Dynamic Analysis of Anisotropic Cylindrical Shells Containing Flowing Fluid

2001 ◽  
Vol 123 (4) ◽  
pp. 454-460 ◽  
Author(s):  
M. H. Toorani ◽  
A. A. Lakis
Keyword(s):  
Transverse Shear ◽  
Equations Of Motion ◽  
Cylindrical Shells ◽  
Fluid Pressure ◽  
Laminated Composite ◽  
Present Theory ◽  
Curvilinear Coordinates ◽  
Structural Element ◽  
Flowing Fluid ◽  
Bernoulli’S Equation

This paper deals with the study of dynamic behavior of anisotropic cylindrical shells, based on refined shell theory, subjected simultaneously to an internal and external fluid. In the present theory, the transverse shear deformation effect is taken into account, therefore, the equations of motion are determined with displacements and transverse shear as independent variables. The solution is divided into three parts: In Section 2, the displacement functions are derived from the exact solution of refined shell equations based on orthogonal curvilinear coordinates. The mass and stiffness matrices of each structural element are derived by exact analytical integration. In Section 3, the velocity potential, Bernoulli’s equation and impermeability condition have been applied to the shell fluid interface to obtain an explicit expression for fluid pressure which yields three forces (inertial, centrifugal, Coriolis). Numerical examples are given in Section 4 for the free vibration of laminated composite and isotropic materials for both open and closed circular cylindrical shells. Reasonable agreement is found with other theories and experiments.

On Crack Growth in Composite Cylindrical Shells

1999 ◽  
Author(s):  
Hayder A. Rasheed ◽  
John L. Tassoulas
Keyword(s):  
Energy Release Rate ◽  
Energy Release ◽  
Crack Growth ◽  
Release Rate ◽  
Cylindrical Shells ◽  
Applied Pressure ◽  
Fluid Pressure ◽  
Laminated Composite ◽  
Stable Crack Growth ◽  
Composite Cylindrical Shells

Abstract Interfacial defects, in the form of cracks or layer separation, may occur in composite cylindrical shells during the manufacturing process, transportation or service life. Such defects are expected to affect the integrity of laminated composite structural elements and may reduce their capacity to resist the applied loads. In this article, the growth of pre-existing cracks in moderately thick composite cylinders is studied for the case of externally applied fluid pressure. The cracks considered separate thick layers, which are unlikely to buckle locally prior to the final collapse of the structural component. The potential of growth is assessed by computing the energy release rate. It is found that any initial out-of roundness imperfection introduces a shear force at the crack tip by causing the cross section to ovalize slightly. The energy release rate is found to vary exponentially with the applied pressure, when geometric nonlinearities are considered. The analysis is applied to a carbon/glass-fiber hybrid composite tube and the parameters influencing growth are examined. Crack length, through the thickness location, circumferential location relative to the ovalization orientation and the amount of imperfection are found to control the nature of growth. Unstable as well as stable crack growth and arrest cases are observed for various combinations of these parameters.

Free Vibrations of Laminated Composite Noncircular Thin Cylindrical Shells

1994 ◽  
Vol 61 (4) ◽  
pp. 861-871 ◽  
Author(s):  
K. Suzuki ◽  
G. Shikanai ◽  
A. W. Leissa
Keyword(s):  
Equations Of Motion ◽  
Cylindrical Shells ◽  
Power Series Expansion ◽  
Laminated Composite ◽  
Energy Functional ◽  
Solution Procedure ◽  
Free Vibrations ◽  
Layer Stacking ◽  
Kinetic Energy Functional ◽  
Energy Principles

An exact solution procedure is presented for solving free vibration problems for laminated composite noncircular cylindrical shells. Based on the classical lamination theory, strain energy and kinetic energy functional are first derived for shells having arbitrary layer stacking sequences. These functional are useful for a general analysis based upon energy principles. However, in the present work equations of motion and boundary conditions are obtained from the minimum conditions of the Lagrangian (Hamilton’s principle). The equations of motion are solved exactly by using a power series expansion for symmetrically laminated, cross-ply shells having both ends freely supported. Frequencies are presented for a set of elliptical cylindrical shells, and the effects of various parameters upon them are discussed.

scholarly journals Bending analysis of laminated composite and sandwich beams according to refined trigonometric beam theory

2015 ◽  
Vol 2 (1) ◽  
Author(s):  
A. S. Sayyad ◽  
Y. M. Ghugal ◽  
N. S. Naik
Keyword(s):  
Shear Deformation ◽  
Transverse Shear ◽  
Virtual Work ◽  
Laminated Composite ◽  
Beam Theory ◽  
Present Theory ◽  
Transverse Shear Deformation ◽  
Transverse Displacement ◽  
Sandwich Beams ◽  
Bending Analysis

AbstractA trigonometric beam theory (TBT) is developed for the bending analysis of laminated composite and sandwich beams considering the effect of transverse shear deformation. The axial displacement field uses trigonometric function in terms of thickness coordinate to include the effect of transverse shear deformation. The transverse displacement is considered as a sum of two partial displacements, the displacement due to bending and the displacement due to transverse shearing. Governing equations and boundary conditions are obtained by using the principle of virtual work. To demonstrate the validity of present theory it is applied to the bending analysis of laminated composite and sandwich beams. The numerical results of displacements and stresses obtained by using present theory are presented and compared with those of other trigonometric theories available in literature along with elasticity solution wherever possible.

Theoretical Analysis of Free Vibrations Based on a New High Order Shell Theory for Cylindrical Shells Conveying Fluid

2017 ◽  
Author(s):  
Ming Ji ◽  
Kazuaki Inaba
Keyword(s):  
Boundary Conditions ◽  
Shell Theory ◽  
Natural Frequencies ◽  
Equations Of Motion ◽  
Cylindrical Shells ◽  
Fluid Pressure ◽  
Free Vibrations ◽  
High Order ◽  
Out Of Plane ◽  
Conveying Fluid

The natural frequencies of free vibrations for thick cylindrical shells with clamped-clamped ends conveying fluid are investigated. Equations of motion and boundary conditions are derived by Hamilton’s principle based on the new high order shell theory. The hydrodynamic force is derived from the linearized potential flow theory. Besides, fluid pressure acting on the shell wall is gotten by the assumption of non-penetration condition. The out-of-plane and in-plane vibrations are coupled together due to the existence of fluid-solid-interaction (FSI). Under the assumption of harmonic motion, the dispersion relationships are presented. Using the method of frequency sweeping, the natural frequencies of symmetric modes and asymmetric modes corresponding to each flow velocity are found by satisfying the dispersion relationship equations and boundary conditions. Several numerical examples with different flow velocities and thickness are presented compared with previous thin shell theory and FEM results and show reasonable agreement. The effects of thickness are discussed.

Three-Dimensional Vibration of Fluid-Conveying Laminated Composite Cylindrical Shells with Piezoelectric Layers

2019 ◽  
Vol 19 (03) ◽  
pp. 1950026
Author(s):  
Seyed Mohammad Miramini ◽  
Abdolreza Ohadi
Keyword(s):  
Cylindrical Shells ◽  
Computational Cost ◽  
Three Dimensional ◽  
Laminated Composite ◽  
Theory Of Elasticity ◽  
Flowing Fluid ◽  
Piezoelectric Layers ◽  
Elastic Layers ◽  
First Time ◽  
Low Computational Cost

Cylindrical shells containing flowing fluid have wide applications in various industries. They can be enhanced as smart structures through inclusion of piezoelectric layers, of which the dynamic behavior, however, has not been fully understood. In this paper, the vibration and dynamic analysis of a laminated composite hollow cylinder with piezoelectric layers, subjected to an internal incompressible fluid flow is investigated. It is assumed that the shell is simply supported and the fluid is inviscid and irrotational. The differential equations of the elastic layers, piezoelectric layers, and flowing fluid are derived by the three-dimensional (3D) theory of elasticity, theory of piezoelectricity, and potential flow theory, respectively. A well-known recursive method is applied and extended for the first time to solve the fluid-conveying pipes using 3D theory. This approach makes it possible for the solutions to converge to the exact ones with reasonable computational cost. After validating the results against those available in the literature, the vibrational behavior of the system is examined for various cases with the effect of each parameter investigated. Also, the influence of fluid on the vibration and stability of the shell has been analyzed. The present method can be used to analyze and design hybrid shells conveying fluid with high accuracy and low computational cost.

Flow-Induced Vibration of Anisotropic Cylindrical Shells

2002 ◽  
Author(s):  
M. H. Toorani ◽  
A. A. Lakis
Keyword(s):  
Natural Frequencies ◽  
Cylindrical Shells ◽  
Fluid Pressure ◽  
Coupled System ◽  
Flow Induced Vibration ◽  
Critical Flow Velocity ◽  
Flowing Fluid ◽  
Coupled Equations ◽  
Stiffness Matrices ◽  
Analytical Integration

This paper deals with the vibration analysis of anisotropic laminated cylindrical shells conveying fluid. We focus on the axi-symmetric (n=0) and lateral (beam-like, n=1) vibration modes of the anisotropic cylindrical shells. Particularly important in this study is to obtain the natural frequencies of the fluid-structure coupled system and also to estimate the critical flow velocity at which the structure loses its stability. The coupled equations between the shell and the fluid are derived from a refined shell theory by taking into account the shear deformation effects. The displacement functions are obtained from the exact solution of refined shell equations and therefore the mass and stiffness matrices of the shell are determined by precise analytical integration. The added mass, stiffness and damping matrices of the fluid are obtained by an analytical integration of the fluid pressure over the liquid element. Thereafter, these matrices are coupled with the dynamic equation of the empty shell. The natural frequencies obtained with the shell partially or completely filled with liquid are in good agreement with those obtained experimentally and from other theories. The stability of the shell subjected to a flowing fluid is also studied. The shell’s anisotropy is discussed.

A Unified Shear Deformation Theory for the Bending of Isotropic, Functionally Graded, Laminated and Sandwich Beams and Plates

2017 ◽  
Vol 09 (01) ◽  
pp. 1750007 ◽  
Author(s):  
Atteshamuddin S. Sayyad ◽  
Yuwaraj M. Ghugal
Keyword(s):  
Boundary Conditions ◽  
Shear Deformation ◽  
Transverse Shear ◽  
Deformation Theory ◽  
Virtual Work ◽  
Shear Deformation Theory ◽  
Laminated Composite ◽  
Present Theory ◽  
Functionally Graded ◽  
Shear Stresses

In this paper, a displacement-based unified shear deformation theory is developed for the analysis of shear deformable advanced composite beams and plates. The theory is developed with the inclusion of parabolic (PSDT), trigonometric (TSDT), hyperbolic (HSDT) and exponential (ESDT) shape functions in terms of thickness coordinate to account for the effect of transverse shear deformation. The in-plane displacements consider the combined effect of bending rotation and shear rotation. The use of parabolic shape function in the present theory leads to the Reddy’s theory, but trigonometric, hyperbolic and exponential functions are first time used in the present displacement field. The present theory is accounted for an accurate distribution of transverse shear stresses through the thickness of plate, therefore, it does not require problem dependent shear correction factor. Governing equations and associated boundary conditions of the theory are derived from the principle of virtual work. Navier type closed-form solutions are obtained for simply supported boundary conditions. To verify the global response of the present theory it is applied for the bending of both one-dimensional (beams) and two-dimensional (plates) functionally graded, laminated composite and sandwich structures. The present results are compared with exact elasticity solution and other higher order shear deformation theories to verify the accuracy and efficiency of the present theory.

Nonlinear Analysis of Transverse Shear Deformable Laminated Composite Cylindrical Shells—Part I: Derivation of Governing Equations

1992 ◽  
Vol 114 (1) ◽  
pp. 105-109 ◽  
Author(s):  
K. P. Soldatos
Keyword(s):  
Transverse Shear ◽  
Cylindrical Shells ◽  
Laminated Composite ◽  
Companion Paper ◽  
Governing Equations ◽  
Initial Stress State ◽  
Static And Dynamic Analysis ◽  
Highly Nonlinear ◽  
Nonlinear Static ◽  
Shear Deformable

Based on the concept of an “intermediate” class of deformations, a theory suitable for the nonlinear static and dynamic analysis of transverse shear deformable circular and noncircular cylindrical shells, composed of an arbitrary number of linearly elastic monoclinic layers, is developed. The theory is capable of satisfying zero shear traction boundary conditions at the inner and outer shell surfaces. Upon assuming that the shell is subjected to a certain initial stress state and applying the highly nonlinear governing equations derived to the adjacent equilibrium criterion, a set of Love-type linearized equations is further derived. These latter equations are suitable for buckling and/or vibration analyses; in a companion paper, they are solved and used for the study of the influence of transverse shear deformation on the buckling loads of axially compressed cross-ply laminated circular and oval cylindrical shells.

A High-Order Theory for Dynamic Buckling and Postbuckling Analysis of Laminated Cylindrical Shells

1999 ◽  
Vol 121 (1) ◽  
pp. 94-102 ◽  
Author(s):  
M. R. Eslami ◽  
M. Shariyat
Keyword(s):  
Equations Of Motion ◽  
Cylindrical Shells ◽  
Strain Tensor ◽  
Shear Deformation Theory ◽  
Laminated Composite ◽  
Order Theory ◽  
High Order ◽  
Nonlinear Equations Of Motion ◽  
Laminated Composite Shells ◽  
Made In

Using a high-order Reisner-Mindlin-type shear deformation theory in a power series form, the general large deformation form of the Green strain tensor for imperfect cylindrical shells is introduced. Then, based on Hamilton’s principle, the equations of motion are derived for laminated composite shells. Related constitutive equations are also proposed. In this formulation, temperature dependency of material properties is considered, too. No simplifications are made in solving the coupled nonlinear equations of motion. Finally, few examples of the well-known references are reconsidered for comparison purposes.

Influence of Geometry on the Non-Linear Vibrations of Cylindrical Shells With Internal Flowing Fluid

2010 ◽  
Author(s):  
Zenon J. del Prado ◽  
Paulo B. Gonc¸alves ◽  
Michael P. Pai¨doussis
Keyword(s):  
Cylindrical Shell ◽  
Degrees Of Freedom ◽  
Lateral Displacement ◽  
Equations Of Motion ◽  
Cylindrical Shells ◽  
Dynamic Environment ◽  
Geometric Parameters ◽  
Flowing Fluid ◽  
Non Linear ◽  
Linear Vibrations

In this work, the influence of the characteristic geometric parameters of a cylindrical shell, such as radius-to-thickness and radius-to-length ratios, on both the linear and non-linear vibrations of a fluid-filled cylindrical shell with internal flowing fluid is studied. The Donnell non-linear shallow shell equations are used to study a simply supported cylindrical shell subjected to both lateral and axial time-dependent loads with internal flowing fluid. The fluid is assumed to be inviscid and incompressible and the flow isentropic and irrotational. An expansion with eight degrees of freedom, containing the fundamental, companion, gyroscopic and five axisymmetric modes is used to describe the lateral displacement of the shell. The Galerkin method is used to obtain the nonlinear equations of motion which are, in turn, solved by the Runge-Kutta method. First, the parametric linear equations are used to study the influence of geometry and physical properties on the natural frequencies, critical flow and critical circumferential wavenumber. Secondly, numerical methods are used to describe the influence of geometric characteristics on the non-linear frequency-amplitude relations of the shell. The results obtained show the influence of the geometric parameters on the vibration characteristics of the shell and can be used as a basic tool for design of cylindrical shells in a dynamic environment.

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