Vibration analysis of bi-layered FGM cylindrical shells

In the present study, a vibration frequency analysis of a bi-layered cylindrical shell composed of two independent functionally graded layers is presented. The thickness of the shell layers is assumed to be equal and constant. Material properties of the constituents of bi-layered functionally graded cylindrical shell are assumed to vary smoothly and continuously through the thickness of the layers of the shell and are controlled by volume fraction power law distribution. The expressions for strain–displacement and curvature–displacement relationships are utilized from Love’s first approximation linear thin shell theory. The versatile Rayleigh–Ritz approach is employed to formulate the frequency equations in the form of eigenvalue problem. Influence of material distribution in the two functionally graded layers of the cylindrical shells is investigated on shell natural frequencies for various shell parameters with simply supported end conditions. To check the validity, accuracy and efficiency of the present methodology, results obtained are compared with those available in the literature.     

Solution of axisymmetric dynamic problems for cylindrical shells on an elastic foundation

A dynamic problem for a cylindrical shell on an elastic foundation is formulated. A numerical algorithm for solving this problem is outlined. The results obtained are analyzed __________ Translated from Prikladnaya Mekhanika, Vol. 43, No. 12, pp. 103–109, December 2007.     

Interaction of an infinite thin elastic cylindrical shell and a pulsating spherical inclusion in potential flow of ideal compressible liquid: internal axisymmetric problem

The paper proposes a method to analyze the behavior of a mechanical system consisting of an infinite thin cylindrical shell filled with a flowing compressible liquid and containing a pulsating spherical inclusion. This coupled problem is solved using linear potential flow theory and the theory of thin elastic shells based on the Kirchhoff–Love hypotheses. Use is made of the possibility to represent the general solutions of equations of mathematical physics in different coordinate systems. This makes it possible to satisfy the boundary conditions on both spherical and cylindrical surfaces and to obtain a solution in the form of a Fourier series. Some numerical results are given     

Dynamics of an elastic half-space with a reinforced cylindrical cavity under moving loads

Partial separation of variables and reexpansion of cylindrical and plane waves are used to find the solution describing the uniform motion of a load along a thin circular cylindrical shell in an elastic half-space with the free surface parallel to the axis of the shell. This is a model problem for studying the dynamics of tunnels and shallow-buried pipelines under transport loads. Dispersion curves for the cases of sliding and tight contact between the shell and the half-space are plotted and analyzed. The effect of the shell parameters on the stress–strain state of the half-space is examined     

Nonlinear vibrations of viscoelastic cylindrical shells taking into account shear deformation and rotatory inertia

The vibration problem of a viscoelastic cylindrical shell is studied in a geometrically nonlinear formulation using the refined Timoshenko theory. The problem is solved by the Bubnov–Galerkin procedure combined with a numerical method based on quadrature formulas. The choice of relaxation kernels is substantiated for solving dynamic problems of viscoelastic systems. The numerical convergence of the Bubnov–Galerkin procedure is examined. The effect of viscoelastic properties of the material on the response of the cylindrical shell is discussed. The results obtained by various theories are compared.     

Explosive projection of liquid from a thick-walled cylindrical container

The process of projection of a layer of an ideal liquid enclosed into a cylindrical elastoplastic shell by products of instantaneous detonation of a high explosive charge is studied numerically in a two-dimensional plane formulation. The processes of shell fracture and liquid exhaustion through the resultant slots are considered. Numerical results are analyzed, and analytical relations for angular distributions of radial velocity and mass of the liquid escaping through the slots are derived. __________ Translated from Prikladnaya Mekhanika i Tekhnicheskaya Fizika, Vol. 50, No. 3, pp. 56–63, May–June, 2009.     

The plane problem on vertical impact of a rotating circular cylindrical shell against the surface of a liquid

The plane nonsymmetric problem on impact against and immersion into a compressible fluid of a thin electic cylindrical shell is considered. The shell rotates about its axis with a given angular velocity. The boundary-value problem is reduced to an infinite system of integral Volterra equations of the second kind. Translated from Prikladnaya Mekhanika, Vol. 36, No. 5, pp. 103–113, May, 2000.     

Solution of the deformation problem for flexible noncircular cylindrical shells subject to bending moments at the edges

An exact analytical solution is found to a nonlinear boundary-value deformation problem for a long noncircular cylindrical shell of variable curvature. The shell is subject to bending moments at the edges. The dependence of the stress-strain state of the shell on the curvature is analyzed __________ Translated from Prikladnaya Mekhanika, Vol. 42, No. 11, pp. 93–100, November 2006.     

Longitudinal impact on the end of a rigid cylindrical shell with an elastic filler

The nonstationary problem on the axisymmetric antiplane deformation of a hollow cylinder due to a longitudinal impact on the end of the rigid cylindrical shell is considered. The solution of the boundary-value problem is reduced to a system of Volterra integral equations of the second kind. A numerical analysis is carried out and its results are plotted. S. P. Timoshenko Institute of Mechanics, National Academy of Sciences of Ukraine, Kiev. Translated from Prikladnaya Mekhanika, Vol. 36, No. 5, pp. 98–102, May, 2000     

Deformation of flexible noncircular cylindrical shells under concurrent loads of two types

The paper presents an exact analytic solution to a nonlinear boundary-value problem for a long noncircular cylindrical shell with variable cross-sectional curvature under two concurrent loads: a surface force and bending moments. The behavior of the shell under these loads is analyzed __________ Translated from Prikladnaya Mekhanika, Vol. 43, No. 7, pp. 58–65, July 2007.     

Solution of a Problem of Free Vibrations of a Nonclosed Shell of Revolution under Conditions of its Singular Perturbation

We develop a variational method for solving the spectral problem of free vibrations of a shell of revolution nonclosed in the meridional direction. This method is equally efficient for both medium and small values of the relative thickness of the shell. Coordinate systems of functions are constructed with regard for the structure of formal asymptotic expansions of a fundamental system of solutions of the initial equations. As an example, we calculate frequencies and forms of vibrations of a circular cylindrical shell and show that the algorithm proposed for solving the considered problem guarantees the uniform convergence of solutions and their first three derivatives in the entire region of integration of the equations. __________ Translated from Neliniini Kolyvannya, Vol. 8, No. 3, pp. 415–432, July–September, 2005.     

Interaction Between an Oscillating Sphere and a Thin Elastic Cylindrical Shell Filled with a Compressible Liquid. Internal Axisymmetric Problem

The problem on the interaction between a spherical body that oscillates in a prescribed manner and a thin elastic cylindrical shell filled with an ideal compressible liquid is formulated. It is assumed that the geometrical center of the sphere is located on the cylinder axis. The problem is solved based on the possibility of representing a partial solution of the Helmholtz equation written in cylindrical coordinates in terms of partial solutions in spherical coordinates, and vice versa. By satisfying the boundary conditions on the surfaces of the sphere and the shell, we obtain an infinite system of linear algebraic equations to determine the coefficients of expansion of the liquid-velocity potential into a Fourier series in terms of Legendre polynomials. The hydrodynamic characteristics of the liquid filling the cylindrical shell are determined and compared with the cases where a sphere oscillates in an infinite liquid and in a rigid cylindrical vessel     

Nonlinear deformation and stability of oval cylindrical shells under pure bending and internal pressure

The stability problem of a cylindrical shell of oval cross section loaded by a bending moment and internal pressure is studied. The variational displacement finite-element method is used. For the prebuckling stress-strain state, the bending and nonlinearity are taken into account. The effects of the nonlinear nature of the deformation and the cross-sectional ovality of the shells on the critical loads and buckling modes are determined. __________ Translated from Prikladnaya Mekhanika i Tekhnicheskaya Fizika, Vol. 47, No. 3, pp. 119–125, May–June, 2006.     

Natural Vibrations of a Cylindrical Shell Reinforced with Two-Layer Rings

The vibrations of a cylindrical shell reinforced with ring ribs attached to the shell by means of elastic elements are studied. The problem is solved by the finite-element method. The shell and ribs are modelled by a plane four-node finite element, which is a combination of a four-node plane stress element and a four-node flexural element. The effect of the stiffness of the elastic elements on the natural frequencies and modes is examined __________ Translated from Prikladnaya Mekhanika, Vol. 41, No. 8, pp. 105–110, August 2005.     

Refined design of longitudinally corrugated cylindrical shells

A refined Timoshenko-type model based on the straight-line hypothesis is used to develop an approach to analyzing the stress state of longitudinally corrugated cylindrical shells with elliptic cross-section. The approach is to reduce the two-dimensional boundary-value problem that describes the stress–strain state of the shell to a one-dimensional one and to solve it with the stable numerical discrete-orthogonalization method. The solutions obtained using the straight-line hypothesis and the equations of three-dimensional elasticity are compared. The dependence of the stress–strain state of the shell on the number and amplitude of corrugations and the aspect ratio of the cross-section is analyzed     

Mass optimization of a compressed cylindrical shell with limited life

A new optimization model is proposed to design corrosion-affected structures with limited life. The optimization problem is stated as a nonlinear-programming problem. The mass of the structure is minimized. The design is considered optimal when physical wear and obsolescence arrive simultaneously. A smooth cylindrical shell compressed in the longitudinal direction is used to illustrate the model __________ Translated from Prikladnaya Mekhanika, Vol. 42, No. 3, pp. 97–101, March 2006.     

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 __________ Translated from Prikladnaya Mekhanika, Vol. 44, No. 5, pp. 68–91, May 2008.     

Study of nonlinear vibrations of cylindrical shells with allowance for energy dissipation

The problem of induced nonlinear harmonic vibrations of a cylindrical shell is solved with allowance for energy dissipation by using a binomial approximation of the displacements. There are several distinctive features of the behavior of the shell due to interaction of two modes of vibration. S. P. Timoshenko Institute of Mechanics, National Academy of Sciences of Ukraine, Kiev, Ukraine. Translated from Prikladnaya Mekhanika, Vol. 35, No. 2, pp. 30–35, February, 1999.     

Identification of nonstationary axisymmetric load distributed along a cylindrical shell

The paper outlines a procedure to identify the space-and time-dependent external nonstationary load acting on a closed circular cylindrical shell of medium thickness. Time-dependent deflections at several points of the shell are used as input data to solve the inverse problem. Examples of numerical identification of various nonstationary loads, including moving ones are presented. The relationship between the external load and the stress-strain state of the shell is described by the Volterra equation of the first kind. The identification problem is solved using Tikhonov's regularization method and Apartsin's h-regularization method __________ Translated from Prikladnaya Mekhanika, Vol. 44, No. 7, pp. 91–100, July 2008.