Laminated Transversely Isotropic Cylindrical Shells

1971 ◽  
Vol 38 (2) ◽  
pp. 400-407 ◽  
Author(s):  
J. A. Zukas ◽  
J. R. Vinson
Keyword(s):  
Shell Theory ◽  
Transverse Isotropy ◽  
Cylindrical Shells ◽  
Pyrolytic Graphite ◽  
Transversely Isotropic ◽  
Sample Problem ◽  
Governing Equations ◽  
Slow Cooling ◽  
Circular Cylindrical Shells ◽  
Thin Shell Theory

A theory for the analysis of stresses in laminated circular cylindrical shells subjected to arbitrary axisymmetric mechanical and thermal loadings has been developed. This theory, specifically for use with pyrolytic-graphite-type materials, differs from the classical thin shell theory in that it includes the effects of transverse shear deformation and transverse isotropy, as well as thermal expansion through the shell thickness. Solutions in several forms are developed for the governing equations. The form taken by the solution function is governed by geometric considerations. A range in which the various solution forms occur was determined numerically. As a sample problem, the slow cooling of pyrolytic graphite deposited onto a commercial graphite mandrel was considered. Investigation of normal and shear stress behavior at the pyrolytic graphite-mandrel interface showed that these stresses decrease in magnitude with increasing E/Gc ratio and increasing deposit to mandrel thickness (ha/hb) ratio. This implies that a thin mandrel and a material weak in shear are desirable to minimize the possibilities of flaking and delamination of the pyrolytic graphite.

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.

Development of beam modal function for free vibration analysis of FML circular cylindrical shells

2017 ◽  
Vol 24 (14) ◽  
pp. 3026-3035 ◽  
Author(s):  
Masood Mohandes ◽  
Ahmad Reza Ghasemi ◽  
Mohsen Irani-Rahagi ◽  
Keivan Torabi ◽  
Fathollah Taheri-Behrooz
Keyword(s):  
Free Vibration ◽  
Shell Theory ◽  
Volume Fraction ◽  
Equations Of Motion ◽  
Cylindrical Shells ◽  
Free Vibration Analysis ◽  
Governing Equations ◽  
Fiber Metal Laminate ◽  
Circular Cylindrical Shells ◽  
Fiber Metal

The free vibration of fiber–metal laminate (FML) thin circular cylindrical shells with different boundary conditions has been studied in this research. Strain–displacement relations have been obtained according to Love’s first approximation shell theory. To satisfy the governing equations of motion, a beam modal function model has been used. The effects of different FML parameters such as material properties lay-up, volume fraction of metal, fiber orientation, and axial and circumferential wavenumbers on the vibration of the shell have been studied. The frequencies of shells have been calculated for carbon/epoxy and glass/epoxy as composites and for aluminum as metal. The results demonstrate that the influences of FML lay-up and volume fraction of composite on the frequencies of the shell are remarkable.

Non-Axisymmetric Vibrations of Stepped Cylindrical Shells Containing Cracks

2014 ◽  
Vol 934 ◽  
pp. 136-142
Author(s):  
Larissa Roots
Keyword(s):  
Shell Theory ◽  
Natural Frequencies ◽  
Cylindrical Shells ◽  
Axisymmetric Vibration ◽  
Approximate Evaluation ◽  
Linear Fracture ◽  
Local Flexibility ◽  
Circular Cylindrical Shells ◽  
Thickness Variations ◽  
Thin Shell Theory

Based on the Donnell’s approximations of the thin shell theory, this paper presents solutions for the problem of free non-axisymmetric vibration of stepped circular cylindrical shells with cracks. The shell under consideration is sub-divided into multiple segments separated by the locations of thickness variations. It is assumed that at thejth step there exists a circumferential surface crack with uniform depthcj. The influence of circular cracks with constant depth on the vibration of the shell is prescribed with the aid of a matrix of local flexibility. The latter is related to the coefficient of the stress intensity known in the linear fracture mechanics. Numerical results are obtained for cylindrical shells of stepped thickness containing cracks at re-entrant corners of steps. Shells with various combinations of boundary conditions can be analyzed by the proposed method. Furthermore, the influences of the shell thicknesses, locations of step-wise variations of the thickness and other parameters on the natural frequencies are examined. The results can be used for the approximate evaluation of dynamic parameters of cylindrical shells with cracks and flaws.

A Multi-Mode Approach for the Nonlinear Vibrations of Circular Cylindrical Shells

2001 ◽  
Author(s):  
Francesco Pellicano ◽  
Marco Amabili ◽  
Michael P. Païdoussis
Keyword(s):  
Degrees Of Freedom ◽  
Nonlinear Vibrations ◽  
Shell Theory ◽  
Cylindrical Shells ◽  
Nonlinear Behavior ◽  
Symbolic Manipulation ◽  
Comparison Functions ◽  
Circular Cylindrical Shells ◽  
Multi Mode

Abstract The nonlinear vibrations of simply supported, circular cylindrical shells, having geometric nonlinearities is analyzed. Donnell’s nonlinear shallow-shell theory is used, and the partial differential equations are spatially discretized by means of the Galerkin procedure, using a large number of degrees of freedom. A symbolic manipulation code is developed for the discretization, allowing an unlimited number of modes. In the displacement expansion particular care is given to the comparison functions in order to reduce as much as possible the dimension of the dynamical system, without losing accuracy. Both driven and companion modes are included, allowing for traveling-wave response of the shell. The fundamental role of the axisymmetric modes, which are included in the expansion, is confirmed and a convergence analysis is performed. The effect of the geometric shell characteristics, radius, length and thickness, on the nonlinear behavior is analyzed.

Collapse of Thin Orthotropic Elliptical Cylindrical Shells Under Combined Bending and Pressure Loads

1979 ◽  
Vol 46 (2) ◽  
pp. 363-371 ◽  
Author(s):  
J. Spence ◽  
S. L. Toh
Keyword(s):  
Shell Theory ◽  
Nonlinear Boundary ◽  
Cylindrical Shells ◽  
Normal Pressure ◽  
Nonlinear Ordinary Differential Equations ◽  
Pure Bending ◽  
Finite Deflection ◽  
Shooting Technique ◽  
Theoretical Predictions ◽  
Thin Shell Theory

The elastic collapse of thin orthotropic elliptical cylindrical shells subject to pure bending alone or combined bending and uniform normal pressure loads has been studied. Nonlinear finite deflection thin shell theory is employed and this reduces the problem to a set of nonlinear ordinary differential equations. The resulting two-point nonlinear boundary-value problem is then linearized, using quasi-linearization, and solved numerically by the “shooting technique.” Some experimental work has been carried out and the results are compared with the theoretical predictions.

Free Asymmetric Vibrations of Composite Full Circular Cylindrical Shells Stiffened by a Bonded Central Shell Segment

2004 ◽  
Author(s):  
U. Yuceoglu ◽  
V. O¨zerciyes
Keyword(s):  
Cylindrical Shell ◽  
Shell Theory ◽  
Natural Frequencies ◽  
Circular Cylindrical Shell ◽  
Cylindrical Shells ◽  
Adhesive Layer ◽  
Shear Stresses ◽  
First Order ◽  
Stress Resultant ◽  
Circular Cylindrical Shells

This study is concerned with the “Free Asymmetric Vibrations of Composite Full Circular Cylindrical Shells Stiffened by a Bonded Central Shell Segment.” The base shell is made of an orthotropic “full” circular cylindrical shell reinforced and/or stiffened by an adhesively bonded dissimilar, orthotropic “full” circular cylindrical shell segment. The stiffening shell segment is located at the mid-center of the composite system. The theoretical analysis is based on the “Timoshenko-Mindlin-(and Reissner) Shell Theory” which is a “First Order Shear Deformation Shell Theory (FSDST).” Thus, in both “base (or lower) shell” and in the “upper shell” segment, the transverse shear deformations and the extensional, translational and the rotary moments of inertia are taken into account in the formulation. In the very thin and linearly elastic adhesive layer, the transverse normal and shear stresses are accounted for. The sets of the dynamic equations, stress-resultant-displacement equations for both shells and the in-between adhesive layer are combined and manipulated and are finally reduced into a ”Governing System of the First Order Ordinary Differential Equations” in the “state-vector” form. This system is integrated by the “Modified Transfer Matrix Method (with Chebyshev Polynomials).” Some asymmetric mode shapes and the corresponding natural frequencies showing the effect of the “hard” and the “soft” adhesive cases are presented. Also, the parametric study of the “overlap length” (or the bonded joint length) on the natural frequencies in several modes is considered and plotted.

Acoustic and Vibration Characteristics of Stiffened Finite Cylindrical Shells in Water under Multiple Axial-Excitations

2013 ◽  
Vol 662 ◽  
pp. 721-725
Author(s):  
Qi Zheng Zhou ◽  
De Shi Wang ◽  
Sheng Yao Gao
Keyword(s):  
Analytical Solution ◽  
Shell Theory ◽  
Acoustic Pressure ◽  
Acoustic Radiation ◽  
Cylindrical Shells ◽  
High Frequencies ◽  
Acoustic Coupling ◽  
Coupling Equations ◽  
Vibration And Sound Radiation ◽  
Thin Shell Theory

A research on the vibration and acoustic radiation of stiffened finite cylindrical shells in water under a multiple axial-excitations driven was presented. The vibro-acoustic coupling equations of shell under multiple axial-excitations based on Flügge thin shell theory were established. The displacements, surface acoustic pressure and stiffener impedances were expressed in terms of the numbers of normal modals and modes, and considering multiple excitations, the forces were expressed in terms of the numbers of normal modals and modes. Then analytical solution was derived for the vibration and sound radiation from the stiffened shell under multiple excitations. Based on the analytical solution, the influences of excitations’ positions to the vibration and acoustic radiation were investigated. The results show that for double excitations, at high frequencies, the distance between excitations was more large, the average velocity was more low. The results could be used to control the underwater vehicle’s vibration and acoustic radiation.

scholarly journals Prediction of Vibrational Behavior of Grid-Stiffened Cylindrical Shells

2014 ◽  
Vol 2014 ◽  
pp. 1-10 ◽  
Author(s):  
G. H. Rahimi ◽  
M. Hemmatnezhad ◽  
R. Ansari
Keyword(s):  
Shell Theory ◽  
Cylindrical Shells ◽  
Element Model ◽  
Geometrical Parameters ◽  
Equivalent Stiffness ◽  
Theoretical Formulation ◽  
Vibrational Behavior ◽  
Thin Shell Theory ◽  
Stiffened Cylindrical Shells ◽  
Good Agreement

A unified analytical approach is applied to investigate the vibrational behavior of grid-stiffened cylindrical shells with different boundary conditions. A smeared method is employed to superimpose the stiffness contribution of the stiffeners with those of shell in order to obtain the equivalent stiffness parameters of the whole panel. Theoretical formulation is established based on Sanders’ thin shell theory. The modal forms are assumed to have the axial dependency in the form of Fourier series whose derivatives are legitimized using Stoke's transformation. A 3D finite element model is also built using ABAQUS software which takes into consideration the exact geometric configuration of the stiffeners and the shell. The achievements from the two types of analyses are compared with each other and good agreement has been obtained. The Influences of variations in shell geometrical parameters, boundary condition, and changes in the cross stiffeners angle on the natural frequencies are studied. The results obtained are novel and can be used as a benchmark for further studies. The simplicity and the capability of the present method are also discussed.

The Influence of Large Deflections on the Behavior of Rigid-Plastic Cylindrical Shells Loaded Impulsively

1970 ◽  
Vol 37 (2) ◽  
pp. 416-425 ◽  
Author(s):  
Norman Jones
Keyword(s):  
Cylindrical Shells ◽  
Dynamic Loads ◽  
Large Deflections ◽  
Finite Deflections ◽  
Shell Material ◽  
Governing Equations ◽  
Rigid Plastic ◽  
Perfectly Plastic ◽  
Dynamic Analyses ◽  
Circular Cylindrical Shells

A theoretical investigation is herein undertaken in order to examine the response of circular cylindrical shells subjected to dynamic loads of an intensity sufficient to cause large permanent deformations. The shell material is assumed to be rigid, perfectly plastic and the influence of finite deflections is retained in the governing equations. It emerges clearly from the study that geometry changes influence markedly the shell behavior even for quite small deflections and, therefore, they should be retained in any dynamic analyses of cylindrical shells with axial restraints.

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