Shells Of Circular Cross Section Research Articles

PROPAGATION OF LINEAR WAVES IN MULTILAYERED STRUCTURAL - INHOMOGENEOUS CYLINDRICAL SHELLS

In this paper, axisymmetric viscoelastic waves in an extended cylindrical shell of circular cross section are considered. The study of axisymmetric viscoelastic waves in multilayer cylindrical systems with the maximum possible use of analytical methods is relevant for the development of a new generation of sounding techniques for wells. The aim of the work is to study the propagation of axisymmetric viscoelastic waves in extended multilayer cylindrical structures, to determine the volumetric structure variant from the responses of one-way sounding using a priori information about the possible structure of the system. The paper uses classical methods of mathematical physics, applied to solving boundary value problems in a cylindrical coordinate system, the spatial Fourier transform, the method of complex amplitudes for the variable components of the displacement vector and the stress tensor. The low-frequency resonances of a cylindrical shell are investigated. The physical laws of the formation of the pitch of its fundamental tone are determined sounding. The impossibility of propagation along the casing of wells is proved low-frequency surface waves, as well as SH-polarization waves at axisymmetric excitation. The thin-walled cylindrical shell in the low-frequency region has two fundamental resonance associated with the resonance of the shell as a whole and resonance of each individual section as a ring. Beats of these frequencies the basic tone of the sound of an extended shell of this type is determined. At frequencies below the cutoff of higher modes, all the features of the dispersion natural waves in the wall of a circular cylinder shell are described approximate algebraic equation of the third degree. One the real root of this equation corresponds to the zero mode antisymmetric Lamb wave, and one of the other two complex conjugate, describes the zero mode of the symmetric wave.

Nonlinear static analysis of an underwater elastic semi-toroidal shell

This paper addresses the nonlinear static behavior of an elastic semi-toroidal shell of circular cross section subjected to external hydrostatic loading by using membrane theory. In this study, semi-toroidal shell geometry can be computed by differential geometry. Energy functional of the semi-toroidal shell can be obtained by principle of virtual work, and written in the appropriate form. The static response of the semi-toroidal shell can be computed by nonlinear finite element method. The nonlinear numerical solutions can be obtained by the iterative method. The effects of sea water depth, cross-sectional radius to thickness, and cross-sectional to bend radii ratios on the displacement responses of the semi-toroidal shell are investigated in this paper. Interestingly, it is found that the maximum value of the displacement responses on the semi-toroidal shell under hydrostatic loading occurred to the toroid internal crest.

Parametric Oscillations of a Stiffened Cylindrical Shell with Account of Its Damageability and of External Effects Exerted on It

The problem on parametric oscillations of a longitudinally stiffened cylindrical shell of circular cross section filled with viscoelastic medium has been solved with the variational principle.

Routes to Chaos Exhibited by Closed Flexible Cylindrical Shells

Complex vibrations of closed cylindrical shells of circular cross section and finite length subjected to nonuniform sign-changeable external load in the frame of classical nonlinear theory are studied. A transition from partial differential equations to ordinary differential equations (Cauchy problem) is carried out using the higher order Bubnov–Galerkin’s approach and Fourier’s representation. On the other hand, the Cauchy problem is solved using the fourth-order Runge–Kutta method. Results are analyzed owing to the application of nonlinear dynamics and qualitative theory of differential equations. The present work is devoted to the analysis of influence of the system dynamics of the following parameters: length of pressure width φ0, relative linear shell dimension λ=L∕R, and frequency ωp and amplitude q0 of external transversal load. Some new scenarios of vibrations of closed cylindrical shells exhibiting a transition from harmonic to chaotic vibrations are illustrated and studied.

Toroidal shells under nonsymmetric loading

The complete asymptotic expansions of four homogeneous solutions, and a particular solution of toroidal shells, based on Novozhilov's thin shell equations, are given, which are valid for the stress and deformation of toroidal shells of circular cross section subjected to nonsymmetric loadings.

Diffusion of magnetic fields in a toroidal conducting shell of circular cross section

The diffusion of an external magnetic field through a toroidal conducting shell is studied under the assumption of a small aspect ratio. The external magnetic field can have an arbitrary field index and magnetic flux on the minor axis of the torus. The diffused field, field index, magnetic flux, and wall current are computed analytically and compared with the numerical results from the TRIDIF code. The analytical and numerical results are in good agreement. Measurements in the toroidal chamber of the NRL modified betatron gave a delay time of 34 μsec, which is less than 10% from the theoretical prediction of 37 μsec.

Scattering by an inhomogeneous dielectric/ferrite cylinder of arbitrary cross-section shape-oblique incidence case

A moment method (MM) solution is developed for the fields scattered by an inhomogeneous dielectric/ferrite cylinder of arbitrary cross-section. The incident field is assumed to be a plane wave of arbitrary polarization with oblique incidence with respect to the axis of the cylinder. The total electric and magnetic fields are the unknown quantities in two coupled equations from which a system of linear equations is obtained. Once the total electric and magnetic fields within the cylinder are computed, the scattered fields at any other point in space can be calculated. It is noted that for the case of oblique incidence, the scattered field has TE/sub z/ and TM/sub z/ polarized fields regardless of the polarization of the incident field. The echo widths of cylinders and shells of circular, semicircular, and rectangular cross section are calculated for TE/sub z/ and TM/sub z/ polarized incident fields. It is shown that the results obtained for dielectric/ferrite cylinders and shells of circular cross section with the solutions developed here agree very well with the corresponding exact eigenfunction solutions. >

Inhibition of downwash of effluent from a triple-flue stack

An excessive fouling of paint has occurred near the top of a chimney stack. The stack was comprised of three separate flues enclosed in a shell of circular cross section. The fouling was caused by the downwash of effluent for the reduced flow rate in one of the flues. Wind tunnel modelling and testing covered a range of modifications of the geometry at the top. Two different types of the modification of the top were tried separately and also combined: 1. 1) Extension of the existing flues above the main shell, 2. 2) Enclosure of the three flues in a perforated shroud The modifications were only partly effective when applied separately. The development of the combined arrangement of extended and shrouded flues showed that the downwash could be almost entirely inhibited.

Critical Velocity for Collapse of Viscoplastic Cylindrical Shells Without Buckling

Successful operation of many practical devices that involve high-speed implosion of shells of circular cross section requires a stable collapse motion. In this paper, the dynamic buckling of imploding viscoplastic cylindrical shells is analyzed, and critical velocities are determined for which amplification factors of initial departures from circularity are 10, 100, and 1000.

Critical Velocity for Collapse of a Shell of Circular Cross Section Without Buckling

Many practical devices involve high-speed collapse of shells of circular cross section, In all of the devices the stability of the collapse motion is of interest and in some it is essential for successful operation. In this paper, the buckling motion of shells of circular cross section during high-speed collapse is analyzed and critical collapse velocities are determined for which the growth of initial nonuniformities by buckling during collapse is 10 and 100.

Stress diffusion from axially loaded stiffeners into cylindrical shells

A load diffusion problem for cylindrical elastic shells is solved. Infinitely long shells of circular cross section and uniform thickness are considered. These cylinders are reinforced by one or more equally spaced, continuously attached axial stiffeners. Each stiffener is loaded by a single concentrated longitudinal force. The magnitude, sense and axial location of application of each force are the same. The stress quantities of interest are the membrane shearing stress transmitted by a loaded stringer to the shell and the axial stress developed within the stringer. The extent to which shell curvature, stringer spacing and stringer bending stiffness affect these stress quantities is illustrated.

Scattering by a dielectric cylinder of arbitrary cross section shape

The theory and equations are developed for the scattering pattern of a dielectric cylinder of arbitrary cross section shape. The harmonic incident wave is assumed to have its electric vector parallel with the axis of the cylinder, and the field intensities are assumed to be independent of distance along the axis. Solutions are readily obtained for inhomogeneous cylinders when the permittivity is independent of distance along the cylinder axis. Although other investigators have approximated the field within the dielectric body by the incident field, we treat the total field as an unknown function which is determined by solving a system of linear equations. In the case of the dielectric cylindrical shell of circular cross section, this technique yields results which agree accurately with the exact classical solution. Scattering patterns are also presented in graphical form for a dielectric shell of semicircular cross section, a thin homogeneous plane dielectric sheet of finite width, and an inhomogeneous plane sheet. The effects of surface-wave excitation and mutual interaction among the various portions of the dielectric shell are included automatically in this solutiom

Green's-Function Technique in the Dynamics of a Finite Cylindrical Shell

The Reissner linearized equations of motion, including hysteretic- and viscous-damping terms, are adopted in the study of the dynamics of a finite, thin, elastic cylindrical shell of circular cross section. The integral representation of the radial displacement solution is obtained for an arbitrary, time-dependent pressure field over the shell surface and the associated Green's-function solution is calculated. In particular, the shell response to a moving shock wave (step-function discontinuity), impinging upon the shell at an arbitrary angle of incidence, is calculated. In the special case of axial symmetry, two additional waveforms are considered, that of a moving exponentially decaying shock wave and of a ramp/step-function wave. Typical numerical results are given in the form of displacement-time curves and the effects of the pressure-wave parameters (decay and rise time) are examined. The dynamic behavior of a prepressurized shell is also considered. It is shown that the Green's-function solution remains form-invariant under the introduction of an internal static pressure P0; this, in turn, leads to a simple rule for deducing the response to a given external pressure field when P0≠0 from known solutions corresponding to the case of P0 = 0.

Green's-Function Technique in the Dynamics of a Finite Cylindrical Shell

The Reissner linearized equations of motion, including hysteretic and viscous-type damping terms, are adopted in the study of the dynamics of a finite, thin, elastic, cylindrical shell of circular cross section. The integral representation of the displacement solution is obtained for an arbitrary, three-dimensional, time-dependent pressure field and the associated Green's-function solution is calculated; it is shown to be of identical form to the Green's function for other elastic systems. In particular, the shell response to a moving shock wave (step-function discontinuity), impinging upon the shell at an arbitrary angle of incidence, is calculated. In the special case of axial symmetry, two additional waveforms are considered, that of a moving exponentially decaying shock wave and a ramp step-function wave. Typical numerical results are given in the form of displacement time curves and the effects of the various parameters are discussed.

Transient Response of a Thin Elastic Cylindrical Shell to a Moving Shock Wave

Using the theory of thin elastic shells, the transient response of a finite cylindrical shell of circular cross section subjected to a moving pressure discontinuity obtained for the axisymmetric case. The response to a moving shock front with a decaying pressure intensity behind the front may be obtained from this solution by the superposition integral. From the solution for the moving pressure discontinuity, the response of the shell, due to an impulsive load applied simultaneously over the entire shell, is obtained by the use of a limiting procedure. The upper bounds for the dynamic loading factors are given as functions of the shell parameter β = l2/rh.

On stresses and deformations in toroidal shells of circular cross section which are acted upon by uniform normal pressure

On stresses and deformations in toroidal shells of circular cross section which are acted upon by uniform normal pressure

Analysis of Axially Loaded Annular Shells With Applications to Welded Bellows

A method is presented for the calculation of stresses and deflections in ring-shaped shells of circular cross section, subjected to axial forces. The solution is derived without the restriction imposed for toroidal shells by previous investigators, that the radius of curvature of the cross section is to be small in comparison with the mean radius of the torus. The range of applicability of the method is extended hereby to include the slightly arched convolutions used in the construction of welded bellows. By a rational reduction of the general solution approximate design formulas are obtained for the maximum stresses and deflections in bellows under axial forces and the calculated values are compared with experimental data.

A Theory of the Thickness Vibrations of a Barium Titanate Cylindrical Transducer

A transducer of barium titanate consisting of an infinitely long cylindrical shell of circular cross section and vibrating in a thickness mode is considered. The equation of motion is derived and solved for the steady-state condition. This solution is approximated by an asymptotic expression, valid when the wavelength is small compared with the radius, and from this asymptotic expression the coupled-circuit equations are derived. An expression is then obtained for the input impedance when the transducer radiates into water, from which expression the conventional equivalent circuit for a resonant system may be derived. This equivalent circuit is considered in two forms and its properties studied.