Forced Motions of Elastic Cylindrical Shells

1975 ◽  
Vol 42 (2) ◽  
pp. 321-325 ◽  
Author(s):  
C. C. Huang
Keyword(s):  
Boundary Value Problem ◽  
Shell Theory ◽  
Initial Conditions ◽  
Formal Solution ◽  
Cylindrical Shells ◽  
Time Dependent ◽  
Axially Symmetric ◽  
Symmetric Motion ◽  
Simply Supported ◽  
Acceleration Method

A formal solution is presented for the dynamic boundary-value problem of the axially symmetric motion of finite, Timoshenko-type, isotropic, linearly elastic, cylindrical shells with time-dependent boundary conditions of any admissible combination, acted upon by time-dependent surface tractions with specified arbitrary initial conditions, obtained by using Herrmann-Mirsky shell theory and modal acceleration method. The method is applied to a simply supported shell subject to longitudinal tensile step forces at both ends. The transient response is studied in detail and the results predicted by the improved and the classical theories are compared.

Methods of Analysis for Very Thick-Walled Cylindrical Shells

1975 ◽  
Vol 97 (1) ◽  
pp. 175-181 ◽  
Author(s):  
J. R. Vinson
Keyword(s):  
Boundary Conditions ◽  
Wall Thickness ◽  
Shell Theory ◽  
Cylindrical Shells ◽  
Explicit Solutions ◽  
Axially Symmetric ◽  
Various Boundary Conditions ◽  
First Approximation ◽  
Methods Of Analysis ◽  
Elasticity Solutions

Methods of analysis are presented for very thick-walled cylindrical, isotropic shells subjected to axially symmetric lateral and in-plane loads. These methods are developed for shells with ratios of wall thickness to mean radius as large as 0.5, as well as being applicable for thin classical shells which involve Love’s First Approximation. The present methods are elasticity solutions and employ no shell theory assumptions. Explicit solutions are presented for the shell subject to in-plane loads and laterally distributed loads which are constant or varying linearly axially for various boundary conditions at the ends.

Effect of Ring Support Position and Geometrical Dimension on the Free Vibration of Ring-Stiffened Cylindrical Shells

2014 ◽  
Vol 580-583 ◽  
pp. 2879-2882
Author(s):  
Xiao Wan Liu ◽  
Bin Liang
Keyword(s):  
Cylindrical Shell ◽  
Free Vibration ◽  
Shell Theory ◽  
Cylindrical Shells ◽  
Ritz Method ◽  
Geometrical Dimension ◽  
Stiffened Cylindrical Shell ◽  
Simply Supported ◽  
Ring Support ◽  
Stiffened Cylindrical Shells

Effect of ring support position and geometrical dimension on the free vibration of ring-stiffened cylindrical shells is studied in this paper. The study is carried out by using Sanders shell theory. Based on the Rayleigh-Ritz method, the shell eigenvalue governing equation is derived. The present analysis is validated by comparing results with those in the literature. The vibration characteristics are obtained investigating two different boundary conditions with simply supported-simply supported and clamped-free as the examples. Key Words: Ring-stiffened cylindrical shell; Free vibration; Rayleigh-Ritz method.

Unstable Vibration of Simply Supported Thin Cylindrical Shells Subjected to Axial Leakage Flows Using Flu¨gge’s Shell Theory

2004 ◽  
Author(s):  
Katsuhisa Fujita ◽  
Makoto Kato
Keyword(s):  
Shell Theory ◽  
Cylindrical Shells ◽  
Axisymmetric Vibration ◽  
Complex Eigenvalue ◽  
Thin Cylindrical Shell ◽  
Navier Stokes Equation ◽  
Flowing Fluid ◽  
Simply Supported ◽  
Leakage Flows ◽  
Unstable Vibration

The unstable vibration of thin cylindrical shells subjected to axial leakage flows is investigated in this paper. Considering the fluid structure interaction between shells and fluids flowing through a narrow passage, the coupled equation of motion between shells and flowing fluids is derived using the Flu¨gge’s shell theory and the Navier-Stokes equation. Focusing on the vibrational characteristics of a thin cylindrical shell with both simply-supported ends, that are the axisymmetric vibration, the lateral vibration and the circumferential vibration, the unstable phenomenon of thin cylindrical shells are clarified by using the root locus based on the complex eigenvalue analysis. The numerical parameter studies on the shells with both simply-supported ends are performed taking the dimensions of shells, the characteristics of flowing fluids and the clearance of an annular gap as parameters. The influences of these parameters on the threshold of the instability of the coupled vibration between a shell and a flowing fluid are discussed.

Nonlinear Analysis of Transverse Shear Deformable Laminated Composite Cylindrical Shells—Part II: Buckling of Axially Compressed Cross-Ply Circular and Oval Cylinders

1992 ◽  
Vol 114 (1) ◽  
pp. 110-114 ◽  
Author(s):  
K. P. Soldatos
Keyword(s):  
Transverse Shear ◽  
Shell Theory ◽  
Cylindrical Shells ◽  
Laminated Composite ◽  
Companion Paper ◽  
Buckling Loads ◽  
Simply Supported ◽  
Laminated Composite Shells ◽  
Shear Deformable ◽  
Oval Cylindrical Shells

A linearized transverse shear deformable shell theory presented in a companion paper is confined to consideration with the buckling problem of axially compressed, cross-ply laminated noncircular cylindrical shells. Based on a solution of its governing differential equations, obtained for simply supported shells by means of Galerkin’s method, a study of the buckling problem of axially compressed circular and oval cylindrical shells, of a regular antisymmetric cross-ply laminated arrangement, is presented. Moreover, by comparing the numerical results obtained with corresponding results based on a classical Love-type shell theory, the combined influence of both the transverse shear deformation and the shell eccentricity on the buckling loads of such laminated composite shells is examined.

Elasticity Solutions for Laminated Orthotropic Cylindrical Shells Subjected to Localized Longitudinal and Circumferential Moments

2003 ◽  
Vol 125 (1) ◽  
pp. 26-35 ◽  
Author(s):  
K. Bhaskar ◽  
N. Ganapathysaran
Keyword(s):  
Differential Equations ◽  
Ordinary Differential Equations ◽  
Shell Theory ◽  
Cylindrical Shells ◽  
Laminated Composite ◽  
Two Dimensional ◽  
Simply Supported ◽  
Elasticity Solutions ◽  
Laminated Composite Shells ◽  
Taylor’S Series

The purpose of this work is to present baseline elasticity solutions for laminated composite shells subjected to localized moments. For simply supported cross-ply cylindrical shells, the problem reduces to one of coupled ordinary differential equations which are solved in terms of Taylor’s series. Results, in the form of tables and graphs, are presented for the cases of longitudinal and circumferential moments. These results would be very useful for judging the accuracy of approximate two-dimensional shell theories. They are used herein to study the errors of a shell theory based on the classical Love-Kirchhoff hypothesis.

scholarly journals Effect of an oscillating time-dependent pressure gradient on Dean flow: transient solution

2020 ◽  
Vol 9 (1) ◽  
Author(s):  
Basant K. Jha ◽  
Dauda Gambo
Keyword(s):  
Pressure Gradient ◽  
Initial Conditions ◽  
Fluid Velocity ◽  
Outer Cylinder ◽  
Time Dependent ◽  
Navier Stokes ◽  
Dean Flow ◽  
Continuity Equations ◽  
Riemann Sum ◽  
Flow Formation

Abstract Background Navier-Stokes and continuity equations are utilized to simulate fully developed laminar Dean flow with an oscillating time-dependent pressure gradient. These equations are solved analytically with the appropriate boundary and initial conditions in terms of Laplace domain and inverted to time domain using a numerical inversion technique known as Riemann-Sum Approximation (RSA). The flow is assumed to be triggered by the applied circumferential pressure gradient (azimuthal pressure gradient) and the oscillating time-dependent pressure gradient. The influence of the various flow parameters on the flow formation are depicted graphically. Comparisons with previously established result has been made as a limit case when the frequency of the oscillation is taken as 0 (ω = 0). Results It was revealed that maintaining the frequency of oscillation, the velocity and skin frictions can be made increasing functions of time. An increasing frequency of the oscillating time-dependent pressure gradient and relatively a small amount of time is desirable for a decreasing velocity and skin frictions. The fluid vorticity decreases with further distance towards the outer cylinder as time passes. Conclusion Findings confirm that increasing the frequency of oscillation weakens the fluid velocity and the drag on both walls of the cylinders.

scholarly journals Vibration of rotating circular cylindrical shells with distributed springs

2021 ◽  
Vol 37 ◽  
pp. 346-358
Author(s):  
Fuchun Yang ◽  
Xiaofeng Jiang ◽  
Fuxin Du
Keyword(s):  
Boundary Conditions ◽  
Galerkin Method ◽  
Shell Theory ◽  
Rotation Speed ◽  
Cylindrical Shells ◽  
Free Vibrations ◽  
Governing Equations ◽  
Natural Response ◽  
Circular Cylindrical Shells ◽  
The Galerkin Method

Abstract Free vibrations of rotating cylindrical shells with distributed springs were studied. Based on the Flügge shell theory, the governing equations of rotating cylindrical shells with distributed springs were derived under typical boundary conditions. Multicomponent modal functions were used to satisfy the distributed springs around the circumference. The natural responses were analyzed using the Galerkin method. The effects of parameters, rotation speed, stiffness, and ratios of thickness/radius and length/radius, on natural response were also examined.

scholarly journals Time Dependent Lyotropic Chromonic Textures in Microfluidic Confinements

Crystals ◽  
2020 ◽  
Vol 11 (1) ◽  
pp. 35 ◽  
Author(s):  
Anshul Sharma ◽  
Irvine Lian Hao Ong ◽  
Anupam Sengupta
Keyword(s):  
Phase Transition ◽  
Aspect Ratio ◽  
Temporal Dynamics ◽  
Initial Conditions ◽  
Flow Behavior ◽  
Medical Diagnostics ◽  
Time Dependent ◽  
Disodium Cromoglycate ◽  
M Phase ◽  
Static Conditions

Nematic and columnar phases of lyotropic chromonic liquid crystals (LCLCs) have been long studied for their fundamental and applied prospects in material science and medical diagnostics. LCLC phases represent different self-assembled states of disc-shaped molecules, held together by noncovalent interactions that lead to highly sensitive concentration and temperature dependent properties. Yet, microscale insights into confined LCLCs, specifically in the context of confinement geometry and surface properties, are lacking. Here, we report the emergence of time dependent textures in static disodium cromoglycate (DSCG) solutions, confined in PDMS-based microfluidic devices. We use a combination of soft lithography, surface characterization, and polarized optical imaging to generate and analyze the confinement-induced LCLC textures and demonstrate that over time, herringbone and spherulite textures emerge due to spontaneous nematic (N) to columnar M-phase transition, propagating from the LCLC-PDMS interface into the LCLC bulk. By varying the confinement geometry, anchoring conditions, and the initial DSCG concentration, we can systematically tune the temporal dynamics of the N- to M-phase transition and textural behavior of the confined LCLC. Overall, the time taken to change from nematic to the characteristic M-phase textures decreased as the confinement aspect ratio (width/depth) increased. For a given aspect ratio, the transition to the M-phase was generally faster in degenerate planar confinements, relative to the transition in homeotropic confinements. Since the static molecular states register the initial conditions for LC flows, the time dependent textures reported here suggest that the surface and confinement effects—even under static conditions—could be central in understanding the flow behavior of LCLCs and the associated transport properties of this versatile material.

Local loads on a toroidal shell

1992 ◽  
Vol 27 (2) ◽  
pp. 59-66 ◽  
Author(s):  
D Redekop ◽  
F Zhang
Keyword(s):  
Cylindrical Shell ◽  
Shell Theory ◽  
Elastic Shell ◽  
Toroidal Shell ◽  
Pipe Bend ◽  
Local Loads ◽  
Simply Supported ◽  
Linear Elastic ◽  
Wide Range ◽  
Theory Solution

In this study the effect of local loads applied on a sectorial toroidal shell (pipe bend) is considered. A linear elastic shell theory solution for local loads is first outlined. The solution corresponds to the case of a shell simply supported at the two ends. Detailed displacement and stress results are then given for a specific shell with loadings centred at three positions; the crown circles, the extrados, and the intrados. These results are compared with results for a corresponding cylindrical shell. The paper concludes with a table summarizing results for characteristic displacements and stresses in a number of shells, covering a wide range of geometric parameters.

Sign in / Sign up

Export Citation Format

Share Document