On the cross section of minimum stress concentration in the Saint-Venant theory of torsion

A lower bound is derived for the maximum stress in the torsion of cylindrical solids of simply-connected cross section. This bound, which is expressed in terms of the applied torque and the cross-sectional area, is isoperimetric in that it coincides with the maximum stress when the cross section is circular. It confirms the notion that given the applied torque and the area of the cross section, the least maximum stress occurs when the section is circular. Related isoperimetric upper bounds are derived for the minimum value of the stress at boundary points.     

Controlling the form of strong converging shocks by means of disturbances

The influence of artificial disturbances on the behavior of strong converging cylindrical shocks is investigated experimentally and numerically. Ring-shaped shocks, generated in an annular cross sectional shock tube are transformed to converging cylindrical shocks in a thin cylindrical test section, mounted at the rear end of the shock tube. The converging cylindrical shocks are perturbed by small cylinders placed at different locations and in various patterns in the test section. Their influence on the shock convergence and reflection process is investigated. It is found that disturbances arranged in a symmetrical pattern will produce a symmetrical deformation of the converging shockfront. For example, a square formation produces a square-like shock and an octagon formation a shock with an octagonal front. This introduces an alternative way of tailoring the form of a converging shock, instead of using a specific form of a reflector boundary. The influence of disturbances arranged in non-symmetric patterns on the shape of the shockfront is also investigated.      

The propagation of elastic surface waves along cylindrical cavities of general cross section

The existence of surface wave modes, propagating along an infinite cylindrical cavity of arbitrary constant cross section in an elastic medium, is investigated theoretically. A general secular equation is derived using the null-field approach and global expansions of the surface displacements. Numerical results for the phase velocities, surface displacements and cut-off frequencies are presented for elliptic cross sections. The largest eccentricity considered is 0.99995 and it is inferred that the flexural mode exists at all frequencies for any eccentricity of the cross section.     

Bounds for the torsional rigidity of inhomogeneous cylindrical bars

The object of this paper is the uniform torsion of inhomogeneous, isotropic, linearly elastic cylindrical bar. The aim is to give lower and upper bounds for the torsional rigidity of the bar with doubly connected cross section. The outer and inner boundary curves of cross section are similar curves. The level lines of the function which gives the change of the shear rigidity on the cross section are also similar curves to the boundary curves. The application of derived bounding formulae is illustrated by examples. An approximated formula to determine the shear stresses is also presented.     

Stress-Strain Analysis of Orthotropic Closed and Open Noncircular Cylindrical Shells

The paper proposes an approach to the stress-strain analysis of orthotropic open and closed cylindrical shells of variable thickness and noncircular cross section under various loading and boundary conditions. As an example, the circumferential distribution of deflection and tangential force in shells with elliptic cross section is analyzed for some cases of orthotropy __________ Translated from Prikladnaya Mekhanika, Vol. 41, No. 7, pp. 83–92, July 2005.     

Study Into the Effect of Circumferential Variation in Thickness and Load on the Deformation of Cylindrical Shells of Elliptic Cross Section

By solving the boundary-value stress–strain problems for cylindrical shells with an elliptical cross section and a thickness varying along the directrix, the effect of variability in the thickness and load on their deformation is studied. Tables and plots present the deflection and the bending moment calculated under various boundary and loading conditions.     

Pool boiling — And the effect of pool geometry

Simple correlationsh=C·qⁿ for experimental results in nucleate pool boiling often exhibit a wide scatter in the constant and the exponent. Among the many parameters responsible, an effect from confining boundaries causing flow recirculation, cannot be excluded. Heat transfer experiments were performed in a cylindrical and rectangular vessel on finned tubes in a single and twin arrangement. The cylindrical vessel had a smaller fluid cross section area than the rectangular vessel. Although the tubes were identical in geometry (except for length) and surface roughness, they yielded clearly different results. The heat transfer coefficients in the cylindrical vessel were always larger than in the rectangular one.     

单层偏心圆柱薄壳的自由振动特性分析研究

本文从偏心圆柱壳截面的几何特性出发,将偏心圆柱壳问题转化为一个周向变厚度圆柱壳问题,随后利用其状态向量之间的传递矩阵将壳体的振动控制方程转化为矩阵微分方程形式,通过Magnus级数法求解传递矩阵得到频率方程。采用Lagrange插值法得到偏心圆柱壳体自由振动状态下的固有频率,并且与圆柱壳的固有频率进行了比较。对影响结构固有频率的主要参数进行了分析,得到了这些参数和固有频率之间的关系。本文不仅提出了一种有效求解偏心圆柱壳固有频率的新方法,同时亦可为检测偏心圆柱壳的偏心距提供一种新的思路和方法。     

Two-dimensional spreading of a cloud of conducting gas in a magnetic field self-similar solution

A self-similar solution of the problem on the spreading in a magnetic field of a cloud of conducting gas, having the shape of a cylinder of noncircular cross section, is constructed. The cylindrical surface of the gas is restrained by a nonconducting sheath that spreads according to a prescribed law. The shape of the transverse cross section of the cylindrical cloud is determined from the solution. Cross sections obtained for a concrete case are represented in graphic form.Translated from Zhurnal Prikladnoi Mekhaniki i Tekhnicheskoi Fiziki, No. 2, pp. 29–36, March–April, 1973.In conclusion the author thanks V. I. Khonichev for assistance with the numerical calculations.     

Study of nonlinear deformation and stability of discretely reinforced elliptic cylindrical shells in transverse bending

A finite-element method for solving problems of nonlinear deformation and stability of nonuniformly discretely reinforced noncircular cylindrical shells is considered. An effective computer algorithm for the study of shells is developed. Stability of stringer cylindrical shells with an elliptical cross section in transverse bending is examined. The effect of ellipticity, nonlinearity of shell deformation at the subcritical stage, reinforcement discreteness, and heterogeneity on shell stability is determined.     

Transversal oscillations of a fluid in a long cylindrical container with membrane or elastic plate on the free surface

We propose approximate solutions of two-dimensional hydroelastic problems that describe free oscillations of an ideal fluid in a horizontal long cylindrical container with arbitrary symmetric cross section. The free surface of the fluid is covered by a plane membrane or an elastic plate. Using specific examples, we analyze the obtained solutions and the results of computation of frequencies and forms of oscillations of the mechanical system under consideration.     

Stress Analysis of Orthotropic Noncircular Cylindrical Shells of Variable Thickness in a Refined Formulation

An approach is developed to solve stress–strain problems in a refined formulation for orthotropic cylindrical shells of variable thickness and noncircular cross section. It is shown, as an example, how the distributions of deflections and stresses depend on changes in the shell thickness at constant weight     

The null-field approach and the propagation of elastic surface waves along cylindrical cavities

The existence of surface wave modes, propagating along an infinite cylindrical cavity of general, constant cross section is demonstrated for two non-elliptic geometries. The method used is the null-field approach with global expansions of the surface displacement. The use of Fourier expansions for the surface fields is carefully investigated. Numerical results are presented for the phase velocities and the surface displacements.     

Response of Wood Bars to Non-Destructive Impact

Experimental Techniques - The wood bars with rectangular cross section (25 × 25 mm, 300 mm in length) were impacted by an aluminum cylindrical bar in R and T...     

Transmission and reflection of acoustic waves by an obstacle in a waveguide

By an extension of the null field approach introduced by Waterman the transmission and reflection of acoustic waves by an obstacle in a waveguide are considered. The waveguide is assumed to have a constant cross section but otherwise the geometry is left arbitrary. The scattered field is obtained as a complicated mode sum containing the transition matrix of the obstacle, the reflection matrix of the waveguide wall and the transformation relations between the cylindrical and spherical basis functions. For a circular cross section of the waveguide relatively explicit expressions are given for the transmission and reflection coefficients, and numerical results are shown for spherical and spheroidal obstacles in rotationally symmetric configurations. Several natural extensions of the present results are finally recognized.     

Effect of a precompressed spring on the discontinuity zone around a cylindrical cavity

This paper discusses the use of a cylindrical spring to increase the stability of a tunnel of circular cross section. __________ Translated from Prikladnaya Mekhanika i Tekhnicheskaya Fizika, Vol. 46, No. 3, pp. 141–148, May–June, 2005.     

Analysis of Stresses and Displacements in Orthotropic Noncircular Cylindrical Shells Under Centrifugal Loads

This paper addresses the class of stress–strain problems for thin orthotropic cylindrical shells of arbitrary cross section under centrifugal loads. Separating out the variables for a simply supported shell yields a system of ordinary differential equations for which the boundary-value problem is solved by a stable numerical method. Study is made of the distribution of displacements in shells of elliptical cross section versus the ratio of ellipse exes and the eccentricity of the axis of revolution relative to the geometrical axis of symmetry     

The influence of cooling rates on the distribution of the structure and phases in hardened cylindrical elements

Summary The paper presents an analysis of the temperature field and phase transformation kinetics for cylindrical steel elements with arbitrary shaped cross sections. The influence of different cooling rates as well as different time intervals to achieve the half of the full austenite into pearlite transformation τ_0.5 and weight fractions of pearlite and martensite are taken into account. The analysis is based on Lomakin's theory [2, 3, 4] and its modification [5] as well as the laws of phase transformation kinetics of [9]. The elaborated program of numerical calculations refers to steel grades characterized by C-shaped T-T-T curves and with carbon content close to that of an eutectoidal steel. The analysis is made for a two-dimensional region. As an example, a spline shaft with arbitrary shaped cross section is investigated. It is assumed that the heat exchange occurs on the boundary of the cross section alone. The solution of the problem is based on the variational difference method, being a combination of the finite element method and the finite difference method. Accepted for publication 6 August 1996     

Direct numerical simulation of the turbulent flow in a pipe with annular cross section

The turbulent flow in a pipe of annular cross section is studied for the first time through a direct numerical simulation (DNS) using the Navier–Stokes equations written in cylindrical coordinates. To this aim a novel numerical method is developed, which extends to the cylindrical coordinate system an existing, efficient method designed for cartesian coordinates, and allows us to eliminate the pressure and formulate the problem in two scalar unknowns. The unnecessary increase of resolution at smaller radius typically brought about by polar coordinates, with its consequent stability limitations, is avoided by changing the number of azimuthal Fourier modes with the radial coordinate itself. In addition, the azimuthal extension of the computational domain is reduced, for the cases with lowest curvature, by considering only a part of the annulus, without loss of physical significance of the results. A computer code based on this method is run on a desktop PC for the simulation (with up to 16 million degrees of freedom) of the turbulent flow in a pipe with annular cross section, in a range of relatively low curvatures. This investigation highlights that curvature effects are already evident, even on first order turbulence statistics like the mean axial velocity distribution, in a low-curvature range where it is commonly believed that the flow should be hardly distinguishable from the flow over a plane surface.     

Experimental study of the effect of vertical vibrations on convection in a horizontal cylindrical layer

An experimental study is made of the effect of vertical vibrations on convection in a cylindrical layer formed by two horizontal coaxial cylinders of circular cross section at different temperatures.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 6, pp. 180–183, November–December, 1985.