the tube were parallel4. In this paper attention is focused on image simulations for complete ideal tubes of circular cross-section in order to elucidate further the structure of the tubes. However, due to the complexity and large range of possible configurations and orientations of the tubes, we have not attempted to match the simulations to a particular tube. Instead we have chosen one representative structure and have varied the parameters of the tube in order to observe the effects on the image of the stacking of the shells relative to each other, tilt of the tube along the long axis and helical pitch of the shells. Features which occur in the simulations are compared qualitatively to experimental images.

Diffraction of acoustic waves by parallel cylindrical piezoceramic systems of coaxial shells filled by a viscous fluid

Calculations were carried out for the cases in which the interior shells are made of the piezoceramic material TsTCNV-1 with a radial polarization, while the exterior shell are made of polyvinyl chloride. As viscous fluid we selected an octane solution of silicon organic rubber

Internal- and annular-flow-induced instabilities of a clamped-clamped or cantilevered cylindrical shell in a coaxial conduit: The effects of system parameters

This paper presents a study of the effect of some of the system parameters on internaland andular-flow-induced instabilities of clamped-clamped or cantilevered cylindrical shells in coaxial conduits; the parameters considered are shell thickness, length of the shell, annular width, and relative directions of the inner and annular flows. Shell motions are described by Flügge's shell equations, and the unsteady fluid dynamic forces are evaluated by means of potential-flow theory. The time-averaged viscous loads on the shell due to flow pressurization and surface traction as well as internal damping of the shell material are also taken into account. Solutions are obtained with the aid of the Fourier transform technique. It is found that in both systems of clamped-clamped and cantilevered shells, where steel shells and water as the working fluid were used, a reduction in the annular width or in the shell thickness destabilizes the system, while a reduction in the length of the shell stabilizes it. Clamped-clamped and cantilevered coaxial shells lose stability at lower annular flow velocities when subjected concurrently to both internal and annular flows; this is more pronounced for counter- as opposed to co-current flows for clamped-clamped shells.

Inertia tensor and tidal transfer of angular momentum for special ellipsoidal mass distributions

This paper deals with ellipsoidal mass distributions made by concentric, coaxial, and similar shells, whose density is specified for two special situations both including the whole range between the limiting cases of homogeneous systems, on one side, and Roche generalized systems, on the other side. The components of the related inertia tensor are calculated and the dependence of the spin growth on the density distribution is shown, concerning tidal transfer of angular momentum to both virialized proto-galaxies and encountering galaxies.

Flows of the hele-shaw type between coaxial shells of revolution

Flows are considered in narrow gaps, whose mean surfaces are being formed by two planar parts of a sphere, a right circular cone, an ellipsoid, one- and two-sheet ellipsoids, a paraboloid, and a torus.

Flow-induced Instabilities of Cylindrical Structures

A kaleidoscopic view of the many diverse and interesting instabilities are presented, to which cylindrical structures are susceptible when in contact with flowing fluids. The physical mechanisms involved are discussed in each case, to the extent that they are understood, and the degree of success of available mathematical models is assessed. Four classes of problems are dealt with, according to the disposition of the flow vis-a`-vis the cylindrical structures: (a) instabilities induced by internal flows in tubular structures; (b) instabilities of solitary or clustered cylinders due to external axial flow; (c) annular-flow-induced instabilities of coaxial beams and shells; (d) instabilities of arrays of cylinders subject to cross-flow. In the first class of problems, the stability of straight tubular beams and cylindrical shells conveying fluid is discussed first, followed by the stability of curved pipes containing flow. In the second class of problems, the instabilities of solitary and clustered cylinders subjected to an external axial flow are treated, and their dynamical behavior is compared to that of systems with internal flow. The third class of problems involves annular flow in coaxial systems of beams and/or shells. Cross-flow-induced instabilities of clustered cylinders, in the form of arrays of different geometrical patterns, are the last class of problems considered; they are fundamentally distinct from the foregoing in terms of the fluid mechanics of the problem, for in this case the flow field is not irrotational—not even approximately.

Free vibration of a circular cylindrical double-shell system closed by end plates

An analysis is presented for the free vibration of a circular cylindrical double-shell system closed by end plates. The governing equations of vibration of an inner or an outer shell and of an end plate are written as matrix differential equations of the first order by using the transfer matrices of the shell and the plate. Once the matrices have been determined, the entire structure matrix is obtained by forming the product of the transfer matrices of the shell and the plate and the point matrices at the joints, and the frequency equation of the system is derived with terms of the elements of the structure matrix. The method has been applied to a uniform thickness double-shell system composed of two co-axial shells and two annular plates, and results of numerical calculations of the natural frequencies and the mode shapes of vibration are presented.

Vibration Analysis of Fluid-coupled Two Coaxial Axisymmetric Shells Containing Liquid

This paper presents a vibration response analysis method of fluid-coupled coaxial axisymmetric shells subjected to a horizontal earthquake. The kinetic energy and the strain energy of two coaxial axisymmetric shells are calculated by the finite element method. On the other hand, the velocity potential of the liquid contained in two shells is obtained analytically by assuming it as an ideal fluid, that is incompressible and inviscid, and then the kinetic energy of the liquid is calculated. Substituting these energies into Lagrange's equation of motion, the seismic response analysis method for a structure-liquid coupled vibration system is derived. As a result of numerical studies, this solution is proved to be an effective and reasonable method, and the seismic response characteristics of the two coaxial axisymmetric shells containing liquid are made clear.

Vibration analysis of two coaxial axisymmetric shells containing liquid.

Vibration analysis of two coaxial axisymmetric shells containing liquid.

Transient Response of Fluid-Coupled Coaxial Shells

An analytical solution for the fluid-structure-foundation interaction of two fluid filled coaxial cylinders on a rigid base slab is presented. The system may be excited horizontally in an arbitary manner at foundation level. The rocking of the base slab is taken into account. The fluid is chosen to be incompressible and inviscid. The analysis is performed in the frequency domain using substructuring technique. A corresponding computer code has been developed. The numerical results illustrate the strong influence of fluid level and structural properties on the response.

Can elliptical galaxies be equilibrium systems?

This paper deals with the question of whether elliptical galaxies can be considered as equilibrium systems (i.e., the gravitational+centrifugal potential is constant on the external surface). We find that equilibrium models such as Emden-Chandrasekhar polytropes and Roche polytropes withn=0 can account for the main part of observations relative to the ratio of maximum rotational velocity to central velocity dispersion in, elliptical systems. More complex models involving, for example, massive halos could lead to a more complete agreement. Models that are a good fit to the observed data are characterized by an inner component (where most of the mass is concentrated) and a low-density outer component. A comparison is performed between some theoretical density distributions and the density distribution observed by Younget al. (1978) in NGC 4473, but a number of limitations must be adopted. Alternative models, such as triaxial oblate non-equilibrium configurations with coaxial shells, involve a number of problems which are briefly discussed. We conclude that spheroidal oblate models describing elliptical glaxies cannot be ruled out until new analyses relative to more refined theoretical equilibrium models (involving, for example, massive halos) and more detailed observations are performed.

Two-dimensional magnetic flux shell model for magnetohydrodynamic simulations

A magnetic flux shell model is described which is suitable for numerical simulations of cylindrically symmetric plasmas. The magnetohydrodynamic equations in magnetic field line coordinates are derived including the effects of finite electrical conductivity and anisotropic heat conductivity. Subsequently, the equations of motion of coaxial plasma shells of constant density, temperature, axial velocity, and axial magnetic field are derived including (a) full radial dynamics and (b) radial pressure balance. Sample simulations of a laser heated solenoid plasma and a ϑ-pinch reactor are described.

Compact Multiwire Proportional Chambers and Electronics for the Crystal Ball Detector

A double gap of cylindrical proportional chambers has been designed and built for use with a large solid angle, modular NaI(Tl) array (The Crystal Ball). The chambers are constructed of three coaxial foam-epoxy shells, covered with an aluminum-mylar laminate. One of the high voltage cathodes in each chamber has been photo-etched to produce a pattern of stripes and precise position measurements of tracks passing transverse to the chamber axis are found by pulse height analyzing the shaped and amplified induced strip signals. Performance of the chamber using both the strip signals and the sense wire readout is presented. The design of both the signal handling electronics and the digital portions of the systems is discussed.

Dynamics of a cylindrical shell system coupled by viscous fluid

This study was motivated by the need to design the thermal shield in reactor internals and other system components to avoid detrimental flow-induced vibrations. The system component is modeled as two coaxial shells separated by a viscous fluid. In the analysis, Flügge’s shell equations of motion and linearized Navier–Stokes equation for viscous fluid are employed. First, a traveling-wave-type solution is taken for shells and fluid. Then, from the interface conditions between the shells and fluid, the solution for the fluid medium is expressed in terms of shell displacements. Finally, using the shell equations of motion gives the frequency equation, from which the natural frequency, mode shape, and modal damping ratio of coupled modes can be calculated. The analytical results show a fairly good qualitative agreement with the published experimental data. With the presented analysis and results, the frequency and damping characteristics can be analyzed and design parameters can be related to frequency and damping.

Vibrations of two concentric cylindrical shells containing a viscous fluid

This study was motivated by the need to design the thermal shield in reactor internals to avoid detrimental flow‐induced vibrations. The system component is modeled as two coaxial shells separated by a viscous fluid. In the analysis, Flugge's shell equations of motion and linearized Navier‐Stokes equation for viscous fluid are employed. First, a traveling‐wave‐type solution is taken for shells and fluid. Then, from the interface conditions between the shells and fluid, the solution for the fluid medium is expressed in terms of shell displacements. Finally, using the shell equations of motion given the frequency equation, from which the natural frequency mode shape, and modal damping ratio of coupled modes can be calculated. Some important conclusions are as follows: (1) There exist structural modes and acoustic modes. If the structural natural frequencies and mode shapes are of primary interest, the fluid may be considered inviscid and incompressible. (2) There exist out‐of‐phase and in‐phase modes. The lowest natural frequency is always associated with the out‐of‐phase mode. (3) The lowest natural frequency of coupled modes are lower than the uncoupled modes. (4) The fluid viscosity contributes significantly to the modal damping.

Stationary states for electron oscillators in a rare-gas afterglow plasma

An explanation is advanced for the presence of populations of low energy oscillating paired electrons in rare-gas afterglow plasmas arranged in a system of coaxial shells, and enclosing a core plasma of free electrons. The common axis of the system is that of the long glass tube containing the plasma. The explanation is based on Fermi's analysis of the collisional interaction of very low energy electrons with gas atoms or molecules. A model afterglow is evolved based on the coaxial shell hypothesis, and is used to interpret two sets of afterglow phenomena, namely the plasma shell resonances obtained when energy is radiated by electrons making transitions from inner to outer shells, and the multiple values for accelerated decay times observed for afterglows of this type.

Quasi-static transient response of a covered permeable inhomogeneous cylinder to a line current source

Transient electromagnetic response of a cylindrical conductor covered by (a) an insulated and (b) a galvanically connected coaxial shell has been obtained. The exciting pulse is produced by switching off a long alternating current source. The study incorporates the influence of magnetic permeability contrast of the cylinder with the surrounding medium and also that of the inhomogeneity in the conductivity. The generalised initial value problem is significant in the study of certain geomagnetic anomalies. The results will also aid to the interpretation of induction prospecting data for elongated porphyry conducting mineral deposits.

The effect of polarized light on the growth of a transparent cell. A theoretical analysis.

It is shown that light lost by reflection before entering a clear and homogeneous sphere or infinite cylinder is precisely compensated by light retained within these bodies by internal reflection; compensation means that the total rate of light absorption by infinitely dilute photoreceptors as integrated through the whole of these bodies or even through any concentric or coaxial shell making them up is independent of surface reflection. In the Phycomyces sporangiophore this theorem precludes a reflection explanation of R, the polarization dependence of the light growth response. An alternative explanation based upon anisotropic absorption by the receptors is explored and found tenable. Formulae are derived for R in any transparent cylindrical cell as a function of the constants of anisotropic absorption by the photoreceptors taken as a group (C(H)' and C(L)'), of the radial position of the receptors, and of the refractive indices of the cell (n) and of the medium (N). It is inferred that the photoreceptors in the Phycomyces sporangiophore are most absorbent for light vibrating in the direction of a hoop around a barrel. Orientation of the receptors by linkage to the cell wall is then shown to be a plausible explanation of the inferred anisotropy. On the basis of anisotropic reception, it is predicted that R should be constant for any N > n, and it is shown how C(H)', C,(L)' and the radial position of the receptors may all be obtained from a careful determination of R as a function of N.

Load Distribution at the Intersection of Several Coaxial Axisymmetric Shells

Abstract A relaxation analysis of the load distribution at the intersection of several axisymmetric coaxial shells is presented. The relaxation process leads to an infinite power series, the summation of which yields explicit expressions for the individual shell loads. The shells are all assumed to be unconstrained axially, thus eliminating axial interaction effects among them. The analysis, consequently, is restricted to radial shear forces and distributed moments at the intersection line, which is taken in a plane perpendicular to the common axis of the shells. Methods of treating temperature and pressure effects are described, and an illustrative example of the analysis of a three-shell intersection is included.