scholarly journals Effects of Elastic Foundation on the Vibration of Laminated Non-Homogeneous Orthotropic Circular Cylindrical Shells

2004 ◽  
Vol 11 (2) ◽  
pp. 89-101 ◽  
Author(s):  
A.H. Sofiyev ◽  
S.N. Keskin ◽  
Ali H. Sofiyev
Keyword(s):  
Elastic Foundation ◽  
Analytical Procedure ◽  
Linear Time ◽  
Cylindrical Shells ◽  
Finite Deformations ◽  
Displacement Amplitude ◽  
Time Dependent ◽  
Thickness Direction ◽  
Young’S Moduli ◽  
Circular Cylindrical Shells

In this paper an analytical procedure is given to study the free vibration characteristics of laminated non-homogeneous orthotropic thin circular cylindrical shells resting on elastic foundation, accounting for Karman type geometric non-linearity. At first, the basic relations and modified Donnell type stability equations, considering finite deformations, have been obtained for laminated thin orthotropic circular cylindrical shells, the Young's moduli of which varies piecewise continuously in the thickness direction. Applying Galerkin method to the latter equations, a non-linear time dependent differential equation is obtained for the displacement amplitude. The frequency is obtained from this equation as a function of the shell displacement amplitude. Finally, the effect of elastic foundation, non-linearity, non-homogeneity, the number and ordering of layers on the frequency is found for different mode numbers. These results are given in the form of tables and figures. The present analysis is validated by comparing results with those in the literature.

scholarly journals An analytical approach to analyze nonlinear dynamic response of eccentrically stiffened functionally graded circular cylindrical shells subjected to time dependent axial compression and external pressure. Part 1: Governing equations establishment

2014 ◽  
Vol 36 (3) ◽  
pp. 201-214
Author(s):  
Dao Van Dung ◽  
Vu Hoai Nam
Keyword(s):  
Axial Compression ◽  
Nonlinear Dynamic ◽  
Analytical Approach ◽  
Cylindrical Shells ◽  
Geometrical Nonlinearity ◽  
External Pressure ◽  
Functionally Graded ◽  
Time Dependent ◽  
Nonlinear Buckling ◽  
Circular Cylindrical Shells

Based on the classical thin shell theory with the geometrical nonlinearity in von Karman-Donnell sense, the smeared stiffener technique and Galerkin method, this paper deals with the nonlinear dynamic problem of eccentrically stiffened functionally graded circular cylindrical shells subjected to time dependent axial compression and external pressure by analytical approach. The present novelty is that an approximate three-term solution of deflection taking into account the nonlinear buckling shape is chosen, the nonlinear dynamic second-order differential three equations system is established and the frequency-amplitude relation of nonlinear vibration is obtained in explicit form.

Creep Buckling of Thin-Walled Circular Cylindrical Shells Subject to Radial Pressure and Thermal Gradients

1971 ◽  
Vol 38 (1) ◽  
pp. 209-216 ◽  
Author(s):  
Y. S. Pan
Keyword(s):  
Circular Cylindrical Shell ◽  
Cylindrical Shells ◽  
Radial Pressure ◽  
Temperature Gradients ◽  
Time Dependent ◽  
Thermal Gradients ◽  
Numerical Examples ◽  
Circular Cylindrical Shells ◽  
Thin Walled ◽  
Inelastic Strains

A method of calculating the creep deflections and predicting the creep collapse of a thin-walled circular cylindrical shell, subject to uniform external radial pressure and arbitrary temperature gradients, is shown. This method may also be applied to investigate the behavior of a shell subject to time-dependent temperature gradients and deformations due to other inelastic causes. The set of simultaneous differential equations of equilibrium in terms of creep, thermal, and other inelastic strains is presented. Applications of this method to long cylindrical shells are illustrated by two numerical examples.

Nonlinear Static and Dynamic Thermal Buckling Analysis of Spiral Stiffened Functionally Graded Cylindrical Shells with Elastic Foundation

2019 ◽  
Vol 11 (01) ◽  
pp. 1950005 ◽  
Author(s):  
Alireza Shaterzadeh ◽  
Kamran Foroutan ◽  
Habib Ahmadi
Keyword(s):  
Elastic Foundation ◽  
Plate Theory ◽  
Cylindrical Shells ◽  
Thermal Buckling ◽  
Buckling Analysis ◽  
Functionally Graded ◽  
Thickness Direction ◽  
Classical Plate Theory ◽  
Linear Temperature ◽  
Nonlinear Static

In this paper, an analytical method is used to study the nonlinear static and dynamic thermal buckling analysis of imperfect spiral stiffened functionally graded (SSFG) cylindrical shells. The SSFG cylindrical shell is surrounded by a linear and nonlinear elastic foundation. The proposed linear model is based on the two-parameter elastic foundation (Winkler and Pasternak). A three-parameter elastic foundation with hardening/softening cubic nonlinearity is used for nonlinear model. The material properties are temperature dependent and assumed to be continuously graded in the thickness direction. Also, for thermal buckling analysis, the uniform and linear temperature distribution in thickness direction is considered. The SSFG cylindrical shells are considered with various angles for spiral stiffeners. The strain–displacement relations are obtained based on the von Kármán nonlinear equations and the classical plate theory of shells. The smeared stiffener technique and the Galerkin method are applied to solve the nonlinear problem. In order to find the nonlinear dynamic thermal buckling responses, the fourth-order Runge–Kutta method is used. To validate the results, comparisons are made with those available in literature and good agreements are shown. The effects of various geometrical and material parameters are investigated on the nonlinear static and dynamic thermal buckling response of SSFG cylindrical shells.

scholarly journals An analytical approach to analyze nonlinear dynamic response of eccentrically stiffened functionally graded circular cylindrical shells subjected to time dependent axial compression and external pressure. Part 2: Numerical results and discussion

2014 ◽  
Vol 36 (4) ◽  
pp. 255-265 ◽  
Author(s):  
Dao Van Dung ◽  
Vu Hoai Nam
Keyword(s):  
Axial Compression ◽  
Nonlinear Dynamic ◽  
Cylindrical Shells ◽  
Geometrical Nonlinearity ◽  
External Pressure ◽  
Dynamic Buckling ◽  
Functionally Graded ◽  
Numerical Results ◽  
Time Dependent ◽  
Circular Cylindrical Shells

Based on the classical thin shell theory with the geometrical nonlinearity in von Karman-Donnell sense, the smeared stiffener technique, Galerkin method and an approximate three-term solution of deflection taking into account the nonlinear buckling shape is chosen, the governing nonlinear dynamic equations of eccentrically stiffened functionally graded circular cylindrical shells subjected to time dependent axial compression and external pressure is established in part 1. In this study, the nonlinear dynamic responses are obtained by fourth order Runge-Kutta method and the nonlinear dynamic buckling behavior of stiffened functionally graded shells under linear-time loading is determined by according to Budiansky-Roth criterion. Numerical results are investigated to reveal effects of stiffener, input factors on the vibration and nonlinear dynamic buckling loads of stiffened functionally graded circular cylindrical shells.

On the Buckling of Rings Subject to Impulsive Pressures

1965 ◽  
Vol 32 (3) ◽  
pp. 511-518 ◽  
Author(s):  
W. Stuiver
Keyword(s):  
Experimental Data ◽  
Plastic Flow ◽  
Analytical Procedure ◽  
Cylindrical Shells ◽  
Elastic Instability ◽  
Circular Cylindrical Shells ◽  
Single Approach

It is shown in this paper that previous, independent analyses of the phenomena of dynamic elastic instability and dynamic plastic-flow buckling of circular cylindrical shells can be combined in a single approach leading to results consistent with those that follow from these analyses. The response of the shell in both cases is governed by the interaction between the fundamental radial, purely extensional mode of deformation and inextensional flexural modes always present in the response. An analytical procedure is given for the determination of dominant modes in the elastic and plastic phases of the response, and the results of this procedure are verified by comparison with numerical and experimental data.

scholarly journals Nonlinear static and dynamic buckling of eccentrically stiffened functionally graded cylindrical shells under axial compression surrounded by an elastic foundation

2014 ◽  
Vol 36 (1) ◽  
pp. 27-47 ◽  
Author(s):  
Vu Hoai Nam ◽  
Nguyen Thi Phuong ◽  
Dao Huy Bich ◽  
Dao Van Dung
Keyword(s):  
Elastic Foundation ◽  
Axial Compression ◽  
Nonlinear Dynamic ◽  
Linear Time ◽  
Cylindrical Shells ◽  
Geometrical Nonlinearity ◽  
Functionally Graded ◽  
Buckling Load ◽  
Dynamic Responses ◽  
Nonlinear Buckling

This paper presents an analytical approach to investigate the nonlinear buckling of imperfect eccentrically stiffened functionally graded thin circular cylindrical shells subjected to axial compression and surrounded by an elastic foundation. Based on the classical thin shell theory with the geometrical nonlinearity in von Karman-Donnell sense, initial geometrical imperfection, the smeared stiffeners technique and Pasternak’s two-parameter elastic foundation, the governing equations of eccentrically stiffened functionally graded cylindrical shells are derived. The functionally graded cylindrical shells are reinforced by homogeneous ring and stringer stiffener system on internal and (or) external surface. The resulting equations are solved by the Galerkin method to obtain the explicit expression of static critical buckling load, post-buckling load-deflection curve and nonlinear dynamic motion equation. The nonlinear dynamic responses are found by using fourth order Runge-Kutta method. The dynamic critical buckling loads of shells are considered for step loading of infinite duration and linear-time compression. The obtained results show the effects of foundation, stiffeners and input factors on the nonlinear buckling behavior of these structures. 

Prediction of natural frequencies for thin circular cylindrical shells

2000 ◽  
Vol 214 (10) ◽  
pp. 1313-1328 ◽  
Author(s):  
M N Naeem ◽  
C B Sharma
Keyword(s):  
Variational Approach ◽  
Analytical Procedure ◽  
Natural Frequencies ◽  
Cylindrical Shells ◽  
Polynomial Functions ◽  
Simply Supported ◽  
Analytical Results ◽  
General Eigenvalue Problem ◽  
Circular Cylindrical Shells ◽  
Good Agreement

In this paper an analytical procedure is given to study the free-vibration characteristics of thin circular cylindrical shells. Ritz polynomial functions are assumed to model the axial modal dependence and the Rayleigh-Ritz variational approach is employed to formulate the general eigenvalue problem. Influence of some commonly used boundary conditions, viz. simply supported-simply supported, clamped-clamped and clamped-free, and also the effects of variations of shell parameters on the vibration frequencies are examined. Natural frequencies for a number of particular cases are evaluated and compared with some available experimental and other analytical results in the literature on this topic. These results are given in the form of tables and figures. A very good agreement between the results of the present analysis and the corresponding experimental and analytical results available in the literature is obtained to confirm the validity and accuracy as well as the efficiency of the method.

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