Hollow Cylinder Of Finite Length Research Articles

Solution of an axisymmetric problem of free vibrations of piezoceramic hollow cylinders of finite length by the spline collocation method

An axisymmetric problem of longitudinal free vibrations of piezoceramic hollow cylinders for some types of boundary conditions on the end faces is considered. The lateral surfaces of the cylinder are covered with thin short-circuited electrodes. The polarization of piezoceramics is directed along the axis of the cylinder. Using the method of separation of variables and method of spline collocation along the length of the cylinder, we reduce the problem to a system of ordinary differential equations, which is solved by the method of step-by-step search. We present results of calculations for a PZT 4 piezoceramic cylinder.

Interaction of a hollow cylinder of finite length and a plate with a cylindrical cavity with a rigid insert

Two problems of the interaction of a hollow circular cylinder with load-free ends and an unbounded plate with a cylindrical cavity and a symmetrically imbedded rigid insert are considered. Homogeneous solutions are found and the generalized orthogonality of these solutions is used when the modified boundary conditions are satisfied. As a result, we have a system of two integral equations in functions of the displacements of the outer and inner surfaces of the hollow cylinder. These functions are sought in the form of sums of a trigonometric series and a power function with a root singularity. The ill-posed infinite systems of linear algebraic equations obtained are regularized by the introduction of small positive parameters. Since the elements of the matrices of the systems as well as the contact stresses are defined by poorly converging numerical and functional series, an efficient method for calculating of the remainders of the above-mentioned series is developed. Formulae are found for the contact pressure distribution function and the integral characteristic. Examples of the calculation of the interaction of the cylinder and the plate with an insert are given. The method of solving contact problems described here has been used earlier 1,2 and the generalized orthogonality of the solutions found for bodies of finite dimensions, that is, for a rectangle and cylinders of finite length, is its basis. Problems for hollow cylinders with a band 2 and an insert reduce to a system of two integral equations, and the problem for a rectangle 1 reduces to one integral equation. Solving these integral equations, ill-posed systems of linear algebraic equations are obtained which are subject to regularization 3 .

Screening attenuation of conducting and ferromagnetic hollow cylinders of finite length

The shielding effectiveness of thin-walled hollow cylinders of finite length in a homogeneous magnetic field with arbitrary direction is determined analytically. Both cylinders with finite conductivity and superconducting as well as ferromagnetic cylinders are examined for this purpose. As a result, the screening attenuation on the axis of a superconducting cylinder in a longitudinal magnetic field turned out to be identical with the screening attenuation on the axis of a ferromagnetic cylinder with a transverse magnetic field. We show how to determine the corresponding values along the cylinder axis on the basis of the shielding in the cylinder center by way of simple approximations. To illustrate the analysis, the lines of magnetic flux for longitudinal field incidence, the equipotential lines for transversal field incidence and the lines of induced eddy currents for the case of a conducting cylinder are shown.

Hollow Cylinder Microwave Model for Stems

Present electromagnetic models represent crop stems as full homogeneous cylinders. However, several ground measurements indicate that mature stems are hollow. In this paper, a model is presented which describes stems as hollow dielectric cylinders. The field on the surface of a hollow infinite cylinder is found at first, then applying the equivalence theorem, the scattered field from a hollow cylinder offinite length and any radius is obtained, and it is applied to the typical dimensions and permittivities ofwheat stems. The effects ofstem hollowness on microwave attenuation are investigated for a case study. Then, the extinction and bistatic scattering cross sections ofthe cylinder are included in the model developed at Tor Vergata University in order to study the effects ofstem hollowness on crop backscattering.

Numerical Analysis of Stationary Dynamic Processes in Anisotropic Inhomogeneous Cylinders

Efficient numerical-analytical approaches are proposed for analyzing stationary dynamic processes. The approaches are used to study the propagation of elastic waves in anisotropic inhomogeneous cylinders with circular and noncircular cross sections and the natural vibrations of anisotropic solid and hollow cylinders of finite length with different end conditions. The dependence of the dynamic characteristics of cylinders on their geometrical and mechanical parameters is analyzed

Investigation of the asymmetric stressed-strained state of transversely isotropic cylinders under different boundary conditions at the ends

Since solving problems of the stressed-strained state of elastic bodies in an exact three-dimensional poses considerable mathematical and computational difficulties, only for a small number of problems have the results of the solution been put in numerical form [8, 10, 15, 16, 18]. The stressed-strained state of three-dimensional bodies must be known in order to evaluate the strength capabilities of structural elements, both as a reference for models of applied theories of shells and as solutions obtained by approximate methods. In this article we consider the class of problems of the stressed-strained state of transversely isotropic hollow cylinders of finite length under asymmetric loads applied to the lateral surfaces and with different boundary conditions at the ends. The solution of that class of problems is constructed on the basis of separation of variables in the circumferential coordinate and solution of the two-dimensional boundary-value problem by the spline-collocation and discrete orthogonalization methods [4, 5, 6, 12, 13]. This approach was used earlier [1, 2, 7, 11] to solve two-dimensional problems of the theory of shells in different formulations. The influence of boundary conditions on the displacement and stress distribution in cylinders is analyzed on the basis of the results obtained. We consider transversely isotropic hollow cylinders in which the plane of isotropy coincides with the tangent to the cylindrical surface and the mechanical characteristics vary only along the normal to it. Asymmetrically distributed loads are applied to the lateral surfaces of the cylinder and boundary conditions are given at the ends. The problem is described on the basis of the three-dimensional theory of elasticity in a cylindrical coordinate system

Wave propagation in anisotropic laminated hollow cylinders of infinite extent

This paper deals with a three-dimensional elasticity investigation of wave propagation in an infinitely long hollow cylinder whose homogeneous or layered structure is made by generally orthotropic or monoclinic materials. The analysis is based on a recursive formulation of a successive approximation method employed elsewhere by the authors for the study of axisymmetric and flexural vibrations of homogeneous orthotropic and cross-ply laminated hollow cylinders of finite length. The method has further been applied in connection with static and thermoelastic analyses of orthotropic homogeneous and cross-ply laminated cylinders and cylindrical panels. In all cases considered, results of this approach converge very rapidly toward corresponding exact three-dimensional elasticity results. Hence the present study is based on essentially exact three-dimensional elasticity results and is further expected to serve as a benchmark for corresponding future investigations based on finite element and/or two-dimensional shell theory formulations.

Dissipative heating of a viscoelastic piezoceramic hollow cylinder of finite length under harmonic electrical excitation

Dissipative heating of a viscoelastic piezoceramic hollow cylinder of finite length under harmonic electrical excitation

AXISYMMETRIC THERMAL STRESSES IN AN ANISOTROPIC FINITE HOLLOW CYLINDER

Abstract The problems of linear thermoelasticity in a transversely isotropic hollow cylinder of finite length are solved by a direct power series approximation through the application of the Lanczos-Chebyshev method. Coefficients in the “economized” series are determined by collocation at selected Chebyshev points. Formulations are given to show that the same approach can be applied to all linear types of boundary conditions. A numerical example has been used for comparison with pubished solutions from a potential function approach, and with “long cylinder” solutions. The magnitude of end effects has been shown.

The gravitational field inside a long hollow cylinder of finite length

The gravitational force inside a finite hollow cylinder has been calculated for the Newtonian potential and for a non-Newtonian potential, and the results of the experiments of Spero et at . (1980) and Long (1976) have been reinterpreted in terms of limits on departures from the Newtonian potential.

The method of lines applied to crack problems including plasticity effect

To seek stress and strain distributions in flawed structures, the governing equations in elasto-plasticity are first derived in terms of displacement increments. The method of lines is then applied to derive the sets of ordinary differential equations with appropriate boundary conditions. Their solutions are sought along continuous lines of a discretized region. They are solved by a combination of power series and modal matrix method. A step by step integration is devised to determine the displacements at nodal points. Non-linear work-hardening is taken care of by the effective stress and strain approach. The cases of uncracked and cracked hollow cylinders of finite length under axisymmetrical loadings are studied in detail. The growth of plastic zone, crack-opening displacement and J-integral along various paths are illustrated.

Static bow of shafts due to rubbing

When rotating shafts contact stationary components, part of the heat liberated due to friction enters the shaft and causes bow, if the distribution of the heat is not uniform. This situation is very common in turborotors rubbing against the steam packings and seals. In this paper, the shaft is modeled as a hollow cylinder of finite length. Uniform heat convection on both surfaces was assumed with arbitrary distribution of the frictional heat. The transient heat conduction equation was used in conjunction with Goodiers formula for the thermoelastic bow. The bow was calculated in closed form in terms of two parameters which were tabulated for a variety of boundary conditions.

Solution to the problem of transient asymmetric heat conduction in a two-layer hollow cylinder of finite length

The problem is solved by the method of finite integral transformations with asymmetric initial and boundary conditions, when heat is generated.

On the State of Plastic Equilibrium of a Rotating Hollow Cylinder of Finite Length

An approximate solution for the stress distribution in a hollow, rotating cylinder of finite length, made of a rigid-perfectly plastic material, in a state of plastic equilibrium is presented. It i...

Temperature stresses in an inhomogeneous cylinder of finite length

An analytic method of determining the temperature stresses in circular cylinders is described. In the solution of the problem, based on a collocation method, together with the finite length of the cylinder its arbitrary inhomogeneity is also taken into account. In a particular case this may be caused by the effect of temperature on the mechanical constants of the material, which is especially typical of polymers at negative temperatures. The results of a calculation of the stresses in a hollow cylinder of finite length with a variable modulus of elasticity are presented as an example.

Comment on 'torsional oscillation of an encased hollow cylinder of finite length'

Covers advancements in spacecraft and tactical and strategic missile systems, including subsystem design and application, mission design and analysis, materials and structures, developments in space sciences, space processing and manufacturing, space operations, and applications of space technologies to other fields.

Approximate solution of the finite cylinder problem using Legendre polynomials

Governing equations of elasticity for small deformations of a hollow cylinder of finite length are examined to define suitable approximate theories. Each dependent variable in the problem is represented as a series expansion in Legendre polynomials in the radial coordinate; such representations permit the field equations to be exactly reduced to two-dimensional sets of equations by separation of variables. Attention is directed toward establishment of a logical approach to truncation of the series; important variables for approximate theories of any order are established by consideration of the strain energy expression, and a truncation scheme is postulated. To establish the validity of the truncation scheme and hence of the resulting approximate theories, the problem of an infinitely long thick cylinder under axisymmetric band loading is considered. Comparisons with exact solutions and with well-known shell theories are obtained; results indicate that the new approximate theories yield predictions in better agreement with exact solutions than previous efforts in this area.

An exact solution to the elastic deformation of a finite length hollow cylinder

An exact elastic analysis is presented for the deformation of a finite length hollow cylinder subjected to thermal and mechanical loads. The solution presented satisfies the surface and end boundary conditions identically. A comparison of the present solution with the classical solution shows that the latter is exact for a certain class of materials.

Axisymmetric problem of thermoelasticity for a hollow cylinder of finite length

The axisymmetric problem of heat conduction is examined for a hollow cylinder of finite length with mixed boundary conditions; a solution is given for the corresponding quasi-static problem of thermoelasticity.

Torsional oscillations of an encased hollow cylinder of finite length.

Covers advancements in spacecraft and tactical and strategic missile systems, including subsystem design and application, mission design and analysis, materials and structures, developments in space sciences, space processing and manufacturing, space operations, and applications of space technologies to other fields.