Convex Cross-section Research Articles

On the kinematics of filament winding on non-axisymmetric cylindrical mandrels. Part I: A generalized model

Abstract Kinematic aspects of filament winding for cylindrical mandrels having any smooth convex cross-section are discussed in this paper. A method is proposed to determine the motion of delivery point relative to the mandrel to ensure that fibre lay-down is of the predetermined path over the mandrel. Experimental verification of the process was carried out on a cylindrical mandrel having an elliptic cross-section with a semi-major axis a = 77.98 mm (3.07 in) and a semi-minor axis b = 39.98 mm (1.574 in). All the experiments were performed on a computer-controlled filament winding machine having two degrees of freedom. The effects of location of delivery point, mandrel geometry, and fibre winding angle on delivery point motion are discussed.

Scattering by an infinitely-long bianisotropic cylinder with electrically small, convex cross-section

The electromagnetic scattering response of an infinitely-long cylinder made of a general linear bianisotropic material is obtained using a long-wavelength approximation. The results obtained apply when the cross-sectional linear dimensions of the cylinder are electrically small, the constitutive dyadics are arbitrary and the cross-sectional shape is convex.

Electromagnetic reflection from an arbitrary smooth convex cylinder

The multiple Laplace transform has been applied to the analysis of electromagnetic scattering by a cylinder of arbitrary convex cross section. Results exhibit the field values segmented into forward-propagating and inverse-propagating integral expressions whose integrands are Hankel functions multiplied by the tangential field components on the boundary. All electric- and magnetic-polarization components of the field can be solved external to the cylinder as a function of the field values on the boundary. Both the electric-field and the magnetic-field integral equations are derived from specific parts of the solution. These equations are derived without invoking the concepts of surface current, scalar potential, or vector potential.

Heat treatment deformation of steel products

The heat treatment deformation of steel products is reviewed and the thermal stress, which is one of the initiators of the deformation, is theoretically analysed taking into account transformation. Other initiators are also discussed, i.e. stress relaxation on heating, creep at high temperature, and change of microstructure on tempering. It was found that the thermal stress during quenching changes the profile of steel products, decreased long axis, increased short axis, and convex cross–section for non–hardenable and for marquenched or oil–quenched small steel parts, and increased long axis, decreased short axis, and concave cross–section for water/oil–quenched hardenable steels. These differences are the results of the different strain hardening rates of the various phases and the temperature distribution through the cross–section over the temperature range of martensite transformation. Some solutions to the problems of deformation are also discussed.MST/21

Arrangement of sources in the charge simulation method–the case of e‐wave scattering by one perfectly conducting cylinder of convex cross section shape

AbstractThe charge simulation method has the following characteristics compared with other approximate methods for the scatteirng problems: (1) Only the zeroth and first‐order Hankel functions are used; (2) no processing of the singularities on the boundary is needed; (3) no numerical integration is necessary. As a result, it is an extremely simple method. However, the arrangements of the sources and contour points are arbitrary and such arrangements affect the accuracy of the approximate solutions. Previously, the source arrangements by the boundary contractions have been used in the charge simulation method. This choice provides good results if the shape of the scatterer is close to a circle or is a circle itself. The accuracy becomes poorer as the shape deviates more from the circle. Also, it is not possible to determine beforehand the arrangement that provides the best result. Hence, the boundary contraction is an important arrangement method. In this paper, arrangement of the sources and contour points is determined by means of the conformal mapping that transforms the boundary to a circle. Numerical calculations have been performed for typical convex shapes. It is found that the charge simulation method based on the present arrangement has the following properties. It exhibits much better accuracy than the arrangement by boundary contraction. The arrangement minimizing the error is found from the conformal mapping. Scatterers with edges on the boundary cannot be analyzed.

High-frequency scattering of elastic waves from cylindrical cavities

The scattering of time-harmonic plane longitudinal elastic waves by smooth convex cylindrical cavities is investigated. The exact solution for a circle is evaluated for wavelengths of the same order as the radius, and the geometrical and physical elastodynamics approximations are shown to be inadequate. The application of Watson's transformation exhibits the various diffraction effects and the relative importance of each is assessed. Excellent approximations for the scattered far-field are obtained with a hybrid method, in which an approximation for the surface field is constructed from the creeping wave contributions and this is then used in an integral representation. A generalization, based on the Geometrical Theory of Diffraction, of the hybrid method to cavities of smooth convex cross-section is presented and applied to the specific case of an ellipse. The predictions of the hybrid method compare well with numerical results obtained by an eigenfunction expansion method.

極希薄気体中の円柱に及ぼす壁面効果

A force acting on a cylinder with a uniform temperature in a semi-infinite expanse of gas bounded by an infinite plane wall with a different temperature (thus, the temperature of the gas is the same as that of the wall) is investigated for highly rarefied gas on the basis of the linearized BOLTZMANN-KROOK-WELANDER equation. First, the free molecular limit is considered for a cylinder with an arbitrary convex cross section. It is shown that the behavior of the gas is not affected by the wall and that the cylinder is not subject to any force. Next, the effect of molecular collision is taken into account for a circular cylinder. When the temperature of the cylinder is higher than that of the wall, the cylinder is subject to a force of the order of (ln Kn)/Kn toward the wall, where Kn is the KNUDSEN number. In the opposite case the force is reversed.

The Collection and Dissemination of Light with the Aid of Diffuse Reflectors

Let a cylindrical absorbing body of convex cross-section be partly surrounded by a cylindrical bowl whose inner surface is a perfect diffuse reflector. The entrance aperture of the system, determined by the positions of the rims of the bowl, is assumed to be illuminated over the whole inward hemisphere by light of uniform brightness. A method is presented for determining the reflector profiles which deliver the greatest possible power to the absorbing body, and a simple expression is found for the power delivered. The same reflector profiles solve the complementary problem of light emission, when the absorbing body is replaced by a uniformly bright diffuse emitter.

On the automorphism group of a cone

Let V be a real finite dimensional vector space, and let C be a full cone in C. In Sec. 3 we show that the group of automorphisms of a compact convex subset of V is compact in the uniform topology, and relate the group of automorphisms of C to the group of automorphisms of a compact convex cross-section of C. This section concludes with an application which generalizes the result that a proper Lorentz transformation has an eigenvector in the light cone. In Sec. 4 we relate the automorphism group of C to that of its irreducible components. In Sec. 5 we show that every compact group of automorphisms of C leaves a compact convex cross-section invariant. This result is applied to show that if C is a full polyhedral cone, then the automorphism group of C is the semidirect product of the (finite) automorphism group of a polytopal cross-section and a vector group whose dimension is equal to the number of irreducible components of C. An example shows that no such result holds for more general cones.

On the elastic-plastic torsion problem

It is shown that solving the elastic-plastic torsion problem is equivalent to solving a nonlinear boundary value problem. The equivalence is valid for a strictly convex cross-section and angles of twist large enough that the plastic region encloses the elastic region. The advantage of this formulation is that no free boundaries are present.

On Saint-Venant's Principle in three-dimensional nonlinear elasticity

Consider a long elastic isotropic beam with a convex cross-section and a sufficiently smooth boundary. Suppose that a self-equilibrated load is applied at each end but the sides are stress-free and there are no internal body forces. It is proved in the context of three-dimensional, nonlinear elastostatics that if the first four derivatives of the displacement vector are a priori assumed to be everywhere sufficiently small with respect to the physical constants and the geometry of the cross-section, then the strains at any point decay exponentially with the distance of the point from the nearest end. This result is an extension of known results on Saint-Venant's Principle in linear and two-dimensional nonlinear elasticity.

Self-consistent GTD formulation for conducting cylinders with arbitrary convex cross section

A user-oriented computer program has been developed for high frequency radiation and scattering from infinitely-long perfectly. conducting convex cylinders. The analysis is based on the self-consistent geometrical theory of diffraction (GTD). The cylinder is modeled as an <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">N</tex> -sided polygon. Two cylindrical waves with unknown amplitudes are assumed to travel in opposite directions on each face of the polygon. The boundary conditions for the corners are applied to set up a matrix equation for <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">2N</tex> unknowns (the amplitudes associated with the traveling cylindrical waves). Crout's method is used to solve the matrix equation. Once the amplitudes for the traveling waves are determined, the radiation or scattered field is readily obtained via the usual GTD techniques. Numerical results are presented for radiation and scattering from rectangular, semi-circular, circular, and elliptic cylinders for both principal polarizations. The results show excellent agreement with GTD, moment, and eigenfunction solutions.

Wide range audio transducer using piezoelectric ceramic

Abstract Piezoelectric circular bending transducers, when properly applied to loudspeakers, can cover a large portion of the audio spectrum and can deliver medium to high power outputs efficiently. In the concept presented in this paper, the bending transducers are mounted circumferentially and are loaded in the center by the cone. The transducers, which have a convex cross-section, are optimized for electro-mechanical coupling factor, capacitance and mechanical impedance. Maximum overall conversion efficiently is achieved through resistive electrodes, which also provide a frequency dependent sliding excitation. Two major problems, stress and field depoling, have been reduced by the transducer design and by the selection of the proper PZT compositions.

Movement of Soil Materials and Soil Formation on the Slope at Kawatabi, Miyagi Prefecture

One of the investigated areas is a ridge type slope with convex cross section consisting of thin vegetation at the upper half and dense vegetation at the lower half. Another area is a valley type slope with concave cross section with dense vegetation. The parent material in these areas is weathered sandy tuff.On the soil formation of this area, it is shown that the thickness of A-horizon varies according to local difference in gradient or vegetation on the slope. On the whole area of valley type slope and on the lower half of ridge type slope, A-horizon is generally thick even where the slopes are steep, then a buried A-horizon is found there. On the upper half of ridge type slope, A-horizon is thin even at gentle slope. On the slopes of either ridge type or valley type, B-horizon is thick at gentle slopes and thin at steep slopes. According to the grain analysis, the soil is rich in fine materials on the valley type slopes and the lower half of ridge type slopes. On the upper half of ridge type slope, the soil is rich in coarse mateSeemingly, those local differences of soil formation were caused by the differences in slope forms and the density of the vegetation.First, the slope forms affect the movement of soil materials. It seems that the denudation of slope surface is active on slopes with poor vegetation, and is weak where the vegetation is dense. Therefore the fine materials supplied from surrounding areas are accumulated on the slopes covered with dense vegetation in the lower part of the slopes. In such cases the vegetation is usually poor in the upper part of the slopes.According to the rapid destruction of vegetation, the denudation is accelerated and so the buried soil is formed at the slope-end. Apparently, the denudation of slope has become active by the human impact to the vegetation since Holocene.According to the destruction of vegetation, such buried soil as was seen in this slope was formed widely in other areas, too.In the study of buried soil on slope, the movement of fine materials on the slopes is considered as an important factor for the soil formation except the cases of the aeolian origin such as volcanic ash or sand.

On the Torsional Rigidity of a Beam of Convex Cross‐section

ZAMM - Journal of Applied Mathematics and Mechanics / Zeitschrift für Angewandte Mathematik und MechanikVolume 49, Issue 1-2 p. 92-93 Kleine Mitteilungen On the Torsional Rigidity of a Beam of Convex Cross-section Dr. E. Makai, Dr. E. Makai Mathematical Institute of the Hungarian Academy of Sciences, Budapest, V. Reáltanoda u. 13–15.Search for more papers by this author Dr. E. Makai, Dr. E. Makai Mathematical Institute of the Hungarian Academy of Sciences, Budapest, V. Reáltanoda u. 13–15.Search for more papers by this author First published: 1969 https://doi.org/10.1002/zamm.19690490113AboutPDF ToolsRequest permissionExport citationAdd to favoritesTrack citation ShareShare Give accessShare full text accessShare full-text accessPlease review our Terms and Conditions of Use and check box below to share full-text version of article.I have read and accept the Wiley Online Library Terms and Conditions of UseShareable LinkUse the link below to share a full-text version of this article with your friends and colleagues. Learn more.Copy URL Share a linkShare onFacebookTwitterLinkedInRedditWechat No abstract is available for this article. Volume49, Issue1-21969Pages 92-93 RelatedInformation

Decay exponents and diffraction coefficients for surface waves on surfaces of nonconstant curvature

The decay exponents and diffraction coefficients for a cylindrical surface of nonconstant curvature are computed by two methods which yield the same results. The results consist of leading terms which depend upon the curvature of the surface and corrections which depend upon the derivative of the curvature. The leading terms coincide with those found previously. With these corrections, the geometric theory of diffraction can be used at longer wavelengths than before. In the first method the solution for diffraction by an elliptic cylinder is expanded asymptotically for wavelengths small compared to the cylinder dimensions. From the expansion the decay exponents and diffraction coefficients are determined. They are then expressed in terms of the curvature and its derivative, and in this form they are assumed to apply to a cylinder of arbitrary convex cross section. This assumption is verified by comparison with the corresponding results for a parabolic cylinder. Then the same results are obtained by asymptotically solving the integral equation for the field on a cylinder of arbitrary convex cross section.

An approximate boundary layer theory for semi-infinite cylinders of arbitrary cross-section

An estimate is given of the distribution of skin frictional force per unit length, and of displacement area, on the outside of a semi-infinite cylinder, of arbitrary cross-section, moving steadily in a direction parallel to its generators. A Pohlhausen method is employed with a velocity distribution chosen to yield zero viscous retarding force on the boundary layer approximations. (The smallness of the fluid acceleration far from the leading edge has been pointed out by Batchelor (1954).) Like the Rayleigh method, this method is expected to yield reasonable results at large distances from the leading edge. However, for a large class of cross-sections, which includes all convex cross-sections and locally concave cross-sections with re-entrant angles greater than ½π, the method yields the expected square root growth of the boundary layer at the leading-edge, with a fairly close approximation to the coefficient, and it is supposed that the skin-frictional force and displacement area are given with reasonable accuracy along the whole length of the cylinder.Results for the elliptic cylinder and the finite flat plate are given in closed form, valid for the whole length of the cylinder, and are expected to be in error by at most 20%. In addition, some estimate is given of the effect of corners on skin frictional force and displacement area.