Cylinder Of Arbitrary Cross Section Research Articles

Approximations to sloshing frequencies for rectangular tanks with internal structures

The frequencies of free oscillation of a fluid in a rectangular tank are reduced by the introduction of a rigid internal structure. This paper gives general, approximate methods for the calculation of the oscillation frequencies when the structure is a cylinder of arbitrary cross section spanning the tank, and with generators normal to one pair of vertical faces. Particular results are given for submerged, circular cylinders and both vertical and horizontal thin baffles.

Vibration of Stress-Free Hollow Cylinders of Arbitrary Cross Section

A three-dimensional elasticity solution to the vibrations of stress-free hollow cylinders of arbitrary cross section is presented. The natural frequencies and deformed mode shapes of these cylinders are obtained via a three-dimensional displacement-based energy formulation. The technique is applied specifically to the parametric investigation of hollow cylinders of different cross sections and sizes. It is found that the cross-sectional property of the cylinder has significant effects on the normal mode responses, particularly, on the transverse bending modes. By varying the length-to-width ratio of these elastic cylinders, interesting results demonstrating the dependence of frequencies on the length of the cylinder have been concluded.

Scattering of electromagnetic waves from a chiral cylinder of arbitrary cross section — GMT approach

AbstractIn this article the generalized multipole technique (GMT) is formulated to obtain the scattering response of a chiral cylinder of arbitrary cross section. The convergence of GMT was verified, and the accuracy of GMT was recognized by comparing with the eigenfunction expansion method. © 1995 John Wiley & Sons, Inc.

Second-Order Diffraction Forces on an Array of Vertical Cylinders in Bichromatic Bidirectional Waves

A complete second-order solution is presented for the hydrodynamic forces due to the action of bichromatic, bidirectional waves on an array of bottom-mounted, surface-piercing cylinders of arbitrary cross section in water of uniform finite depth. Based on the constant structural cross section, the first-order problem is solved utilizing a two-dimensional Green function approach, while an assisting radiation potential approach is used to obtain the hydrodynamic loads due to the second-order potential. Results are presented which illustrate the influence of wave directionality on the second-order sum and difference frequency hydrodynamic forces on a two-cylinder array. It is found that wave directionality may have a significant influence on the second-order hydrodynamic forces on these arrays and that the assumption of unidirectional waves does not always lead to conservative estimates of the second-order loading.

The currents on a cylinder illuminated by a general obliquely-incident plane wave

A relation is presented that determines the total current induced by a general plane wave obliquely incident or a perfectly electrically conducting cylinder of arbitrary cross section from the total current induced by a normally incident plane wave. Remarkably, this same relation ran also be used to determine the physical optics (PO) and nonuniform (NU) currents for oblique incidence directly from the PO and NU currents, respectively, for normal incidence.

A finite-element analysis of electromagnetic scattering from a moving dielectric cylinder of arbitrary cross section

This paper deals with the electromagnetic scattering of a plane wave obliquely incident on an infinite penetrable cylinder in uniform motion with velocity v along its axis. The analysis is carried out by means of a hybrid technique, which combines the finite-element method and the well-known modal expansion of a field scattered by cylindrical structures. The method presented allows for analysis of moving cylinders of arbitrary cross section and material properties.

Scattering by a random set of parallel cylinders

A theory of scattering by a finite number of cylinders of arbitrary cross section is presented. This theory is based on a self-consistent approach that identifies incident and scattered fields around each cylinder and then uses the notion of a scattering matrix in order to get a linear system of equations. Special attention is paid to the simplified case of a sparse distribution of small cylinders for low frequencies. Surprisingly, it is found that the classical rules of homogenization must be modified in that case. The phenomenon of enhanced backscattering of light is investigated from numerical data for a dense distribution of cylinders.

Novel differential formulation of electromagnetic scattering by dielectric cylinders of arbitrary cross-section

A new differential method of electromagnetic scattering from dielectric cylinders is presented. The formulation is based on a harmonic expansion of fields in terms of cylindrical wave functions and their matching at appropriate boundaries. An infinite dimensional differential system results in for the unknown expansion coefficients. This system is projected into a finite dimensional one whose numerical solution is the essential step. The method is seen to produce highly reliable results in the resonance region for TM, TE and line-source excitations.

Second-Order Wave Interaction with Vertical Cylinder of Arbitrary Cross Section

ABSTRACTAn approximate calculation method is proposed for the second-order interactions between water waves and vertical cylinders of arbitrary cross section. In mathematical formulations, perturbation method is used to derive the first- and second-order boundary value problems, and Green's Identity Formula is also used to express the velocity potentials in a horizontal plane. Second-order wave forces and wave deformations near a vertical circular cylinder are computed, and the results are verified through comparison with wave tank experiments and other theories in the valid range of the second-order Stokes wave theory.

A finite element approach to the electromagnetic interaction with rotating penetrable cylinders of arbitrary cross section

A method for evaluating the fields excited by an obliquely incident plane wave inside and outside a rotating cylinder is presented. A differential formulation of the problem is developed with respect to the comoving reference frame of the scatterer on a closed circular domain including the scatterer cross section; the boundary conditions account for the far-field conditions through a series expansion of the total field on the domain contour. The results at oblique incidence are then particularized for normal incidence and a hybrid finite element numerical solution is presented and discussed for TM incidence. The present FEM approach and the related computer code are directly applicable to the study of rotating piecewise-homogeneous cylinders at normal incidence, as well as metallic cylinders coated by layers of penetrable materials. Through a comparison, for normal incidence, between the quasi-stationary and the Galileian relativistic approach, a method for approximately reconstructing the Doppler frequency shift in the quasi-stationary method is derived. Far-field and near-field numerical results for circular and arbitrarily shaped (metallic or dielectric) cylinders are presented.< <ETX xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">&gt;</ETX>

Mixed element formulation for the efficient solution of electromagnetic scattering problems

The use of a mixed element formulation for the solution of the scattering of an electromagnetic wave by an infinite cylinder of arbitrary cross section and material composition is examined. A method that combines the conventional finite-element method (FEM) with the generalized scattering amplitude formulation is presented. In the immediate region of the scatterer, the conventional FEM is used to represent the scattered fields. In the exterior region, finite elements are used to model the generalized scattering amplitude, and a weak-form equation based on the transformed Helmholtz equation is derived. The exterior region is then truncated via a local absorbing boundary condition. The two regions are then coupled via a natural boundary condition. It is found that the mesh density can be reduced on the exterior region, and a significant savings in computational time and memory can be realized. >

TE Scattering from Multiple Conducting and Dielectric Cylinders of Arbitrary Cross Section Using Solenoidal Basis Functions

A simple volume and surface formulation is presented to analyze the problem of scattering of TE waves by multiple perfectly conducting and dielectric cylinders of arbitrary cross section. The Method of Moments and the principle of equivalence are used to replace the cylinders by equivalent surface and volume currents radiating in an unbounded medium. The surface currents are obtained by enforcing the boundary conditions on the surface of the conducting cylinders, and the volume currents are obtained by applying the equivalence principle inside the volume of the material cylinders. This procedure leads to integral equations for the currents in each of the cylinders considered. The Method of Moments is used to solve the integral equations. Triangular functions are used to expand the surface currents on the conducting cylinders and a set of volume solenoidal basis functions is used to expand the volume currents in the dielectric cylinders. Some of the deficiencies of the formulation are discussed. Results ar...

Natural Convection Heat Transfer From Cylinders of Arbitrary Cross Section

Analytical, numerical, and experimental studies of free convection heat transfer from the external surface of isothermal two-dimensional bodies, especially circular cylinders and vertical flat plates, have been conducted by many investigators. A review of the existing literature shows that most workers have focused mainly on experimental data of circular cylinders and vertical plates with air (Pr[approximately]0.71) as working fluid. The results of these studies have been empirical correlations restricted either to some simple geometries or to a narrow range of Rayleigh numbers. Only a few scientists have carried out numerical techniques, which unfortunately, are also restricted to simple geometries such as circular cylinders. There are a few analytical solutions for cylinders of fairly arbitrary cross section, but, unfortunately, those solutions are restricted to a very narrow range of Rayleigh were the boundary layer is thin compared to the local radius of curvature of the cylinder. The approximate method suggested by Raithby and Hollands, however, is capable of predicting heat transfer from cylinders of various cross sections and for wide ranges of Prandtl and Rayleigh numbers. Unfortunately, following the steps of their approximate method is complex, and engineers might be discouraged from using it. Therefore it is the goal of thismore » study to simplify this approximate method and introduce an expression for predicting natural convection heat transfer from isothermal two-dimensional bodies of arbitrary cross section over a wide range of Rayleigh and Prandtl numbers. In this paper, following a similar procedure to that outlined by Hassani and Hollands, an expression for predicting the convection heat transfer from two-dimensional bodies (cylinders of different convex cross sections) is derived.« less

Scattering by a Chiral Cylinder of Arbitrary Cross Section in the Presence of a Half-Plane

An integral equation and method of moments/Green's function solution to the problem of scattering by a chiral cylinder of arbitrary cross section in the presence of a perfectly conducting half-plane is presented. The volume equivalence theorem for chiral media is used to formulate a pair of coupled vector integral equations for the equivalent electric and magnetic volume polarization currents representing the chiral cylinder. The presence of the half-plane is accounted for by including the half-plane Green's function in the kernel of the integral equations, and efficient techniques for accurately evaluating the integrals in this Green's function are presented. Numerical results illustrate that a chiral cylinder surrounding the half-plane edge can significantly modify the scattering from the edge. The chiral cylinder is also seen to produce significant cross-polarized scattered fields, which are a direct result of the rotation of field polarization in a chiral medium.

Scattering by a Chiral Cylinder of Arbitrary Cross Section in the Presence of a Half-Plane

Scattering by a Chiral Cylinder of Arbitrary Cross Section in the Presence of a Half-Plane

The surface potential method in the problem of wave diffraction by a penetrable cylinder of arbitrary cross section in a layered medium

The surface potential method in the problem of wave diffraction by a penetrable cylinder of arbitrary cross section in a layered medium

BACKSCATTERING OF ELECTROMAGNETIC MISSILES BY A PERFECTLY CONDUCTING CYLINDER WITH ARBITRARY CROSS SECTION

In this paper, we present a general study on backscattering of electromagnetic (EM) missile by a perfectly conducting cylinder of arbitrary cross section. We find that, when an EM missile with energy decreasing as r-ε(0 -εR/(2r + R), where R is the radii of curvature at tie specular point of the target.

Two-dimensional problem of diffraction by dielectric cylinder of arbitrary cross-section in plane-layered medium. TheE-polarization case

An algorithm is developed for numerical solution of the two-dimensional problem of scattering of an E-polarized field by a dielectric cylinder in a plane-layered medium. Plane-wave scattering by a cylinder imbedded in a homogeneous dielectric layer with rectangular and rhombic cross-sections is studied.

TE-scattering from dense homogeneous infinite dielectric cylinders of arbitrary cross-section

A numerical approach to obtain the fields scattered by a homogeneous dielectric cylinder of arbitrary cross section which is illuminated by a TE plane wave is presented. The equivalence theorem is used to transform the problem of solving Maxwell's equations in the whole space, subject to the conditions imposed by the presence of the cylinder and the incident field, into an operator equation for the volume polarization currents in the cylinder. A set of expansion functions is then used to solve the problem using Galerkin's technique. These expansion functions are obtained by dividing the cylinder cross-section into a number of triangular patches and defining, for each node in the mesh of triangles, a basis function which depends on the dimensions of the triangles attached to it. This basis function is divergence-free for all the internal nodes, with surface charges associated to the external nodes only. The computed results include the radar cross sections. Several geometries are studied, and the computed results are compared with exact or numerical results.< <ETX xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">&gt;</ETX>

Discussion on Venkat &amp; Spaulding: “Numerical Simulation of Nonlinear Free-Surface Flows Generated by a Heaving Body of Arbitrary Cross Section”

A method has been presented recently by Venkat and Spaulding to solve the nonlinear boundary-value problem of oscillating two-dimensional cylinders of arbitrary cross section on the free surface of a fluid. The method relies on a second-order finite-difference technique with a modified Euler method for the time domain and a successive over-relaxation procedure for the spatial domain. The authors compare their numerical results with those of other authors (theoretical and experimental), as they have published data for specialized forms like a wedge, circular cylinders, and ship-like sections in forced heave motion (references [4] to [7] and [22], [23] of the paper).