Circular Shells Research Articles

Equation in complex variable of axisymmetrical deformation problems for a general shell of revolution

In this paper, the equation of axisymmetrical deformation problems for a general shell of revolution is derived in one complex variable under the usual Love-Kirchhoff assumption. In the case of circular ring shells, this equation may be simplified into the equation given by F.Tolke(1938)[3], R.A.Clark(1950)[4]and V.V.Novozhilov(1951)[5]. When the horizontal radius of the shell of revolution is much larger than the average radius of curvature of meridian curve, this equation in complex variable may be simplified into the equation for slander ring shells. If the ring shell is circular in shape, then this equation can be reduced into the equation in complex variable for slander circular ring shells given by this author (1979)[6]. If the form of elliptic cross-section is near a circle, then the equation of slander ring shell with near-circle ellipitic cross-section may be reduced to the complex variable equation similar in form for circular slander ring shells.

Free vibration analysis of laminated composite truncated circular conical shells

All components of translatory and rotatory inertia are included. The applicability of linear shell theory due to Reissner is assumed, and governing equations are solved for the natural frequencies and mode shapes by using a combination of modal iteration and transfer matrix approach for different boundary conditions

Ray acoustics models for sound radiation from vibrations of fluid‐loaded circular shells

A theory of sound radiation by shells is developed using the canonical model of an elastic coaxial cylinder, with inner radius R − 12h and outer radius R + 12h immersed in a compressible fluid. As can be constructed from the earlier work of Pochhammer, Mindlin, Herrmann, Miklowitz, Greenspon, Veksler, and others, this dynamical system admits guided wave solutions of constant angular frequency ω, in which all of the appropriate field variables vary with azimuthal angle θ and axial coordinate xthrough a common factor Eih einθ Admissible solutions that do not grow at large positive x or at large r are governed by a dispersion relation of the form F(ω,kv, n) = 0, where F is a highly transcendental function involving Bessel and Neumann functions of various orders and with various arguments. In the present paper, n is not required to be an integer and kv = n/R is identified as another wavenumber component. In various limits, all with h/R ⩽ 1, simpler analytic approximations for possible dispersion relations result, which can be cast in the form k = k (ω,θλ), where wavenumber k for phase propagation in direction θλ has a positive non‐zero imaginary part, which is interpreted in terms of sound radiation into the surrounding fluid. For length and frequency scales relevant to structural acoustics, the most important dispersion relations are those that correspond to longitudinal, shear, and flexural waves on plates, only with corrections to account for fluid loading and curvature. All modes radiate sound. [Work supported by ONR and by the William E. Leonhard endowment to Penn State Univ.]

Propagation of elastic waves on thin cylindrical shells at frequencies below the ring frequency

Recent experimental results (to appear) by Williams and colleagues at NRL suggest that wave propagation concepts apply to vibrations caused by point excitations on circular shells even at frequencies substantially below the ring frequency. A previous analysis by Pierce and Kil [ASMEJ. Vib. Acoust. (1990)] has given general dispersion relations for such waves, but with detailed analysis only for frequencies far above the ring frequency. The present paper examines the propagation in the opposite limit. In this limit two types of propagating waves are excited, which in the axial direction correspond to shear waves in bulk media [phase velocity equal to (G/p)1/2] and to longitudinal waves in rods [phase velocity equal to (E/p)1/2]. At low frequencies these waves are nondispersive with phase velocities that do not vary with frequency. The propagation, however, is anisotropic and the mode that nominally coresponds to shear waves has zero phase velocity for propagation in the circumferential direction. Hence wave fronts for the two types of waves are not circular; the “shear wave's” lines of constant phase resemble figure‐eight's aligned in the axial direction; those for the mode that nominally corresponds to the longitudinal (thin rod) mode resemble ellipses elongated in the axial direction. Numerical examples are also presented for amplitudes and radiation patterns associated with point excitation. [Work supported by ONR and by the William E. Leonhard endowment to Pennsylvania State University. The author acknowledges the advice of A. D. Pierce.]

The singular perturbation method applied to the nonlinear stability problem of a shallow spherical shell (II)

In this paper we consider the nonlinear stability of a thin elastic circular shallow spherical shell under the action of uniform normal pressure with a clamped edge. When the geometrical parameter k is large, the uniformly valid asymptotic solutions are obtained by means of the singular perturbation method. In addition, we give the analytic formula for determining the centre deflection and the critical load, and the stability curve is also derived. This paper is a continuation of the author's previous paper[11].

Load-carrying capacity of circular cylindrical shells in cyclic loading with internal pressure

Results are presented of experimental examination of the strength and endurance of smooth cylindrical circular shells in cyclic loading with internal pressure with a constant amplitude in uniaxial and biaxial tensile loading. It is shown that the level of fracture stresses in these shells in the biaxial stress state can be evaluated using the criterion of static strength on the basis of a fatigue curve constructed in uniaxial tensile loading.

Transmission through dielectric-filled slots in a conducting cylindrical shell of arbitrary cross section: TE case

A simple moment solution is summarized for the problem of electromagnetic transmission through dielectric-filled slots in a conducting cylindrical shell of arbitrary cross section. The system is excited by a plane-wave polarized transverse electric (TE) to the axis of the shell. The equivalence principle is used to replace the shell and the dielectric by equivalent electric and magnetic surface currents radiating into an unbounded medium. Two different sets of coupled integral equations involving the surface currents are obtained by enforcing the boundary conditions on the tangential components of the total electric and magnetic fields. The method of moments is used to solve the integral equations. Pulses are used for both expansion and testing functions. Special attention is paid to circular and rectangular shells. Results for shell surface current, the internal field, and the aperture field are presented. For the case of air dielectric filling, the results computed using the electric field and/or the magnetic field formulation are in very good agreement with published data. In general, it is observed that the effect of filling a slot with a dielectric is not predictable from a simple theory.< <ETX xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">&gt;</ETX>

Dynamic stability of viscoelastic shells under time-dependent membrane loads

The stability of the undeflected middle surface of a uniform Voigt-Kelvin cylindrical circular shell is studied. The shell is being subjected to a time-varying axial compression as well as a time-varying uniformly distributed radial loading. Using the direct Liapunov method sufficient criteria for the asymptotic stability and the almost sure asymptotic stability are obtained. Asymptotic stability regions as functions of a reduced retardation time, geometric and material parameters of shell and characteristics of loading are calculated. It was shown that the stability regions do not change qualitatively in going from a Gaussian force to a harmonic one. The change of membrane loading direction from the axial direction to the circumferential one on the stability regions is also discussed.

The stress analysis for a pressure vessel which consists of two concentric circular shells and cover plates.

The stress analysis for a pressure vessel which consists of two concentric circular shells and cover plates.

On second order asymptotic solutions of axial symmetrical problems ofr&gt;0 thin uniform circular toroidal shells with a large parametera 2/R0h

According to the classical shell theory based on the Love-Kirchhoff assumptions, the basic differential equations for the axial symmetrical problems of r>0 thin uniform circular toroidal shells in bending are derived, and the second order asymptotic solutions are given for r>0 thin uniform circular toroidal shells with a large parameter a2/R0h. In the resent paper, the second order asymptotic solutions of the edge problems far from the apex of toroidal shells are given, too. Their errors are within the margins allowed in the classical theory based on the Love-Kirchhoff assumptions.

On the determination of the optimum blank shape of a nonaxisymmetric drawn cup by the finite element method. 2nd report. The influence of plastic anisotropy on the optimum blank shape.

In order to determine the optimum shape and size of a blank for a deep drawing cup with a flat-headed punch, the authors have improved their finite element procedure, having taken account of the effects of the plastic anisotropy of sheet metal. The influence of the plastic anisotropy on the optimum blank shapes for circular, false elliptical and square cups have been analyzed. The predictions were made in terms of the optimum blank shapes ad products with a uniform drawing height around their peripheries. Close agreement is recognized between the theoretical predictions and the experimental results for circular, false elliptical and square hollow shells of annealed aluminum sheet metal which shows plastic anisotropy.

High-resolution radio observations of W50, the remnant associated with SS 433

The NRAO VLA has been used to observe the radio source W50 with 30 arcsec and 1 arcmin resolutions at 20 cm. It is found that the overall structure of W50 is well delineated by filamentary structure. W50 possesses a nearly circular shell reminiscent of an evolved supernova remnant such as CTB1 and the Cygnus Loop. The most unusual features of W50 are the edge-brightened radio ears which extend beyond the shell. These ears appear morphologically distinct from the shell and have minimum energy pressures three times greater than are present in the shell. Thus, while no direct connection is observed between SS433 and the ears, it is suggested that the ears are the result of the interaction of the ram pressure of the collimated jets of SS433 with a supernova remnant shell. At 30 arcsec resolution the western ear of W50 is depolarized, suggesting that W50 and S74 are at a common distance of about 3 kpc.

On exact solution of kármán's equations of rigid clamped circular plate and shallow spherical shell under a concentrated load

It is extremely difficult to obtain an exact solution of von Karman's equations because the equations are nonlinear and coupled. So far many approximate methods have been used to solve the large deflection problems except that only a few exact solutions have been ised to solve the large deflection problems except that only a few exact solutions have been investigated but no strict proof on convergence is presented yet. In this paper, first of all, we reduce the von Karman's equations to equivalent integral equations which are nonlinear, coupled and singular. Secondly the sequences of continuous function with general form are constructed using iterative technique. Based on the sequences to be uniformly convergent, we obtain analytical formula of exact solutions to von Karman's equations related to large deflection problems of circular plate and shallow spherical shell with clamped boundary subjected to a concentrated load at the centre.

TM Transmission Through Dielectric-Filled Slots in a Conducting Cylindrical Shell of Arbitrary Cross Section

A simple moment solution is summarized for the problem of electromagnetic transmission through dielectric-filled slots in a conducting cylindrical shell of arbitrary cross section. The system is excited by a plane-wave polarized transverse electric (TE) to the axis of the shell. The equivalence principle is used to replace the shell and the dielectric by equivalent electric and magnetic surface currents radiating into an unbounded medium. Two different sets of coupled integral equations involving the surface currents are obtained by enforcing the boundary conditions on the tangential components of the total electric and magnetic fields. The method of moments is used to solve the integral equations. Pulses are used for both expansion and testing functions. Special attention is paid to circular and rectangular shells. Results for shell surface current, the internal field, and the aperture field are presented. For the case of air dielectric filling, the results computed using the electric field and/or the magnetic field formulation are in very good agreement with published data. In general, it is observed that the effect of filling a slot with a dielectric is not predictable from a simple theory. >

Nonlinear Axisymmetric Static Analysis of Shallow Spherical Shells on Winkler-Pasternak Foundation

In the present investigation nonlinear static analysis of thin axisymmetric circular plates, annular plates and shallow spherical shells resting on linear elastic Winkler-Pasternak foundation under uniformly distributed normal loads, has been carried out. Donnell-type governing differential equations expressed in terms of normal displacement and stress function have been employed and solved using Chebyshev series. A convergence study for Chebyshev series has been conducted. The influence of foundation stiffness parameters (K and G) on the response of circular plates, annulus and spherical shells has been studied for both the clamped and simply supported immovable edge conditions. A few typical snap-through results for shells are also included.

Volterra’s series solutions of free boundary plasma equilibria

In this paper the nonlinear problem of the free boundary equilibrium of a plasma inside a conducting circular shell has been solved analytically in the high beta limit. The unknown function describing the plasma shape has been expanded in a Volterra functional series, the functional analogous to the Taylor series. The hierarchy of the linear integral equations obtained from the expansion is, at least in principle, analytically solvable, so that the solution of each equation can be given in a closed form. The analytical computations have been carried out up to the fourth order and the results compared with numerical computations.

Radio observations of the remnant of the supernova of A.D. 1006. I - Total intensity observations

VLA observations are presented of the supernova of A.D. 1006 at 1370 and 1665 MHz with 16 x 20 arcsec resolution. A circular shell whose peak brightness varies by a factor of about 11 with azimuth is seen, with two bright regions dominating the emission; these have extremely sharp outer edges. Several discrete filaments can be followed for substantial portions of the remnant diameter. 29 references.

Laminar convection in wall sub-channels and transport rates for finite rod-bundle assemblies by superposition

Finite rod-clusters in circular, square and hexagonal shells have been divided along the symmetry lines into a number of interior, wall and corner subchannels. Laminar fluid flow and heat transfer results have been generated for these subchannels with varying pitch-to-diameter and wall distance-to-diameter ratios. Wall shear stress and temperature variations for typical wall subchannels are presented. Friction factor values for finite bundles are then obtained by superposing the results of the subchannels that constitute the bundles. The values so generated are in excellent agreement with previous work in the literature obtained by the method of symmetry sectors. Considerable disagreements were, however, observed in the superposed values of Nusselt number, apparently due to conduction effects.

Fundamental Studies on Underwater Sound Radiated from a Vibrating Ship Hull

In the preceding report, we have dealt with underwater sound radiated from a semi-submerged simple circular shell, and shown the basic role of free water surface. However these results are all about the simple circular cylinder so that they might not be applied to actual ships.This report deals with this point, namely, to know the influence of the hull section shape on the property of underwater radiated sound, we show the numerical analysis method of the mutual coupled vibration of fluid-hull interaction, in which the vibrations of hull are solved by F. E. M. and the sound into fluid by B. E. M..At first, we calculate the semi-submerged simple circular shell by this method, compare with the preceding report results, and find a good agreement between them. Next, we show the effect of changing drafts of a circular shell and the effect of hull section shapes. Finally, we calculate the realistic cross section of ships and show the effect of the plate thickness and rigidity on underwater radiated sound.

Diffraction tomography approach to acoustical imaging and media characterization

An ultrasonics diffraction tomography method is discussed that images cylindrical inhomogeneous fluid targets located in a fluid environment. This method is based on an exact model of the interaction between a compressional plane wave and the target (multiple scattering is not neglected). First the theoretical background is summarized. Then numerical simulations illustrate the behavior of the imaging procedure. These simulations are conducted under conditions close to those of experiments that we perform concurrently. Emphasis is put on the retrieval of large but weakly refractive two-layer circular shells, into which can be inserted a high-speed core. The influence of the conditions of the image formation and the discrepancy between images derived from exact scattered pressures and Born’s approximated ones are especially investigated. Finally, procedures of reconstruction of the target’s sound velocity and attenuation are presented and discussed using synthetically generated data.