Cylindrical Shell Of Finite Length Research Articles

Investigation of sound transmission through a finite length cylindrical shell in the presence of an exterior turbulent boundary layer

This paper studies sound transmission through a thin cylindrical shell of finite length. The structure is subjected to an exterior turbulent boundary layer (TBL) excitation and the boundary conditions of its two ends are considered as simply-supported. The classical shell theory (CST) is employed to derive wave propagation in the cylindrical shell, and the Corcos model is applied to describe pressure fluctuation due to TBL. According to the existence of two axial and radial modes, a complete convergence study is presented. To examine sound transmission through the structure, a comprehensive parameters study is provided on the resulting power spectral density (PSD) of the kinetic energy. To validate the results of the present method, the statistical energy analysis (SEA) method is used. For this purpose, modeling is performed by SEA in VA One software, which shows the high accuracy of the results of the present method. The analytical predictions suggest that the sound insulation performance of such a finite length structure is enhanced considerably by increasing the thickness of the shell in a broad-band frequency range. Similar effects on sound transmission are observed for Young’s modulus and density of the shell particularly in the low and high-frequency ranges, respectively. Whereas, enhancing the turbulent pressure and freestream velocity adversely affects sound radiation into the structure.

Thermoelastic Analysis of Functionally Graded Cylindrical Shells

We perform the analytic investigation of the stress-strain state of a functionally graded cylindrical shell of finite length heated by a two-dimensional temperature field. The properties of the shell material are regarded as analytic functions of the thickness coordinate. In our investigations, we use the equations of the refined theory of shells that takes into account the deformation of transverse shear and the transverse normal deformation. The heat-conduction equation is deduced under the assumption of linear temperature distribution over the thickness of the shell. For the boundary conditions of simply supported shell, the quasistatic uncoupled problem of thermoelasticity is solved by the methods of Fourier and Laplace transforms. Numerical examples are presented and discussed to show that it is important to take into account the influence of inhomogeneity of the properties of materials of the metal–ceramics composites.

Influence of Fluid in Dynamic Calculation of Thin-Walled Cylindrical Tanks by Means of Calculating Added Masses of Fluid

This paper presents the exact solution for the problem of the added masses of fluid, oscillating inside a cylindrical tank. A thin smooth cylindrical shell of finite length, filled with the ideal incompressible fluid that is subjected to transient dynamic load (it may be an earthquake, air explosion impact, etc.), is taken as a design model. In this case, the shell of a tank becomes a part of the oscillating process along with the fluid stored inside. The shell bending equation (stipulated by the membrane theory of shells) is taken as a design model for this case. In this equation, the shell deflection is expanded into Fourier series by oscillation modes, and the velocity potential takes the form of the Laplace’s equation. Fluid’s inertial reaction to the shell motion is covered by the shallow water theory, which is specified by the boundary free surface conditions and the influence of the tank hard bottom. These mathematical expressions of the shell response to the external transient impact are solved by the Bubnov–Galerkin method with the transformation of the initial relations into a system of ordinary differential equations, which include expressions for determining added masses of fluid by oscillation modes of the elastic shell.

Vibration and Stability of Coaxial Cylindrical Shells with a Gap Partially Filled with Liquid

AbstractThe problem of vibration and stability of coaxial circular cylindrical shells of finite length is considered when the region between the shells is partially filled with an incompressible li...

Cylindrical Shell of Finite Length with Low Shear Stiffness Under the Action of Local Heat Sources

We consider a quasistatic problem of thermoelasticity for a cylindrical shell of finite length in a variable temperature field. The surface of the shell exchanges heat with the ambient medium of constant temperature according to Newton’s law. The problem is solved with regard for the shear strains. The asymptotic state of the shell in which the computed quantities attain their maximal values is studied in detail. We also perform the comparative analysis of the thermoelastic state of the shell of finite length and the corresponding state of a shell of infinite length.

Calculation of nonlinear elastic three-layer cylindrical shell of finite length with taking into account the continuous inhomogeneity caused by the temperature field

The article deals with the problem of determining the stressstrain state of a thick-walled cylindrical shell hinged on the rim near the ends, which is exposed to temperature effects. The shell consists of three layers: two layers of heat-resistant concrete and a steel outer layer. The calculation takes into account the continuous inhomogeneity of materials caused by a stationary temperature field, as well as the nonlinear nature of concrete deformation. The nonlinear problem with variable parameters of elasticity E and ν was solved by the method of successive approximations.

Cross-Like Surface Waves Between Finite Cylindrical Shells

We construct a new mathematical model of the interaction of two resonant surface waves in a volume between two cylindrical shells of finite length. For the first time, we establish the existence of chaotic attractors for a system satisfying the resonance conditions for cross-like and forced waves. We also study the regular modes in the system and describe their phase portraits and frequency spectra.

Magnetic field created by a conducting cylindrical shell of finite length

A conceptually simple result, which was recently derived for the circulation of the magnetic field created by a finite portion of wire carrying a slowly varying current, is used with the superposition principle and symmetry considerations to obtain an expression for the magnetic field of a thin cylindrical shell of finite length. This expression is combined with a new formula for an oblique solid angle, to obtain closed form solutions for the magnetic field created by the thin cylindrical shell segment in all regions of space. The solutions derived herein are applied in the limiting situations where the cylindrical shell’s length or radius is very large and compared to the known results for the magnetic field of a long conducting tube, and of an infinite plane, respectively. In addition, the use of physical principles of superposition and symmetry in this study is instructive from an educational perspective.

Large-Amplitude Vibration Analysis of 3D Braided Composite Cylindrical Shells in an Elastic Medium

AbstractLarge-amplitude vibration analysis for a three-dimensional (3D) braided composite cylindrical shell of finite length subjected to static or periodic axial forces has been presented. Based on a new micro-macro-mechanical model, a 3D braided composite may be treated as a cell system, which has been introduced as a representative cell of a 3D braided composite and its components, and the geometry of each cell is deeply dependent on its position in the cross section of the cylindrical shell. The shell is embedded in an elastic medium, which is modeled as a Pasternak elastic foundation. The motion equations are based on a higher-order shear deformation shell theory with a von Karman-Donnell–type of kinematic nonlinearity. A two-step perturbation technique is used to determine the linear and nonlinear frequency and parametric resonances of the 3D braided cylindrical shells. The numerical illustrations concern the nonlinear vibration behavior of braided composite cylindrical shells with different values ...

Stability of Differently Fixed Composite Cylindrical Shells Interacting with Fluid Flow

The problem of the stability of a fluid-conveying pipeline modeled by a composite orthotropic cylindrical shell of finite length with different boundary conditions at the ends is solved. The shell is subject to hydrodynamic pressure and uniform external static load. The effect of boundary conditions of the shell under external loading on the qualitatively different types of instability, quasistatic (divergence) and dynamic (flutter), that occur at certain “critical” velocities of the fluid is studied

Buckling and postbuckling of anisotropic laminated cylindrical shells under combined external pressure and axial compression in thermal environments

The buckling and postbuckling analysis for an anisotropic laminated thin cylindrical shell of finite length subjected to combined loading of external pressure and axial compression using the boundary layer theory is presented. The material of each layer in the shell is assumed to be linearly elastic, anisotropic and fiber-reinforced. The governing equations are obtained utilizing classical shell theory and von Kármán–Donnell strain displacement relations. The nonlinear prebuckling deformations and initial geometric imperfections of the shell are both taken into account. A boundary layer theory of shell buckling, which includes the effects of nonlinear prebuckling deformations, large deflections in the postbuckling range, and initial geometric imperfection of the shell, is extended to the case of anisotropic laminated thin cylindrical shells under combined loading cases. A singular perturbation technique is employed to determine interactive buckling loads and postbuckling equilibrium paths. Postbuckling response of perfect and imperfect, anisotropic laminated cylindrical shells with respect to the material and geometric properties and load-proportional parameters under different sets of thermal environmental conditions is numerically illustrated. The analytical model developed can be used as a versatile and accurate tool to study the buckling and postbuckling behavior of composite structures.

Beam-Column and Tie-Bar Effects in Internally Pressurized Thin Arbitrarily Laminated Cantilever Cylindrical Shells

An arbitrarily laminated, anisotropic cantilever cylindrical shell of finite length, under uniform internal pressure, is analyzed using kinematic relations under the framework of classical lamination theory. Extensive numerical results are presented for two model problems, pertaining to two-layer, asymmetrically laminated, anisotropic cantilever cylindrical shells, illustrating the influence of layer anisotropy and lamination sequence on the beam-column/tie-bar effects, which, in turn, severely affect the free-end displacements and other response quantities of interest. Furthermore, because the beam-column effect can cause severe wrinkling in a thin asymmetrically laminated cylindrical shell, the possibility of its elimination through composite tailoring (a combination of stacking sequence and fiber orientation angle in a constituent lamina) has also been explored. Finally, the effect of length-to-radius ratio is also numerically investigated.

Nonlinear vibration analysis of geodesically-stiffened laminated composite cylindrical shells in an elastic medium

Nonlinear free vibration and parametric resonance analysis for a geodesically-stiffened anisotropic laminated thin cylindrical shell of finite length subjected to static or periodic axial forces using the boundary layer theory is presented. The shell is embedded in an elastic medium which is modeled as a Pasternak elastic foundation. The material of each layer of the shell is assumed to be linearly elastic, anisotropic and fiber-reinforced. The equations of motion are developed using the Donnel shell theory with a von Kármán-type of kinematic nonlinearity, and the shell-foundation interaction and the extension-shear, extension-flexural and flexural-twist couplings are included. A two-step perturbation technique is employed to determine the linear and nonlinear frequency and parametric resonance of the geodesically-stiffened anisotropic laminated cylindrical shells. The numerical analysis involves the nonlinear vibration behavior of laminated composite cylindrical shells with respect to the material properties and the influences of initial stress, geometric shell characteristics (i.e., radius, length and thickness, including geodesic, axial and ring stiffeners), and stacking sequence. The results reveal that the shell geometric parameters, elastic medium, and periodic axial excitation have a significant effect on the nonlinear vibration behavior of anisotropic laminated composite cylindrical shells.

Two-dimensional theory of piezoelectric shells considering surface effect

Two-dimensional (2D) general equations of piezoelectric shells with nano-thickness are presented in an orthogonal curvilinear coordinate system, in which the surface effect is considered by treat the shell as a bulk core plus two surface layers. The general 2D equations can be directly degenerated into those of particular shells such as flat plates, cylindrical shells and so on by setting the Lamé coefficients and the principal radii of curvature to certain values. Using the derived 2D equations of cylindrical shells, the free vibration of a radially polarized piezoelectric cylindrical shell of finite length is analyzed. Numerical results show that the surface effect has a remarkable influence on the natural frequency of the shell at the nano-scale.

Цилиндрические оболочки конечной длины под внешним давлением

Цилиндрические оболочки конечной длины под внешним давлением

Thermal Postbuckling of Shear Deformable FGM Cylindrical Shells Surrounded by an Elastic Medium

AbstractThis paper presents a study on the thermal postbuckling response of a shear deformable functionally graded cylindrical shell of finite length embedded in a large outer elastic medium. The surrounding elastic medium is modeled as a Pasternak foundation. Two kinds of micromechanics models, namely the Voigt model and Mori-Tanaka model, are considered. The governing equations are based on a higher-order shear deformation shell theory that includes shell-foundation interaction. The thermal effects are also included and the material properties of functionally graded materials (FGMs) are assumed to be temperature dependent. The governing equations are solved by a singular perturbation technique. The numerical results show that in some cases the FGM cylindrical shell with intermediate volume fraction index does not have intermediate buckling temperature and thermal postbuckling strength. The results reveal that Voigt model and Mori-Tanaka model have the same accuracy for predicting the thermal buckling an...

Postbuckling of Axially-Loaded Laminated Cylindrical Shells Surrounded by an Elastic Medium

This article investigates the buckling and postbuckling behavior of an anisotropic laminated cylindrical shell of finite length embedded in a large outer elastic medium and subjected to axial compressive loads in thermal environments. The surrounding elastic medium is modeled as a tensionless Pasternak foundation that reacts in compression only. The governing equations are based on a higher order shear deformation shell theory with von Kármán-type of kinematic nonlinearity and including the extension-twist, extension- flexural, and flexural-twist couplings. The thermal effects are also included and the material properties are assumed to be temperature-dependent. The nonlinear prebuckling deformations and the initial geometric imperfections of the shell are both taken into account. A singular perturbation technique is employed to determine the postbuckling response of the shells and an iterative scheme is developed to obtain numerical results without using any assumption on the shape of the contact region between the shell and the elastic medium. Numerical illustrations concern the buckling and postbuckling response of laminated cylindrical shells surrounded by an elastic medium of tensionless Pasternak foundation, from which the postbuckling results for laminated shells with conventional elastic foundations are also obtained for comparison purposes. The results reveal that the unilateral constraint has a significant effect on the postbuckling response of shells subjected to axial compression in thermal environments when the foundation stiffness is sufficiently large.

Thermal postbuckling of shear-deformable anisotropic laminated cylindrical shells with temperature-dependent properties

Thermal postbuckling analysis is presented for shear-deformable anisotropic laminated cylindrical shell of finite length. The temperature field considered is assumed to be a uniform or non-uniform parabolic temperature distribution varying in the circumferential or axial direction. Temperature-dependent material properties are taken into account. The governing equations are based on Reddy's higher order shear deformation shell theory with von Karman-Donnell-type of kinematic non-linearity and including the extension/torsion, extension/flexure, flexure/torsion couplings and thermal effects. The non-linear prebuckling deformations and initial geometric imperfections of the shell are both taken into account. A singular perturbation technique is employed to determine the buckling temperature and postbuckling load-deflection curves. The numerical illustrations concern the postbuckling response of perfect and imperfect, anisotropic laminated cylindrical shells with different values of shell parameters and stacking sequence. The results confirm that there exists a compressive stress along with an associated shear stress and torsional effect when the anisotropic shell is subjected to thermal loads. They also confirm that the thermal postbuckling equilibrium path is stable or weakly unstable for the moderately long cylindrical shell and the shell structure is virtually imperfection- insensitive.

Influence of external loading on the stability of a fluid-conveying pipeline

A section of a fluid-conveying pipeline is analyzed for stability. The section is modeled by an elastic cylindrical shell of finite length under external static loading. Two qualitatively different instability modes are studied: “quasistatic” (divergence) and dynamic (flutter). The effect of uniform radial pressure and uniform axial pressure on the instability modes is analyzed

Nonlinear vibration of shear deformable FGM cylindrical shells surrounded by an elastic medium

This paper investigates the large amplitude vibration behavior of a shear deformable FGM cylindrical shell of finite length embedded in a large outer elastic medium and in thermal environments. The surrounding elastic medium is modeled as a Pasternak foundation. Two kinds of micromechanics models, namely, Voigt model and Mori–Tanaka model, are considered. The motion equations are based on a higher order shear deformation shell theory that includes shell-foundation interaction. The thermal effects are also included and the material properties of FGMs are assumed to be temperature-dependent. The equations of motion are solved by a two step perturbation technique to determine the nonlinear frequencies of the FGM shells. Numerical results demonstrate that in most cases the natural frequencies of the FGM shells are increased but the nonlinear to linear frequency ratios of the FGM shells are decreased with increase in foundation stiffness. The results confirm that in most cases Voigt model and Mori–Tanaka model have the same accuracy for predicting the vibration characteristics of FGM shells.