Mechanical buckling of functionally graded material cylindrical shells surrounded by Pasternak elastic foundation

In this study, the mechanical buckling of functionally graded material cylindrical shell that is embedded in an outer elastic medium and subjected to combined axial and radial compressive loads is investigated. The material properties are assumed to vary smoothly through the shell thickness according to a power law distribution of the volume fraction of constituent materials. Theoretical formulations are presented based on a higher-order shear deformation shell theory (HSDT) considering the transverse shear strains. Using the nonlinear strain–displacement relations of FGMs cylindrical shells, the governing equations are derived. The elastic foundation is modelled by two parameters Pasternak model, which is obtained by adding a shear layer to the Winkler model. The boundary condition is considered to be simply-supported. The novelty of the present work is to achieve the closed-form solutions for the critical mechanical buckling loads of the FGM cylindrical shells surrounded by elastic medium. The effects of shell geometry, the volume fraction exponent, and the foundation parameters on the critical buckling load are investigated. The numerical results reveal that the elastic foundation has significant effect on the critical buckling load.     

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.     

Fabrication of thin wall cylindrical shells by sputtering

In this paper we describe the process used to grow thin wall cylindrical shells by sputtering. The shells are grown on both sacrificial aluminum and reusable stainless steel mandrels. The post-deposition process used to remove the shells from the mandrels is described. The effects of deposition conditions and post-deposition treatment on crystallographic structure are presented. Comparisons of sputtered shells are made with conventionally machined shells with respect to crystallography, dimensional uniformity and performance. Some test results of sputtered thin wall cylindrical shells used as pressure-sensing elements are given.     

Twin-characteristic-parameters analysis for elastic dynamic buckling of thin cylindrical shells under axial step loading

The relations of the critical stress and transverse inertia effect to the loading duration are investigated for the dynamic buckling of thin cylindrical shells under axial step loading. The critical stress and the inertial exponent are treated as the two characteristic parameters. The criterion of energy conservation is used to derive the supplementary restraint condition for buckling deformations at compression wave front. By use of the Galerkin method, an algebraic eigenvalue problem for the two characteristic parameters is derived from the governing equations and boundary conditions. The solution of the eigenvalue problem, which satisfies the supplementary restraint condition, gives the values of the critical stress and the inertial exponent for the dynamic buckling. The relation of critical stress to loading duration, predicted by the theoretical analysis, is in reasonable agreement with the experimental results.     

The general theory of thin elastic shells

Variationsl methods can consistently be used to derive the equations of shell theory, by introducing a finite number of internal constraints. A systematic derivation of particular nonlinear and linear theories becomes then possible. Variational methods serve also to prove the existence and in some cases the uniqueness of the solution. They provide also with error estimates.     

Impact of nonlocal thin elastic plates by a cylindrical projectile

This paper is concerned with the analysis of the problem of dynamic impact of an elastic thin plate by a cylindrical projectile. The behavior of the plate material is assumed to be nonlocal elastic, and the effect of the impact is represented by a uniform velocity distribution over a circular region of the plate surface. Assuming the plate is thin, only the contributions of vertical shearing stress are considered, and the expressions of shear stress, axial displacement and the corresponding velocity components are obtained. Finally, the value of the total strain energy—crack initiation energy—for which the plastic flow will start, has been calculated and compared with experiments.     

Vibrations of functionally graded cylindrical shells based on elastic foundations

In this paper, a study on the vibrations of functionally graded cylindrical shells based on the Winkler and Pasternak foundations is presented. The shell equations are amended by inducting the moduli of the Winkler and Pasternak foundations. The wave propagation method is employed to solve the shell dynamical equations. The method is based on the approximate eigenvalues of characteristic beam functions. The validity and accuracy of the present approach are verified by a number of comparisons.     

Vibration characteristics of fluid-filled cylindrical shells based on elastic foundations

In this paper, vibrations of fluid-filled isotropic circular cylindrical shells are studied based on elastic foundations. The wave propagation approach is employed to solve the shell problem. This approach is formulated by approximating the eigenvalues of the characteristic beam functions. Vibrations of natural frequencies for both empty and fluid-filled cylindrical shells based on elastic foundations are evaluated and their comparisons are performed to confirm the validity and accuracy of the present method. An excellent agreement has been found between the present and previous ones available in the literature. It is observed that frequencies are strongly affected when a cylindrical shell is attached with elastic foundations.     

转动薄壁圆柱壳行波振动响应分析

考虑由转动引起的科氏力、离心惯性力及环向初应力影响,利用Hamilton原理,建立了基于Sanders壳体理论的转动薄壁圆柱壳振动微分方程。选取满足相应边界条件的轴向梁函数近似地表达各类边界条件下圆柱壳的轴向振型分布。在此基础上,提出了一种适用于求解各种边界约束的转动薄壁圆柱壳行波振动响应的方法。基于此方法,分别针对静坐标系下横向简谐力和恒力作用下的两端固支转动薄壁圆柱壳的行波振动响应进行了求解,并对结果进行了相应分析。     

Axisymmetric response of nonlinearly elastic cylindrical shells to dynamic axial loads

The axisymmetric response of nonlinearly elastic cylindrical shells subjected to dynamic axial loads is analysed by using an incremental formulation. The material elastic nonlinearity is modeled by the generalized Ramberg—Osgood representation. The time-dependent displacements of the shell are assumed to be governed by nonlinear equations of motion based on the von Karman—Donnell kinematic relations; moreover, both in-surface and out-of-surface inertia terms are included. The finite difference method with respect to the spatial coordinate and the Runge—Kutta method with respect to time are employed to derive a solution. Numerical results demonstrate the effect of the material nonlinearity on the deflections, stiffness matrices and dynamic buckling behavior of cylindrical shells.     

The elastic response of functionally graded cylindrical shells to low-velocity impact

This paper deals with the problem of functionally graded (FG) cylindrical shells subjected to low-velocity impact by a solid striker. An analytic solution to predict the impact response of the FG cylindrical shells with one layer or multi-layers is presented. The solution includes both contact deformation and transverse shear deformation. The effective material properties of functionally graded materials (FGMs) for the cylindrical shells are assumed to vary continuously through the shell thickness and are graded in the shell thickness direction according to a volume fraction power law distribution. This is implemented in the governing equation of motion and thus included in the present solution. Four types of FG cylindrical shells composed of stainless steel and silicon nitride are configured and their transient responses to impact are computed using the present solution. The effects of the constituent volume fraction and the FGM configuration on the transient response of the laminated cylindrical shell induced by impact are examined.     

On finite axi-symmetrical deformations of thin elastic shells of revolution

We derive a generalized version of the known system of two simultaneous second order differential equations for the problem of axi-symmetric torsionless deformations of elastic shells of revolution, for finite deformations and including transverse shear deformations and membrane drilling moments. Our generalization, which involves the introduction of a semicomplementary energy density, comes out in a particularly simple and compact form. We furthermore consider the effect of transverse normal stress deformations and discover the possibility of reducing this problem to a system of three simultaneous second order equations, with the supplementary third equation harmoniously adding itself to the two equations without consideration of transverse normal stress deformation effects.     

Wave propagation in a cylindrical viscous layer between two elastic shells

Propagation of longitudinal waves in a liquid-filled layer between two thin coaxial shells is investigated. Both liquid viscosity and elasticity of the shells are accounted for. Dynamics of the shells is treated using the Kirchhoff–Love approximation. The elastic deformations of the shells in the sound wave are coupled with the liquid flow in the gap through appropriate dynamic and kinematic boundary conditions. Hydrodynamics of the liquid is described using the quasi-one-dimensional (hydraulic) approach. It is assumed that the external and internal shells are composed of different isotropic elastic materials and have different widths. The dispersion equation for harmonic waves in the system is obtained; it is valid in the low frequency range where the wave length is greater than the external shell radius. In the limiting case for an ideal liquid the dispersion equation yields water hammer speed in the system. The analysis of the dispersion equation has shown strong influence of viscous losses on dispersion and attenuation of pressure signals in the low frequency region. The wave speed and attenuation are highly dependent on the geometrical parameters of the system and elastic properties of the shells.