Cylindrical Shells Of Variable Thickness Research Articles

Free Vibration Analysis of a Cylindrical Shell of Variable Thickness Partially Filled with Fluid

Free Vibration Analysis of a Cylindrical Shell of Variable Thickness Partially Filled with Fluid

DYNAMIC PROBLEM OF AXISYMMETRIC OSCILLATIONS OF CYLINDRICAL SHELLS OF VARIABLE THICKNESS UNDER THE ACTION NON – STATIONARY LOAD

Analyzing the publications in which the dynamic problems of cylindrical shells of non-uniform thickness under the action of various types of loading are considered, a conclusion can be drawn. that there are practically no works devoted to the dynamic behavior of heterogeneous cylindrical shells under non-stationary loads. In this work, the formulation of the dynamic problem of axisymmetric oscillations of a cylindrical shell of variable thickness under the action of non-stationary loading and the algorithm for solving the given problem are considered. In particular, the resulting system of differential equations is based on the theory of Tymoshenko-type shells, while constructing a numerical algorithm, the integro-interpolation method of constructing finite-difference schemes for spatial coordinates is used using Richardson approximations and an explicit difference scheme for time. An example of calculating the dynamic behavior of a variable thickness under non-stationary loading is considered and an analysis of numerous results is given.

Приближённые уравнения колебаний цилиндрических оболочек переменной толщины

Приближённые уравнения колебаний цилиндрических оболочек переменной толщины

Free Vibrations of Nonthin Elliptic Cylindrical Shells of Variable Thickness

The problem of the free vibrations of nonthin elliptic cylindrical shells of variable thickness under various boundary conditions is solved using the refined Timoshenko–Mindlin theory. To solve the problem, an effective numerical approach based on the spline-approximation and discrete-orthogonalization methods is used. The effect of the cross-sectional shape, thickness variation law, material properties, and boundary conditions on the natural frequency spectrum of the shells is analyzed.

Analytical-Numerical Solution of Static Problems for Noncircular Cylindrical Shells of Variable Thickness

An analytical-numerical method of solving boundary-value static problems for transversally isotropic infinitely long noncircular cylindrical shells of variable thickness is formulated and developed. The system of basic equations is derived using the relations of the refined theory of deep shells with low shear stiffness. Expressions for internal power factors and generalized displacements of closed and open cylindrical shells with arbitrary cross-section acted upon by surface and linear forces are presented. The integrals appearing in these expressions are calculated with the method of trapezoids. The numerical results for a closed shell of elliptic cross-section under uniform internal pressure presented in the form of tables and plots are analyzed

Holographic Interferometry Study of the Free Vibrations of Cylindrical Shells of Constant and Variable Thickness

A holographic interferometry technique is used to determine the natural frequencies of isotropic circular cylindrical shells of constant and variable thickness and equivalent mass. It is established that the resonant frequencies of the cylindrical shell of variable thickness exceed those of the cylindrical shell of constant thickness of the same mass if circumferential halfwaves are few

Stability of a cylindrical shell of variable thickness depending on the nonuniform radial load

Based on the Vlasov semi-momentless theory, a problem of stability of a cylindrical isotropic shell, variable along the thickness generatrix, under the effect of an axially symmetric radial pressure varying along the shell axis is considered. At one ratio of thickness and pressure, an exact solution for finding one of the variables in the pressure variation law, at which the shell loses the stability, is found.

On the investigation of free vibrations of nonthin cylindrical shells of variable thickness by the spline-collocation method

For determining the dynamic characteristics of free vibrations of circular unclosed cylindrical shells of variable thickness in two coordinate directions, we have used the spline-collocation method together with the method of discrete orthogonalization. The problem has been solved within the framework of the refined Timoshenko–Mindlin theory. We have also investigated the influence of different laws of change in the shell thickness on the character of its natural vibrations. Our calculations have been carried out for different geometrical and elastic parameters of the shell under study and different boundary conditions.

Influence of the boundary conditions on the stress state of a flexible cylindrical shell of variable stiffness in a magnetic field

The effect of the boundary conditions on the stress state of a circular cylindrical shell of variable thickness (stiffness) is analyzed using a geometrically nonlinear problem statement. The cylindrical shell is subject to a magnetic field, external electric current, and nonstationary mechanical load. Numerical results are presented and analyzed

Free vibration of symmetric angle-ply laminated cylindrical shells of variable thickness including shear deformation theory

Free vibrational study of symmetric angle-ply laminated cylindrical shells of variable thickness including first order shear deformation theory using spline function approximation is studied. The equations of motion for the cylindrical shells are derived using first order shear deformation theory. The solutions of displacement functions are assumed in a separable form to obtain a system of coupled differential equations in terms of displacement and rotational functions, and these functions are approximated by Bickley-type splines of order three. The vibrations of three and five layered shells, made up of two different types of order of the layers of materials and two types of boundary conditions are considered. A generalized eigenvalue problem is obtained and solved numerically for an eigenfrequency parameter and an associated eigenvector of spline coefficients. Parametric studies are made for the frequency parameters with respect to the coefficients of thickness variations, length-to-radius ratio, length-to-thickness ratio and ply angles under different boundary conditions. In the present work, the results are expected to be more accurate and more suitable for immediate application in the areas of missiles, aviation, shipping, surface transport and a large number of industries related to the cement and chemicals.

Free vibration of symmetric angle-ply laminated cylindrical shells of variable thickness

In this paper, free vibrations of symmetric angle-ply laminated cylindrical shells are presented under different thickness variations. The thickness variations of the shells are linear, exponential, and sinusoidal. Spline function techniques are adopted to approximate the displacement functions, and the point collocation method is used to obtain the generalized eigenvalue problem with appropriate boundary conditions. The effects of the geometric parameters, thickness parameters, and material parameters on the frequencies of symmetric angle-ply laminated cylindrical shells with two kinds of material properties under different boundary conditions are analyzed.

On one approach to studying free vibrations of cylindrical shells of variable thickness in the circumferential direction within a refined statement

We used the spline collocation method for finding the frequencies of free vibrations of circular closed cylindrical shells of variable thickness in the circumferential direction. The problem was formulated within the framework of Mindlin’s refined theory. We studied the influence of change in the shell thickness on the distribution of its natural frequencies. Our calculations were carried out for different geometrical parameters of the shell and different boundary conditions. The validity of results obtained was verified by increasing the number of collocation points in our calculations and by comparing them with the results of computations according to the three-dimensional theory.

Free Vibration of Layered Circular Cylindrical Shells of Variable Thickness Using Spline Function Approximation

Free vibration of layered circular cylindrical shells of variable thickness is studied using spline function approximation by applying a point collocation method. The shell is made up of uniform layers of isotropic or specially orthotropic materials. The equations of motions in longitudinal, circumferential and transverse displacement components, are derived using extension of Love's first approximation theory. The coupled differential equations are solved using Bickley-type splines of suitable order, which are cubic and quintic, by applying the point collocation method. This results in the generalized eigenvalue problem by combining the suitable boundary conditions. The effect of frequency parameters and the corresponding mode shapes of vibration are studied with different thickness variation coefficients, and other parameters. The thickness variations are assumed to be linear, exponential, and sinusoidal along the axial direction. The results are given graphically and comparisons are made with those results obtained using finite element method.

Buckling of Imperfect, Axisymmetric, Homogeneous Shells of Variable Thickness: Perturbation Solution

This paper presents the first of a series of solutions to the buckling of imperfect cylindrical shells subjected to an axial compressive load. The initial problem is the case of a homogeneous cylindrical shell of variable thickness that is of an axisymmetric nature. The equilibrium equations as first introduced by Donnell over 70 years ago are thoroughly presented as basis for a solution employing perturbation methods. The ultimate objective of these calculations is to achieve a quantitative assessment of the critical buckling load considering the small axisymmetric deviations from the nominal shell wall thickness. Clearly in practice, large diameter thin wall shells of revolution that form stacks (as found in flue gas desulphurization absorber assemblies) are never fabricated with constant diameters and thicknesses over the entire length of the assembly. As such, ASME Boiler and Pressure Vessel Code Section VIII shell thickness tolerances as supplemented by ASME Code Case 2286-1 are reviewed and addressed in comparison to the resulting solutions with respect to the critical buckling loads. The method and results described herein are in stark contrast to the “knockdown factor” approach currently utilized in ASME Code Case 2286-1. Recommendations for further study of the imperfect cylindrical shell are also outlined in an effort to improve on the current rules regarding column buckling of large diameter shells designed in accordance with ASME Section VIII, Divisions 1 and 2 and ASME STS-1 in combination with the suggestions contained within Code Case 2286-1.

On stability of cylindrical shells of variable thickness with initial imperfections

The paper outlines a numerical method for stability analysis of cylindrical shells with initial imperfections. We solve a nonlinear buckling problem for a cylindrical shell with variable wall thickness under surface pressure. The imperfections of the shell are modeled as the first buckling mode. A probabilistic approach is used to determine the reliability against buckling of the cylindrical shell with the probability density of initial imperfections represented by uniform distribution, triangular distribution, or Gaussian distribution

Axisymmetric vibrations of layered cylindrical shells of variable thickness using spline function approximation

Free axisymmetric vibrations of layered cylindrical shells of variable thickness are studied using spline function approximation techniques. Three different types of thickness variations are considered namely linear, exponential and sinusoidal. The equations of axisymmetric motion of layered cylindrical shells, on the longitudinal and transverse displacement components are obtained using Love?s first approximation theory. A system of coupled differential equations on displacement functions are obtained by assuming the displacements in a separable form. Then the displacements are approximated using Bickley-spline approximation. The vibrations of two-layered cylindrical shells, made up of several types of layered materials and different boundary conditions are considered. Parametric studies have been made on the variation of frequency parameter with respect to the relative layer thickness, length ratio and type of thickness variation parameter.

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

Application of Discrete Fourier Series in the Stress Analysis of Cylindrical Shells of Variable Thickness with Arbitrary End Conditions

An approach is proposed to solve boundary-value stress—strain problems for cylindrical shells with thickness varying in two coordinate directions. The approach employs discrete Fourier series to separate circumferential variables. This makes it possible to reduce the problem to a one-dimensional one, which can be solved by the stable discrete-orthogonalization method. Examples are given

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

Solution of the problem of the stress state of noncircular cylindrical shells of variable thickness

A procedure is proposed for solving two-dimensional boundary-value problems on the stress-strain state of open and closed noncircular cylindrical shells of variable thickness under surface loads. The solution is based on the use of the spline-collocation method along the directrix and the method of discrete othogonalization along the generatrix. Examples of solutions for ellipsoidal shells of variable thickness are given.