Response Of Circular Cylindrical Shell Research Articles

Analyses of nonlinear dynamics of imperfect nanocomposite circular cylindrical shells with swirling annular and internal fluid flow using higher order shear deformation shell theory

The paper focuses on nonlinear dynamical responses of circular cylindrical shell made of carbon nanotubes reinforced polymer conveying to internal and external fluid flow. The fluid flows are assumed incompressible. The governing equations are derived from the Third order shear deformation theory (TSDT), the fluid velocity potential, then using the Galerkin′s technique and the fourth-order Runge-Kutta method to give the characteristics of nonlinear dynamics of fluid-structures interaction. The product of the velocity U.V of the two liquid streams (swirling flow and straight flow) is considered to investigate the stable domain of the structure under the effect of two velocity factors. In addition, the dynamical behaviors as time histories and bifurcation diagram as well as the effects of materials, geometries and the critical velocities of losing stability caused by internal and external flow fluid are scrutinized in the present. The obtained results are also compared and validated with those of other studies and can be used as benchmark solutions for an analytical approach serving in further research.

Experiments on shells under base excitation

The aim of the present paper is a deep experimental investigation of the nonlinear dynamics of circular cylindrical shells. The specific problem regards the response of circular cylindrical shells subjected to base excitation. The shells are mounted on a shaking table that furnishes a vertical vibration parallel to the cylinder axis; a heavy rigid disk is mounted on the top of the shells. The base vibration induces a rigid body motion, which mainly causes huge inertia forces exerted by the top disk to the shell. In-plane stresses due to the aforementioned inertias give rise to impressively large vibration on the shell. An extremely violent dynamic phenomenon suddenly appears as the excitation frequency varies up and down close to the linear resonant frequency of the first axisymmetric mode. The dynamics are deeply investigated by varying excitation level and frequency. Moreover, in order to generalise the investigation, two different geometries are analysed. The paper furnishes a complete dynamic scenario by means of: (i) amplitude frequency diagrams, (ii) bifurcation diagrams, (iii) time histories and spectra, (iv) phase portraits and Poincaré maps. It is to be stressed that all the results presented here are experimental.

Vibration analysis of FG cylindrical shells with power-law index using discrete singular convolution technique

AbstractIn the present manuscript, free vibration response of circular cylindrical shells with functionally graded material (FGM) is investigated. The method of discrete singular convolution (DSC) is used for numerical solution of the related governing equation of motion of FGM cylindrical shell. The constitutive relations are based on the Love’s first approximation shell theory. The material properties are graded in the thickness direction according to a volume fraction power law indexes. Frequency values are calculated for different types of boundary conditions, material and geometric parameters. In general, close agreement between the obtained results and those of other researchers has been found.

Dynamic Response of Functionally Graded Circular Cylindrical Shells

In this paper the response of circular cylindrical shell made of Functionally Graded Material (FGM) subjected to lateral impulse load was investigated. The effective material properties are assumed to vary continuously along the thickness direction according to a volume fraction power law distribution. First order shear deformation theory (FSDT) and Love's first approximation theory were utilized in the equilibrium equations. The boundary condition was considered to be simply supported. Displacement components are product of functions of position and time. Equilibrium equations for free and forced vibrations were solved using the Galerkin method. The impulse load in the form of time varying uniform pressure was applied onto a small rectangular area of the shell surface. The function of time for displacement components is obtained using the results of free vibration and convolution integral. Finally time response of displacement components is derived using mode superposition method. The influence of material composition (power law exponent), geometrical parameters (length to radius and radius to thickness ratios) and load parameters (position and size of the area of the applied load and peak pressure value for different pulse type) on the dynamic response was investigated.

Inertial effects in ductile failure of cylindrical tubes under internal pressure

The dynamic response of circular cylindrical shells under pressure impact is investigated using a finite element approach. Finite changes of geometry are accounted for within the framework of a membrane theory development. A strain-hardening solid with elastic-viscoplastic material characteristics is considered. Only failure modes in the cross-sectional plane of the specimen are examined, by limiting the analysis to plane-strain deformations. Numerical results are generated for the full pressure-expansion-time history of the specimen. Dynamic results at high expansion rates are presented under pressure-controlled loading. Since rapid straining all around the circumference can be triggered under increasing pressure, a distinctly different deformation mode involving slower neck development is encountered. The experimentally observed multiple neck formation behaviour under dynamic loading is discussed by examining the prevalence of shorter wavelength deformation modes. Some insight to the configuration dependency of the applied loading is provided by an extension of the analysis to different displacement-rate and traction boundary conditions.

Layer-wise shell theory for postbuckling of laminated circular cylindrical shells

The layer-wise shell theory of Reddy is used to study the postbuckling response of circular cylindrical shells. The Rayleigh-Ritz method is used to solve the equations by assuming a double Fourier expansion of the displacements with trigonometric coordinate functions. Numerical results for postbuckling response of axially compressed multilayer cylinders with simply supported edge conditions are presented for different values of shell imperfections.

Response of moderately thick laminated cross-ply composite shells subjected to random excitation

This study deals with the dynamic response of transverse shear deformable laminated shells subjected to random excitation. The analysis encompasses the following problems: (1) the dynamic response of circular cylindrical shells of finite length excited by an axisymmetric uniform ring loading, stationary in time, and (2) the response of spherical and cylindrical panels subjected to stationary random loadings with uniform spatial distribution. The associated equations governing the structural theory of shells are derived upon discarding the classical Love-Kirchhoff (L-K) assumptions. In this sense, the theory is formulated in the framework of the first-order transverse shear deformation theory (FSDT).

Experimental and finite element studies of circular cylindrical shells loaded radially through a central pad

Examination is made of the static linear response of circular cylindrical shells to a radial loading applied halfway along the shells: the chief concern is with shells in which the loading is applied by way of a circular pad containing a small concentric hole. The examination comprises tests on physical models, in which point displacements and strains are measured, and numerical studies based on the use of the finite element method. In the numerical studies two markedly different types of element are used and particular attention is paid to the modelling of the pad region of the cylinder pad combination. Good correlation between test measurements and numerical results is exhibited for radial displacement and for stresses, even when the pad itself is removed from the finite element models by appropriate specification of boundary conditions which reflect full pad rigidity.

Non-linear oscillation of circular cylindrical shells

The method of multiple scales is used to analyze the non-linear forced response of circular cylindrical shells in the presence of a two-to-one internal (autoparametric) resonance to a harmonic excitation having the frequency Ω. If ωr and ar denote the frequency and amplitude of a flexural mode and ωb and ab denote the frequency and amplitude of the breathing mode, the steady-state response exhibits a saturation phenomenon when ωb ≈ 2ωr, if the excitation frequency Ω is near ωb. As the amplitude ƒ of the excitation increases from zero, ab increases linearly whereas ar remains zero until a threshold is reached. This threshold is a function of the damping coefficients and ωb−2ωr. Beyond this threshold ab remains constant (i.e. the breathing mode saturates) and the extra energy spills over into the flexural mode. In other words, although the breathing mode is directly excited by the load, it absorbs a small amount of the input energy (responds with a small amplitude) and passes the rest of the input energy into the flexural mode (responds with a large amplitude). For small damping coefficients and depending on the detunings of the internal resonance and the excitation, the response exhibits a Hopf bifurcation and consequently there are no steadystate periodic responses. Instead, the responses are amplitude- and phase-modulated motions. When Ω ≈ ωr, there is no saturation phenomenon and at close to perfect resonance, the response exhibits a Hopf bifurcation, leading again to amplitude- and phase-modulated or chaotic motions.

Modal response of circular cylindrical shells with structural damping

Although a vast literature exists dealing with the free vibrations of circular cylindrical shells, relatively little can be found for the problem of dynamic response due to sinusoidally varying exciting forces, especially when damping exists. In the present work the response of a shell subjected to a sinusoidal radial pressure is studied, when the pressure has the same distribution as the normal mode shape. Structural (hysteresis) damping is considered. For a unit amplitude of exciting pressure, the lowest frequency modes are found to yield the largest resonant response. Because of a small amount of mode coupling, the peak amplitudes are found to be not quite inversely proportional to the strength of the damping, and there is a slight shift in the locations of the resonant peaks.

Effects of Cracks on the Response of Circular Cylindrical Shells

A simple model for the cracked cylindrical shell, which employs only familiar concepts from applied mechanics, gives insight into the effects of cracks on structural response. The model provides analytical expressions for plane-strain bending deformations induced by the cracks and enables qualitative and quantitative generalizations to be made about the effects of different sizes and numbers of cracks and different loading conditions. These bending deformations, which are absent in a uniformly pressurized flawless shell, can dominate the response of a deeply cracked shell.The simple model may be calibrated with only two static deflection measurements made on a real shell or determined from a finite element model. Then the dynamic response is easily established for arbitrary time-dependent loadings. The predictions of the simple model are in agreement with finite element results and provide conservative bounds on the additional elastic bending deflections induced by cracks in reactor vessels, piping, and other shell-like components.

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

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.

Dynamic of Submerged Reinforced Cylindrical Shells

An approximate analytic technique is developed for the determination of the dynamic transient elastic response of circular cylindrical shells which are immersed in acoustic media. For a simple example, a comparison is made between the approximate technique developed and the exact analytic response. Comparison is also made between the proposed approximate technique and the existing approximate techniques, i.e., the plane wave and cylindrical wave approximations. The proposed approximate technique compares quite favorably with the exact solution and is superior to the existing approximate techniques. Making use of the proposed approximate technique the dynamic elastic response of a reinforced circular cylindrical shell to a moving pressure pulse applied through a surrounding acoustic medium is investigated. The pressure pulse is assumed to have its wave front parallel to the axis of the shell. The shell is assumed to be reinforced with periodically spaced rigid septa or stiffening rings. The response of each mode of a steel shell having typical geometry is calculated for a pressure pulse applied through an acoustic medium of water. This response is compared to the modal response of the shell in a vacuum but subjected to the same pressure pulse. It is found that in general the presence of an acoustic medium such as water reduces the amplitude in each mode and reduces the free vibration frequency.