Elastic Circular Cylindrical Shell Research Articles

Applicability and Limitations of Simplified Elastic Shell Theories for Vibration Modelling of Double-Walled Carbon Nanotubes

The applicability and limitations of simplified models of thin elastic circular cylindrical shells for linear vibrations of double-walled carbon nanotubes (DWCNTs) are considered. The simplified models, which are based on the assumptions of membrane and moment approximate thin-shell theories, are compared with the extended Sanders–Koiter shell theory. Actual discrete DWCNTs are modelled by means of couples of concentric equivalent continuous thin, circular cylindrical shells. Van der Waals interaction forces between the layers are taken into account by adopting He’s model. Simply supported and free–free boundary conditions are applied. The Rayleigh–Ritz method is considered to obtain approximate natural frequencies and mode shapes. Different aspect and thickness ratios, and numbers of waves along longitudinal and circumferential directions, are analysed. In the cases of axisymmetric and beam-like modes, it is proven that membrane shell theory, differently from moment shell theory, provides results with excellent agreement with the extended Sanders–Koiter shell theory. On the other hand, in the case of shell-like modes, it is found that both membrane and moment shell theories provide results reporting acceptable agreement with the extended Sanders–Koiter shell theory only for very limited ranges of geometries and wavenumbers. Conversely, for shell-like modes it is found that a newly developed, simplified shell model, based on the combination of membrane and semi-moment theories, provides results in satisfactory agreement with the extended Sanders–Koiter shell theory in all ranges.

Longitudinal vibrations of a cylindrical shell filled with a viscous compressible liquid

This article investigates the longitudinal vibrations of a semi-infinite circular cylindrical elastic shell filled with a viscous compressible fluid. It is believed that the vibrations are excited by a suddenly switched on longitudinal displacement at the end. To solve the problem, the refined equations of longitudinal vibrations of a circular cylindrical elastic shell interacting with an internal viscous compressible fluid, previously proposed by the authors, were taken as the main resolving equations. In this case, the lateral surfaces of the shell are considered free from external loads; in addition, considering purely longitudinal vibrations, it can be assumed that the radial displacements of the points of the shell are equal to zero.

Frequency analysis of longitudinal-radial vibrations of a cylindrical shell

The article solves the problem of harmonic longitudinal-radial vibrations of a circular cylindrical shell with freely supported ends. To solve the problem, we used the refined equations of oscillation of such a shell, derived earlier from the exact three-dimensional formulation of the problem and its solution in transformations. An extensive review of works devoted to the study of harmonic and nonstationary processes in elastic bodies on the basis of classical (Kirchhoff-Love, Flyugge) and refined Timoshenko type (Hermann-Mirsky, Filippov-Khudoinazarov) theories is given. Four frequency equations are obtained for the main parts of the longitudinal and radial displacements of the cylindrical shell. These frequency equations admit, as special cases, frequency equations and a thin-walled shell. Based on the solution of the obtained frequency equations, the frequencies of natural vibrations of the shell, including the thin-walled one, are determined. A comparative frequency analysis of longitudinal vibrations of a circular cylindrical elastic shell is carried out on the basis of the classical Kirchhoff-Love theory, refined theories of Hermann-Mirsky and Filippov-Khudoinazarov. On the basis of the results obtained, conclusions were drawn regarding the applicability of the studied oscillation equations, depending on the waveform and shell length. In particular, it was found that all the considered equations are unsuitable for describing wave processes in short shells, the lengths of which are commensurate with the transverse dimensions of the shells.

Scattering of Frequency-Modulated Sound Pulses on a Circular Cylindrical Thin Elastic Shell Containing a Slit

We study the nonstationary problem of scattering of plane sound waves by a hollow elastic circular cylindrical shell weakened by an infinitely long linear slit. It is known that, in this case, the secondary components of the echo-pulse reradiated by circumferential waves of the Lamb type are very weak as compared with the first geometrically reflected pulse. At the same time, the secondary pulses carry information about the material of the shell and the location of the defect in it. The sinusoidal frequency-modulated pulse of finite duration in the incident wave and the cross-correlation function are used to amplify the amplitudes of these components of the echo-signal. We perform the classification of arrival times of the pulses reradiated by circumferential waves after their reflection from the edges of the slit in the shell. The numerical calculations are carried out for the case of the stainless steel shell immersed in seawater.

An efficient approach for prediction of the nonlocal critical buckling load of double-walled carbon nanotubes using the nonlocal Donnell shell theory

This paper aims to apply the nonlocal Donnell shell theory to study the buckling of double-walled carbon nanotubes (DWCNTs) under axial compression taking into account the effects of internal small length scale and the Van der Waals interactions between layers. The DWCNTs is modeled as nonlocal double circular cylindrical elastic shells. On the basis of nonlocal elasticity theory, governing equations for buckling of Donnell shells are obtained taking into account the Van der Waals force. The nonlocal buckling load of DWCNT is derived without any assumption on radius tubes. However, it is a very difficult task to obtain the analytical solution of nonlocal critical buckling load. In this paper, we develop an approach for prediction of the nonlocal critical buckling load of DWCNTs.

Свободные интерфейсные и краевые колебания тонких упругих круговых цилиндрических oболочек со свободными торцами.

Свободные интерфейсные и краевые колебания тонких упругих круговых цилиндрических oболочек со свободными торцами.

Nonlinear stability of elastic elliptical cylindrical shells under uniform bending

Cylindrical metal shells with elliptical cross-sections are gaining increasing popularity as hollow sections due to their unique aesthetic appearance and different geometric properties about their two principal axes, with one axis exhibiting properties that are significantly more favourable than the other under flexure. However, in comparison with other hollow geometries, elliptical cross-sections have only recently begun receiving significant research attention. This is partly because even simple analytical treatments inevitably encounter cumbersome elliptical integrals that have no closed-form solutions, a problem now attenuated by powerful modern computing capabilities.A recent computational study investigated the nonlinear buckling resistance of perfect elastic circular cylindrical shells under uniform bending, establishing four distinct length-dependent domains of behaviour and characterising these in compact form using specially chosen dimensionless parameters. The present study extends this work to cylinders with elliptical cross-sections under bending about both principal axes. The same qualitative domains of length-dependent nonlinear elastic behaviour are found as for circular cylinders, but requiring a different algebraic characterisation that takes account of the varying elliptical radii. On the basis of computational results, a reference equation for the moment governing the ‘Brazier’ ovalisation cross-sectional failure mode for long elliptical thin-walled cylinders is deduced and presented for publication for the first time.

Theoretical Study on Fluid Velocity for Viscous Fluid in a Circular Cylindrical Shell

A theoretical algorithm by united Lagrangian-Eulerian method for the problem in dealing with viscous fluid and a circular cylindrical shell is presented. In this approach, each material is described in its preferred reference frame. Fluid flows are given in Eulerian coordinates whereas the elastic circular cylindrical shell is treated in a Lagrangian framework. The fluid velocity in a two-dimensional uniform elastic circular cylindrical shell filled with viscous fluid is studied under the assumption of low Reynolds number. The coupling between the viscous fluid and the elastic circular cylindrical shell shows kinematic conditions at the shell surface. Also, the radial velocity and axial velocity of the fluid are discussed with the help of graphs.

ANALYTICAL PERTURBATION METHOD FOR CALCULATION OF SHELLS BASED ON 2D PADÉ APPROXIMANTS

Calculations of nonlinear displacements and vibrations of inhomogeneous loaded shells with developable principal surface by means of different analytical methods are represented. It is shown that solutions to these methods are the expansions of exact solution in the Taylor series for an independent variable, and in the particular case — for the powers of a natural parameter. A method that provides a polynomial asymptotic approximation of the exact solution of the general form and its meromorphic continuation based on 1D and 2D Padé approximations is proposed. Calculations of nonlinear deformation and stability of elastic flexible circular cylindrical shell under uniform external pressures and of free oscillations of simply supported stringer shell demonstrate the efficiency and accuracy of the proposed method.

Dynamics of a cylindrical shell with a locally damaged protective coating

An approximate solution of a problem on the dynamic behavior of a thin elastic circular cylindrical shell with the damaged heat-protective layer section is presented. The influence of the fracture zone size and its mass on the frequencies of shell natural vibrations and its dynamic deflections is analyzed.

Stability analysis of cylindrical shells containing a fluid with axial and circumferential velocity components

The stability of an elastic circular cylindrical shell of revolution interacting with a compressible liquid (gas) flow having both axial and tangential components is analyzed. The behavior of the fluid is studied within the framework of potential theory. The elastic shell is described in terms of the classical theory of shells. Numerical solution of the problem is performed using a semianalytical finite element method. Results of numerical experiments for shells with different boundary conditions and geometric dimensions are presented. The effects of fluid rotation on the critical flow velocity and the effect of axial fluid flow on the critical angular velocity of fluid rotation were estimated.

Wave propagation in and free vibrations of gradient elastic circular cylindrical shells

The governing equations of motion for a gradient elastic circular cylindrical thin shell are derived. The basic equations of dynamic equilibrium and strain-displacement relations due to Donnell are combined with the stress–strain equations of the gradient theory of elasticity involving one microstructural and one microinertial elastic constant in addition to the two classical elastic moduli. The shell governing equations of motion are first used to study the propagation of harmonic waves and then free vibrations for the particular case of a circular cylindrical shell simply supported at its two ends. The results of these analyses are compared against those of the classical case in order to assess the microstructural and microinertial effects on the dynamic behavior of the shell.

Reduction of Flexural Vibration of Railway Vehicle Carbody Utilizing Multi-Axis Deformation of Elastic Body

Recent railway vehicle carbodies are getting light-weight and structurally-simplified in terms of speed-up and energy saving. They often lead to increase the vertical flexural vibration of carbody which causes deterioration of the ride comfort. Therefore, it has been required to reduce the flexural vibration. An elastic body deforming both vertical and horizontal direction in response to a vertical input has possibility to be a simple but effective vibration absorber, according to previous studies. This paper proposes a new numerical model called “equivalent deformation model” which is able to represent the vibration of such elastic body. The validity of the model is verified through excitation tests for elastic circular cylindrical shells filled with water. And its vibration reduction effect is examined using 1:5 scale model of a Shinkansen. It is confirmed that the equivalent deformation model is applicable for designing an elastic circular cylindrical shell as a dynamic vibration absorber (elastic DVA). And the first-mode of bending vibration of the scale model can be successfully reduced by utilizing the elastic DVA.

An Analytical Method for Cylindrical Shells With Nozzles Due to Internal Pressure and External Loads—Part I: Theoretical Foundation

An improved version of the analytical solutions by Xue, Hwang and co-workers (1991, “Some Results on Analytical Solution of Cylindrical Shells With Large Opening,” ASME J. Pressure Vessel Technol., 113, 297–307; 1991, “The Stress Analysis of Cylindrical Shells With Rigid Inclusions Having a Large Ratio of Radii,” SMiRT 11 Transactions F, F05/2, 85–90; 1995, “The Thin Theoretical Solution for Cylindrical Shells With Large Openings,” Acta Mech. Sin., 27(4), pp. 482–488; 1995, “Stresses at the Intersection of Two Cylindrical Shells,” Nucl. Eng. Des., 154, 231–238; 1996, “A Reinforcement Design Method Based on Analysis of Large Openings in Cylindrical Pressure Vessels,” ASME J. Pressure Vessel Technol., 118, 502–506; 1999, “Analytical Solution for Cylindrical Thin Shells With Normally Intersecting Nozzles Due to External Moments on the Ends of Shells,” Sci. China, Ser. A: Math., Phys., Astron., 42(3), 293–304; 2000, “Stress Analysis of Cylindrical Shells With Nozzles Due to External Run Pipe Moments,” J. Strain Anal. Eng. Des., 35, 159–170; 2004, “Analytical Solution of Two Intersecting Cylindrical Shells Subjected to Transverse Moment on Nozzle,” Int. J. Solids Struct., 41(24–25), 6949–6962; 2005, “A Thin Shell Theoretical Solution for Two Intersecting Cylindrical Shells Due to External Branch Pipe Moments,” ASME J. Pressure Vessel Technol., 127(4), 357–368; 2005, “Theoretical Stress Analysis of Two Intersecting Cylindrical Shells Subjected to External Loads Transmitted Through Branch Pipes,” Int. J. Solids Struct., 42, 3299–3319) for two normally intersecting cylindrical shells is presented, and the applicable ranges of the theoretical solutions are successfully extended from d/D≤0.8 and λ=d/(DT)1/2≤8 to d/D≤0.9 and λ≤12. The thin shell theoretical solution is obtained by solving a complex boundary value problem for a pair of fourth-order complex-valued partial differential equations (exact Morley equations (Morley, 1959, “An Improvement on Donnell’s Approximation for Thin Walled Circular Cylinders,” Q. J. Mech. Appl. Math. 12, 89–91; Simmonds, 1966, “A Set of Simple, Accurate Equations for Circular Cylindrical Elastic Shells,” Int. J. Solids Struct., 2, 525–541)) for the shell and the nozzle. The accuracy of results is improved by some additional terms to the expressions for resultant forces and moments in terms of complex-valued displacement-stress function. The theoretical stress concentration factors due to internal pressure obtained by the improved expressions are in agreement with previously published test results. The theoretical results discussed and presented herein are in sufficient agreement with those obtained from three dimensional finite element analyses for all the seven load cases, i.e., internal pressure and six external branch pipe load components involving three orthogonal forces and the respective three orthogonal moments.

On Inhomogeneous Deformations in ES Materials

Electro-sensitive (ES) elastomers or electro-rheological (ER) elastomers deform under the application of an electric field and their mechanical properties can be changed rapidly under the influence of electric field. The present paper deals with inhomogeneous deformations in ES elastomers. We have solved two problems namely inhomogeneous shearing deformation of a slab and inhomogeneous radial expansion and longitudinal shearing of an isotropic incompressible elastic circular cylindrical shell in the presence of electric field.

Stability analysis of gradient elastic circular cylindrical thin shells

The governing equation of equilibrium of gradient elastic circular cylindrical thin shells under axial compressive forces is explicitly derived. This is accomplished by appropriately combining the equations of equilibrium and the strain–displacement relations according to Donnell’s theory and the stress–stain equations of a simple strain gradient elastic theory with just one constant (the internal length squared) in addition to the classical elastic moduli. The resulting partial differential equation in terms of the radial displacement of the shell is of the tenth order instead of the eighth, for the classical elastic case. The boundary value problem of buckling of a circular cylindrical shell with simply supported ends is solved analytically and the critical loading is obtained analytically–numerically. An assessment of the effect of the gradient coefficient (internal length) on the buckling load is made by comparing that load against the classical one.

Shear-Horizontal Vibration of an Elastic Circular Cylindrical Shell With Two Piezoelectric Transducers

We analyze the excitation and detection of shear-horizontal vibrations in a circular cylindrical elastic shell with 2 piezoelectric actuators, one for excitation and the other for detection. The equations of linear elasticity and linear piezoelectricity are used. The mathematical problem is solved using trigonometric series. Basic vibration characteristics including resonant frequencies, mode shapes, and electric output are calculated. It is found that significant responses occur near resonances. The displacement distribution in the elastic shell is particularly strong under and close to the exciting transducer.

Fluid–structure interaction during the impact of a cylindrical shell on a thin layer of water

Abstract A two-dimensional unsteady analysis of an elastic circular cylindrical shell that enters a thin layer of an ideal incompressible liquid is considered. The cylinder initially touches the liquid free surface at a single point and then penetrates the liquid layer at a constant vertical velocity. The problem is coupled because the liquid flow, the shape of the elastic shell and the geometry of the contact region between the body and the liquid must be determined simultaneously. The flow region is subdivided into four complementary regions that exhibit different properties: the region beneath the entering body surface, the jet root, the spray jet, and the outer region. A complete solution is obtained by matching the solutions within these four subdomains. The structural analysis is based on the normal-mode method. Strain-time histories of the inner surface of the cylinder are of particular interest. In the case of a very flexible shell three distinct regimes of the impact process were found. For a high impact velocity the lower part of the shell flattens and the shell does not enter the water. For a moderate impact velocity the shell reaches the bottom and an effect of “fluid capture” may occur. For a low impact velocity the shell penetrates the liquid, but the size of the contact region decreases before the shell reaches the bottom. This behaviour corresponds to exit or “reflection” of the shell from the water layer.

Electrically forced shear horizontal vibration of a circular cylindrical elastic shell with a finite piezoelectric actuator

We analyze anti-plane vibrations of a circular cylindrical elastic shell electrically driven by a piezoelectric actuator. The equations of linear elasticity and linear piezoelectricity are used. The mathematical problem is solved using trigonometric series. Basic vibration characteristics including resonant frequencies, mode shapes and electric admittance are calculated.

Natural vibrations of a cantilever thin elastic orthotropic cylindrical shell

The natural vibrations of a cantilever thin elastic orthotropic circular cylindrical shell are studied. Dispersion equations for the determination of possible natural frequencies of cantilever closed shells and open shells with Navier hinged boundary conditions at the longitudinal edges are derived from the classical dynamic theory of orthotropic cylindrical shells. It is proved that there are asymptotic relationships between these problems and the problems for a cantilever orthotropic strip plate and for a cantilever rectangular plate and the eigenvalue problem for a semi-infinite closed orthotropic cylindrical shell with free end and for the same but open shell with Navier hinged boundary conditions at the longitudinal edges. A procedure to identify types of vibrations is presented. Orthotropic cylindrical shells with different radii and lengths are used as an example to find approximate values of the dimensionless natural frequency and damping factor for vibration modes