SEM approach to transient scattering by a lossy,radially inhomogeneous dielectric circular cylinder

The singularity expansion method is applied to the computation of fields associated with the transient scattering of a pulsed electromagnetic plane wave of finite duration by an isotropic, lossy, radially inhomogeneous dielectric circular cylinder. An angular Fourier transformation reduces the problem to solving a series of one-dimensional transient scattering problems, each of which is similar to the problem of scattering by a dielectric slab. Each of the resulting time-dependent Fourier coefficients is then expressed as a Laplace inversion integral over the Bromwich contour. This integral is evaluated by supplementing the contour of integration by circular arcs at infinity, and applying Cauchy's theorem. For each angular order, this leads to contributions from a denumerable set of poles and from a branch cut along the negative half of the real-frequency axis. Procedures are devised to determine these singularities and their contributions numerically. For a representative configuration, results are presented and discussed. A physical interpretation of these results is given.     

The indentation of a Newtonian fluid in a finite cylindrical container by a right circular cylinder

The indentation of the free surface of a Newtonian fluid in a finite cylindrical container by a right circular cylinder is considered. It is assumed that weight and inertia effects are negligible compared to viscous effects. A finite difference technique is used to obtain approximate values for initial velocities, pressures, and stresses at any point in the fluid as well as an estimate of the force required to indent the fluid with a given velocity. The solution obtained forms the basis for a primary indenter viscometer for very viscous fluids which have viscosities in the range of 10⁴–10¹⁰ poises.     

Geometrically non-linear free and forced vibrations of simply supported circular cylindrical shells: A semi-analytical approach

The non-linear free and forced vibrations of simply supported thin circular cylindrical shells are investigated using Lagrange's equations and an improved transverse displacement expansion. The purpose of this approach was to provide engineers and designers with an easy method for determining the shell non-linear mode shapes, with their corresponding amplitude dependent non-linear frequencies. The Donnell non-linear shell theory has been used and the flexural deformations at large vibration amplitudes have been taken into account. The transverse displacement expansion has been made using two terms including both the driven and the axisymmetric modes, and satisfying the simply supported boundary conditions. The non-linear dynamic variational problem obtained by applying Lagrange's equations was then transformed into a static case by adopting the harmonic balance method. Minimisation of the energy functional with respect to the basic function contribution coefficients has led to a simple non-linear multi-modal equation, the solution of which gives in the case of a single mode assumption an expression for the non-linear frequencies which is much simpler than that derived from the non-linear partial differential equation obtained previously by several authors. Quantitative results based on the present approach have been computed and compared with experimental data. The good agreement found was very satisfactory, in comparison with previous old and recent theoretical approaches, based on sophisticated numerical methods, such as the finite element method (FEM), the method of normal forms (MNF), and analytical methods, such as the perturbation method.     

Dynamic thermal stresses in a circular cylinder subjected to asymmetric heating

Summary This paper is concerned with the two-dimensional dynamic thermal stress problems in an infinitely long circular cylinder subjected to two kinds of asymmetric heatings at the lateral surface, assuming that the cylinder is initially undeformed and at zero temperature. The equations of motion including the inertia terms are expressed in terms of the dilatation and rotation and solved by applying the Fourier-cosine, Fouriersine transforms and the Laplace transform to the resulting differential equations. The solutions to the dynamic thermal displacements and stresses in the cylinder valid for the short period after the asymmetric heatings are obtained and the numerical calculations are carried out for the thermal boundary condition of the prescribed temperature distribution.

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Dynamische Wärmespannungen in Kreiszylindern bei asymmetrischer Erwärmung

übersicht Es werden dynamische WÄrmespannungsprobleme für einen unendlich langen Kreiszylinder untersucht, der zwei verschiedenen Arten von ErwÄrmung der OberflÄche unterworfen ist. Die Bewegungsgleichungen schlie\en die TrÄgheitsterme ein; sie werden in der Dilatation und der Rotation geschrieben und mit Hilfe von Fourier- und Laplace-Transformationen gelöst. Asymptotische Lösungen für kurze Zeiten werden ebenfalls hergeleitet, und numerische Ergebnisse werden grafisch dargestellt.

     

Magneto–thermo–electro–elastic transient response in a piezoelectric hollow cylinder subjected to complex loadings

The article presents an analytical solution for magneto–thermo–electro–elastic problems of a piezoelectric hollow cylinder placed in an axial magnetic field subjected to arbitrary thermal shock, mechanical load and transient electric excitation. Using an interpolation method solves the Volterra integral equation of the second kind caused by interaction among magnetic, thermal, electric and mechanical fields, the electric displacement is determined. Thus, the exact expressions for the transient responses of displacement, stresses, electric displacement, electric potential and perturbation of the magnetic field vector in the piezoelectric hollow cylinder are obtained by means of Hankel transforms, Laplace transforms, and inverse Laplace transforms. From sample numerical calculations, it is seen that the present method is suitable for a piezoelectric hollow cylinder subjected to arbitrary thermal shock, mechanical load and transient electric excitation, and the result carried out may be used as a reference to solve other transient coupled problems of magneto–thermo–electro–elasticity.     

Interaction of a spherical shockwave and an elastic circular cylindrical shell

The paper studies the interaction of a spherical shock wave with an elastic circular cylindrical shell immersed in an infinite acoustic medium. The shell is assumed infinitely long. The wave source is quite close to the shell, causing deformation of just a small portion of the shell, which makes it possible to represent the solution by a double Fourier series. The method allows the exact determination of the hydrodynamic forces acting on the shell and analysis of its stress state. Some characteristic features of the stress state are described for different distances to the wave source. Formulas are proposed for establishing the safety conditions of the shell.Translated from Prikladnaya Mekhanika, Vol. 40, No. 9, pp. 94–104, September 2004.     

Flow of non-Newtonian fluid contained in a fixed circular cylinder due to the longitudinal oscillation of a concentric circular cylinder

Summary The flow of a Reiner-Rivlin fluid between two coaxial porous circular cylinders has been studied. The inner cylinder performs a steady oscillation while the outer one is fixed.The exact solution of this problem has been obtained and approximate solutions for the two extreme cases, very small and very high frequencies, have been derived.     

An approximate solution to the problem of a circular cylindrical shell with a circular hole subjected to an arbitrary self-equilibrated edge loading

Summary In this investigation, we shall use Donnell's equation of shallow circular cylindrical shell to obtain an approximate solution for stresses in an infinitely long circular cylindrical shell with a circular hole about which there acts a self-equilibrated load. To satisfy the edge conditions, we first shall expand the appropriate solutions of the differential equation into series containing powers, products of powers and logarithm, of the characteristic parameter ₀ defined in (1). We then shall represent the unknown coefficients of the solutions in similar series including new constants which depend only on the material property and the type of loading. We determine the new unknown constants through simple algebraic equations. In conclusion, we shall present two examples for symmetric and anti-symmetric loadings, including expressions which illustrate their accuracy, and expressions for stress concentration.

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Übersicht Es wird eine Näherungslösung für die Spannungen in einer unendlich ausgedehnten kreiszylindrischen Schale mit einem kreisförmigen Loch mit Hilfe der Donnel-Gleichung für flache Schalen angegeben. Der Lochrand wird durch eine im Gleichgewicht befindliche Last beansprucht. Zur Erfüllung der Randbedingungen werden die Eigenlösungen der Differentialgleichung in Reihen entwickelt, die neben Potenzen auch Produkte von Potenzen und logarithmischen Gliedern des charakteristischen Parameters ₀ enthalten, der in Gl. (1) definiert ist. Die unbekannten Koeffizienten der Lösungen werden in entsprechender Weise durch Reihen dargestellt. Sie enthalten neue Konstante, die nur noch von den Materialeigenschaften und der Belastungsart abhängen. Diese Konstanten werden durch einfache algebraische Gleichungen bestimmt. Zwei Beispiele für symmetrische und antimetrische Belastung werden durchgerechnet, wobei die Spannungskonzentration und die Genauigkeit des Verfahrens erkennbar werden.

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The author is indebted to Dr. E. F. Casebeer for invaluable editorial suggestions.     

Momentum and heat transfer from an asymmetrically confined circular cylinder in a plane channel

Unsteady momentum and heat transfer from an asymmetrically confined circular cylinder in a plane channel is numerically investigated using FLUENT for the ranges of Reynolds numbers as 10≤Re≤500, of the blockage ratio as 0.1≤β≤0.4, and of the gap ratio as 0.125≤γ≤1 for a constant value of the Prandtl number of 0.744. The transition of the flow from steady to unsteady (characterized by critical Re) is determined as a function of γ and β. The effect of γ on the mean drag and lift coefficients, Strouhal number (St), and Nusselt number (Nu _w ) is studied. Critical Re was found to increase with decreasing γ for all values of β. and St were found to increase with decreasing values of γ for fixed β and Re. The effect of decrease in γ on was found to be negligible for all blockage ratios investigated.     

Penny-shaped crack in a long circular cylinder subjected to a uniform shearing stress

This paper contains an analysis of the stress distribution in a long circular cylinder of elastic material containing a penny-shaped crack when it is deformed by the application of a uniform shearing stress. The crack with its center on the axis of the cylinder lies on the plane perpendicular to that axis, and the cylindrical surface is stress-free. By making a suitable representation of the stress function for the problem, the problem is reduced to the solution of a pair of Fredholm integral equations of second kind. These are solved numerically, and the percentage increase in the stress intensity factor due to the effect of the finite radius of the cylinder is presented in graphical form for various proximity ratios.     

Nonlinear interfacial waves in a circular cylindrical container subjected to a vertical excitation

Singular perturbation theory of two-time scale expansions was developed in inviscid fluids to investigate the motion of single interface standing wave in a two-layer liquid-filled circular cylindrical vessel, which is subjected to a vertical periodical oscillation. It is assumed that the fluid in the circular cylindrical vessel is inviscid, incompressible and the motion is irrotational, a nonlinear amplitude equation including cubic nonlinear and vertically forced terms, was derived by the method of expansion of two-time scales without taking the influence of surface tension into account. By numerical computation, it is shown that different patterns of interface standing wave can be excited for different driving frequency and amplitude. We found that the interface wave mode become more and more complex as increasing of upper to lower layer density ratio γ$\gamma$. The traits of the standing interface wave were proved theoretically. In addition, the dispersion relation and nonlinear amplitude equation obtained in this article can reduce to the known results for a single fluid when γ=0,_h2→_h1$\gamma =0,h_2\to h_1$.     

A long circular cylinder with a circumferential edge crack subjected to a uniform shearing stress

This paper contains an analysis of the stress distribution in a long circular cylinder of isotropic elastic material with a circumferential edge crack when it is deformed by the application of a uniform shearing stress. The crack with its center on the axis of the cylinder lies on the plane perpendicular to that axis, and the cylindrical surface is stress-free. By making a suitable representation of the stress function for the problem, the problem is reduced to the solution of a pair of singular integral equations. This pair of singular integral equations is solved numerically, and the stress intensity factor due to the effect of the crack size is tabulated.