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.

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.

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.

Free Asymmetric Vibrations of Composite Full Circular Cylindrical Shells With a Bonded Central Lap Joint

2003 ◽  
Author(s):  
V. O¨zerciyes ◽  
U. Yuceoglu
Keyword(s):  
Cylindrical Shell ◽  
Differential Equations ◽  
Shell Theory ◽  
Natural Frequencies ◽  
Cylindrical Shells ◽  
Adhesive Layer ◽  
Lap Joint ◽  
First Order ◽  
Single Lap Joint ◽  
Circular Cylindrical Shells

In this study, the problem of the free asymmetric vibrations of composite “full” circular cylindrical shells with a bonded single lap joint is considered. The “full” circular cylindrical shell adherends to be made of dissimilar and orthotropic materials are connected by relatively very thin, yet flexible and linearly elastic adhesive layer. The bonded single lap joint is a centrally located in the composite shell system. The analysis is based on a “Timoshenko-Mindlin (and Reissner) Type Shell Theory” which is a “First Order Shear Deformation Shell Theory (FSDST)”. In the formulation, the set of governing differential equations is reduced to a system of first order ordinary differential equations in the “state vector” form. Then, they are integrated by means of a numerical procedure, that is, the “Modified Transfer Matrix Method (with Chebyshev Polynomials)”. The mode shapes and the natural frequencies of the “full” cylindrical shell lap joint system are investigated for various boundary conditions. Also, the effects, on the modes and natural frequencies, of the “hard” (or rather relatively stiff) and the “soft” (or relatively very flexible) adhesive layer cases are considered and presented. Some of the numerical results of the important parametric studies are computed and plotted.

scholarly journals Natural frequencies analysis of functionally graded circular cylindrical shells

2021 ◽  
Vol 15 (2) ◽  
Author(s):  
Nabeel T. Alshabatat ◽  
Mohammad Zannon
Keyword(s):  
Shear Deformation ◽  
Power Law ◽  
Shell Theory ◽  
Natural Frequencies ◽  
Cylindrical Shells ◽  
Functionally Graded ◽  
Radius Ratio ◽  
Third Order ◽  
The Third ◽  
Circular Cylindrical Shells

In the present work, a study on natural frequencies of functionally graded materials (FGM) circular cylindrical shells is presented. TheFGM is considered to be a mixture of two materials. The volumetric fractions are considered to vary in the radial direction (i.e., through the thickness) in compliance with a conventional power-law distribution. The equivalent material properties are estimated based on the Voigt model. The analysis of the FGM cylindrical shells is performed using the third-order shear deformation shell theory and the principle of virtual displacements. Moreover, the third-order shear deformation shell theory coupled with Carrera’s unified formulation is applied for the derivation of the governing equations associated with the free vibration of circular cylindrical shells. The accuracy of this method is examined by comparing the obtained numerical results with other previously published results. Additionally, parametric studies are performed for FGM cylindrical shells with several boundary conditions in order to show the effect of several design variables on the natural frequencies such as the power-law exponent, the circumferential wave number, the length to radius ratio and the thickness to radius ratio.

Effect of Rotation on Vibration of Moderately Thick Circular Cylindrical Shells

1994 ◽  
Vol 116 (2) ◽  
pp. 198-202 ◽  
Author(s):  
K. R. Sivadas ◽  
N. Ganesan
Keyword(s):  
Fourier Expansion ◽  
Shell Theory ◽  
Natural Frequencies ◽  
Cylindrical Shells ◽  
Rotational Energy ◽  
Damping Factor ◽  
Thick Shell ◽  
Material Anisotropy ◽  
Rotatory Inertia ◽  
Circular Cylindrical Shells

Circular cylindrical shells rotating about their axis of revolution are analyzed for natural frequencies and damping factor using moderately thick shell theory with shear deformation and rotatory inertia. A subparametric axisymmetric finite element with 5 nodes to represent the function variations, and 2 nodes to represent coordinate variations is used for the solution. Full Fourier expansion is used in the circumferential direction to overcome the effect of material anisotropy and Coriolis component. The effect of rotation on frequencies is studied by incorporating the Coriolis acceleration, rotational energy, prestressing due to centrifugal force, and damping due to material.

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.

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.

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