Rods Of Arbitrary Cross Section Research Articles

КОЛЕБАНИЕ МНОГОСЛОЙНОГО ЕСТЕСТВЕННО-ЗАКРУЧЕННОГО СТЕРЖНЯ ИЗ АНИЗОТРОПНЫХ МАТЕРИАЛОВ В ПОЛЕ ЦЕНТРОБЕЖНЫХ СИЛ

We study the vibrations of multilayer composite rod. In order to influence the definition-tion features multilayered rods, clarify the roles and forms orthotropy-layers fluctuations regarded rod of arbitrary cross section and a compressor blade Nye. The numerical results obtained for ratios compared with the results calculated by ANSYS program.

Material tailoring in functionally graded rods under torsion

Material tailoring in functionally graded isotropic hollow rods of arbitrary cross section under torsion is studied. The purposes of material tailoring pursued in this paper are divided into two categories. In the first category, we find the variation of the volume fractions of constituents of a functionally graded member under torsion to obtain an appropriate distribution of shear stress over the cross section. In the second category, the torsional rigidity of a rod with a pre-defined mass is maximized by appropriate determination of the variation of constituents of the functionally graded material. Hollow rods are studied in this paper since they have higher torsional rigidity compared to solid members with the same mass. Meshless numerical methods are used for torsional analysis of the cross sections. Moreover, numerical optimization methods are used for material tailoring of the rods. Several examples with different cross sections are presented to investigate the usefulness of the proposed technique on achieving the mentioned purposes.

A technique of analyzing critical forces and moments for isotropic rods of arbitrary cross-section in the general case of their complex resistance

The derivation of parametric equations for a limiting surface in the space of internal forces and moments that act in the rod cross-sections, using the basic concepts of plasticity theory and conventional hypotheses of the rod theory, is presented. The plastic properties of rod material are described by the Mises criterion. A case of small displacements and strains under static simple loading is considered. The results of solving a number of problems of constructing limiting curves in the planes of internal forces and moments are given.

The method of ray expansions for solving boundary-value dynamic problems for spatially curved rods of arbitrary cross-section

The method of ray expansions is developed for solving boundary-value problems connected with the propagation of planes of strong and weak discontinuity in spatially curved linearly elastic rods of arbitrary cross section. The equations of the three-dimensional theory of elasticity are utilized, which are written on the wave surface using the theory of discontinuities and then are integrated over the cross-sectional area. It is assumed that the plane of discontinuity remains perpendicular to the centroidal axis of the rod all the time during its propagation; the discontinuities in the normal stresses in the sections with the normals perpendicular to the centroidal axis can be ignored as compared to the discontinuities in stresses in the sections with the normals parallel to the centroidal axis. The cross-sections of the rod remain plane during the process of the rod deformation. These assumptions lead to the generation of two wave surfaces propagating in the spatially curved rod with the velocities of longitudinal-flexural and transverse-torsional waves of elastic rods. As this takes place, on the longitudinal-flexural wave, the bulk deformations experience a discontinuity not only at the sacrifice of shortening-elongation of the medium’s element locating along the centroidal axis, but also at the expense of thickening–thinning of this element in the directions of the principle axes of the rod cross-section. For the transverse-torsional wave, there exist discontinuities in the components of the velocities directed along the principle axes of the cross-section, in the angular velocity of the cross-section rotation as a rigid whole with respect to the centroidal axis, as well as in transverse deformations occurring due to the inhomogeneity of the transverse displacements. During the solution of boundary-value problems, the values to be found are represented in terms of the power series, the coefficients of which are the discontinuities in arbitrary order partial time-derivatives of the desired functions, while the time of arrival of the wave front is the independent variable; in so doing the order of the partial time-derivative coincides with the power exponent of the independent variable. The ray series coefficients are determined from the recurrent equations of the ray method within the accuracy of arbitrary constants, while the arbitrary functions themselves are found from the boundary conditions. Examples illustrating the efficiency of the ray method for solving the problems of dynamic contact interaction, resulting in the propagation of transient waves of strong discontinuity in spatially curved rods, are presented.

Menisci masses and weights in Stepanov (EFG) technique: ribbon, rod, tube

The present paper deals with the integration of the famous Laplace equation resulting in the expressions of full mass and weight of the liquid menisci in the system “melt–crystal” during the crystal growth process by Stepanov (EFG) technique. The problem for the cases of growing ribbon, cylindrical rod, cylindrical tube, rod of arbitrary cross-section and tube of arbitrary inner and outer cross-sections is solved. The problem for a hydrostatic approximation of the menisci of growing crystals is solved and it is shown via an analysis of the full energy functional, that the hydrodynamic factor is too small to be considered in the automated crystal growth systems.

Accurate analysis of helix slow-wave structures

In this paper, the helix slow wave structure (SWS) of traveling wave tubes (TWT's) has been analyzed. Dielectric supporting rods of arbitrary cross section have been considered in this analysis. The inhomogeneous dielectric loading factor has been accounted for by modeling the discrete support with a number of continuous dielectric tubes of appropriate effective dielectric permittivity. The helix tape model has been used for the field analysis. Furthermore the thickness of the helix tape has been considered. A rigorous solution of the field equations, including the contribution of the space harmonics, was performed to evaluate the phase velocity and the interaction impedance up to millimeter-wave frequencies. The nonuniformity of radial propagation constant over the structure cross section has been also included. With respect to other approaches, a closed-form expression of the field constants has been obtained. A study to choose the optimum number of space harmonics and dielectric tubes to be used in the analysis, has shown how the results are more sensitive to the number of space harmonics than to the number of dielectric tubes, beyond a certain number of the latter. The validity of this theory has been proved by comparison between measurements and simulations for helix SWS with different dimensions, rod shapes and operating frequency band.

The method of fictitious sources as applied to the conical diffraction by a homogeneous rod

This paper is a contribution to the study of the diffraction of an electromagnetic plane wave by a cylindrical rod of arbitrary cross-section and optical index. The incident wave vector is not necessarily perpendicular to the rod. This vectorial diffraction problem is solved using the method of fictitious sources which has proven to be effective for scalar problems. Theoretical and numerical aspects are both studied.

Comparison of approximations for effective parameters of artificial dielectrics

Formulas available in the literature for approximating the effective permittivity and permeability of a periodic array of (possibly lossy) dielectric rods of arbitrary cross section are assessed for their accuracy by comparing them with precise numerical values for special forms of the arrays. The literature on effective properties of arrays of dielectric rods is reviewed, covering what is known about general bounds, as well as the numerical results that are available for two specific arrays of square rods. It is found that while no single formula is capable of very high precision in every case, it is possible to construct good approximate formulas in individual cases as a result of this comparison.< <ETX xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">&gt;</ETX>

Electromagnetic scattering from dielectric rods of arbitrary cross section

A previous integral equation method for calculating time-harmonic scalar-wave scattering from objects of arbitrary shape is specialized to the case of electromagnetic scattering from dielectric rods of irregular cross section. Formulas of a relatively simple form are derived for both E and B wave scattering. Results are presented for the scattering cross section of rectangular and elliptic dielectric rods as a function of size, eccentricity, and index of refraction for different incident wave polarization and angles of incidence. Certain useful limiting approximation methods are also discussed.

Wave propagation in elastic rods of arbitrary cross section

Asymptotic expansions are found for both long and short waves propagating in elastic rods of arbitrary cross section. The results are compared with the well known approximate theories for long waves and show to what extent those theories are accurate. They also yield corrections to them.

Closure to “Discussion of ‘Elastic Wave Propagation in Rods of Arbitrary Cross Section’” (1966, ASME J. Appl. Mech., 33, pp. 476–477)

Closure to “Discussion of ‘Elastic Wave Propagation in Rods of Arbitrary Cross Section’” (1966, ASME J. Appl. Mech., 33, pp. 476–477)

Elastic Wave Propagation in Rods of Arbitrary Cross Section

A study is made of the problem of transient elastic wave propagation when a load is applied to one end of an infinitely long rod of arbitrary cross section. Fourier and Laplace transforms aid in developing a general solution in the form of a sum over all modes of harmonic wave propagation and integrals over all wavelengths. An expansion at long wavelength reveals two types of modes of propagation which are called longitudinal and radial shear modes. For a suddenly applied pressure, the long-distance, long-time response is found to be an integral of the Airy integral.

A Useful Analogy for Single-Group Neutron Diffusion Theory

It is shown that an analogy exists between the neutron flux as predicted by single-group neutron diffusion theory and the axial component of the electric field intensity in a field excited as a plane transverse-magnetic wave in a cylindrical cavity. The buckling of a homogeneous bare core could be determined using simple microwave devices to an accuracy on the same order as the uncertainty of the cavity dimensions. Experimental techniques are described for measuring control rod worth for fully extended cylindrical control rods of arbitrary cross section. Illustrative solutions are shown for circular, hexagonal, square, cruciform, Y, and sheet cross sections located at the center and at radial positions in a circular core. A method is described for predicting the flux distribution in the core region and experimental examples are shown. (auth)