Dynamic stability of a viscoelastic orthotropic cylindrical shell

A method based on the use of Laplace transforms has been developed for reducing the system of equations of motion of a viscoelastic orthotropic cylindrical shell to a single integro-differential equation. The effect of the viscous components on the regions of dynamic instability is investigated (creep due to the action of the shear stresses is taken into account).Institute of Polymer Mechanics, Academy of Sciences of the Latvian SSR, Riga. Translated from Mekhanika Polimerov, No. 4, pp. 714–721, July–August, 1973.     

Effect of an elastic core on the dynamic stability of an orthotropic cylindrical shell

A method of determining the regions of dynamic instability of an orthotropic cylindrical shell "bonded" to an elastic cylinder is proposed. An expression for the core reaction is obtained from the coupling conditions for the forces normal to the lateral surface and the radial displacements of the shell and the core at the contact surface. When the reaction is substituted in the system of equations of motion of the shell, the part corresponding to the free vibrations of the cylinder is discarded. The system of equations of motion of the shell is reduced to an equation of Mathieu type, from which transcendental equations for determining the boundaries of the regions of dynamic instability are obtained. These regions are analyzed for various modes of loss of stability and different values of the core modulus of elasticity.     

Dynamic stability of cylindrical orthotropic shells with an elastic core under a longitudinal periodic load

The dynamic instability of a cylindrical orthotropic shell with an elastic core subjected to a longitudinal periodic load is considered. Equations are obtained for determining the regions of dynamic instability for different core models.     

Bending of a multilayer cylindrical shell with an elastic core under a local radial load

The problem of the state of stress and strain of a multilayer cylindrical shell with a soft elastic core subjected to an external, locally distributed radial load is solved under the simplifying assumption that all the layers satisfy the generalized Hooke's law and work together without slip. A numerical example is given.     

Optimization of a cylindrical composite shell with a viscoelastic core in axial compression

The problem of the optimal design of a composite shell in creep is formulated. The progressive buckling of a cross-wound reinforced cylindrical shell supported on a viscoelastic core is considered as a particular case. The reinforcement structure and shell thickness corresponding to minimum weight for a given load and service life are found.Institute of Polymer Mechanics, Academy of Sciences of the Latvian SSR, Riga. Translated from Mekhanika Polimerov, No. 3, pp. 442–446, May–June, 1975.     

Parametric vibrations of an orthotropic cylindrical shell with an elastic core. 2. Some numerical results

It is shown that the operator of the problem belongs to the class of oscillation operators. The first five regions of dynamic instability of an elastic orthotropic cylindrical shell with an elastic isotropic core are determined in the first approximation. The effect of the core and transverse shear in the shell on the width and location of these regions of dynamic instability of the system is determined. The effect of transverse shear on the natural frequencies of the empty shell is established.     

Dual problem of optimizing an orthotropic cylindrical shell

The problem of optimizing the weight of an orthotropic cylindrical shell is examined, using the duality theory of geometrical programing.     

Effect of transverse shear on the stability of an orthotropic cylindrical shell with an elastic core in axial compression

The effect of transverse shear on the stability of a composite shell in axial compression has been investigated. The core is treated as an isotropic elastic cylinder bonded to the inner surface of the shell. The effect of the tangential shearing forces between the shell and the core is taken into account.Institute of Polymer Mechanics, Academy of Sciences of the Latvian SSR, Riga. Translated from Mekhanika Polimerov, No. 2, pp. 267–273, March–April, 1973.     

The numerical analysis of an orthotropic cylindrical shell

This paper is devoted to an orthotropic cylindricall simply supported shell subjected to external pressure. This analysis is focused on determining geometrical shape of shell. Main subject of investigation is to maximize the stability of the shell. Mathematical model of double layer shell was implemented. Numerical solution was obtained for particular class of shells by using the finite element code ABAQUS. (© 2008 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Axisymmetric vibrations of an orthotropic non-uniform cylindrical shell

The axisymmetric vibrations of a circular cylindrical shell of constant thickness, orthotropic along the principal geometrical directions and non-uniform along the generatrices, are considered. It is shown, using a particular problem as an example, that the non-uniform physical-mechanical characteristics of the shell material may lead to qualitatively new results in problems of shell dynamics.     

Axially symmetrical deformation of an orthotropic layered cylindrical shell

An orthotropic layered cylindrical sheet subject to axially symmetrical loading is considered. A solution free from the hypothesis of the straight normal is presented; the material of the shell is regarded as incompressible in the radial direction. An attempt is made to allow for the real character of the rigid fixing at the edge of the shell. The stressed state in the neighborhood of the edge is analyzed.S. Ordzhonikidze Moscow Aviation Institute. Translated from Mekhanika Polimerov, No. 5, pp. 816–823, September–October, 1972.     

Dynamic stability of an elastic orthotropic cylindrical shell with allowance for transverse shears

The resolvents for the dynamic stability of an elastic orthotropic cylindrical shell are obtained in accordance with the Ambartsumyan and Timoshenko-type refined theories. The regions of instability given by the classical and refined theories are compared. The dependence of the refinements on the shell parameters, the shear moduli of the material, and the buckling modes are investigated.Institute of Polymer Mechanics, Academy of Sciences of the Latvian SSR, Riga. Translated from Mekhanika Polimerov, No. 2, pp. 312–320, March–April, 1973.     

Parametric oscillations of a viscoelastic cylindrical shell

The formulation of the problem of parametric oscillations of viscoelastic shells is given. It was shown that this problem is reduced to the study of the equations, investigated in [4, 5].Moscow Institute of Geodesy, Aerophotography, and Cartography Engineers. Translated from Mekhanika Polimerov, No. 3, pp. 479–483, May–June, 1974.     

Effect of a local load on an orthotropic glass-reinforced plastic shell

The deformation of a layered orthotropic cylindrical shell under a local normal load is investigated on the basis of equations that do not depend on the hypothesis of straight normals. The solutions of the analogous classical problems were analyzed in [3]; a solution based on equations that take transverse shear strains approximately into account was proposed in [4]. The high degree of variability of the state of stress created by local loads indicates that it is quite important to take transverse shear strains rigorously into account in problems of this class. An attempt is made to estimate the error introduced by the hypothesis of straight normals and to calculate the load leading to debonding of the shell.S. Ordzhonikidze Moscow Aviation Institute. Translated from Mekhanika Polimerov, No. 1, pp. 95–101, January–February, 1970.     

Local stability of an orthotropic cylindrical shell partially filled by an elastic core and subjected to external pressure

The local stability of an infinitely long orthotropic cylindrical shell partially filled by an elastic thick-walled cylindrical core and subjected to external pressure is investigated.Scientific-Research Institute of Chemical Technology, Moscow Region. Translated from Mekhanika Polimerov, No. 3, pp. 538–542, May–June, 1971.     

Numerical analysis of axisymmetric oscillations of an orthotropic cylindrical shell

The frequency spectrum of shells is analyzed by numerical methods using three-dimensional and applied theories. The axisymmetric oscillations of an orthotropic cylindrical shell with Navier conditions on the edges are investigated. The effect of boundary conditions on the frequency spectrum is also studied numerically.Translated from Vychislitel'naya i Prikladnaya Matematika, No. 55, pp. 106–109, 1985.     

Parametric vibrations of cylindrical shells with a viscoelastic core

The method of calculating the axisymmetric and nonaxisymmetric parametric vibrations of a cylindrical shell bonded to an elastic core [2] is extended to the case of hollow and solid viscoelastic cores by substituting for the material moduli in the equations of motion of the core integral operators with kernels in the form of an exponential and a sum of exponentials. Expressions are given for the reaction of the viscoelastic core, together with the equation of the boundaries of the spectrum of principal regions of dynamic instability. The effect of relaxation time and the long-term modulus of elasticity of the core on the shape and location of the regions of dynamic instability is analyzed.     

Torsional stability of a glass-reinforced plastic cylindrical shell with an elastic core

The problem of the stability of a glass-reinforced plastic cylindrical shell with an elastic core subjected to twisting moments applied to the edges of the shell is considered. As in various other studies [4–6], the glass-reinforced plastic is treated as an elastically orthotropic material. The core is treated as an isotropic elastic cylinder, whose outer surface is bonded to the shell. Expressions for the critical stresses are obtained for an infinitely long shell and a shell of finite length.Moscow. Translated from Mekhanika Polimerov, No. 6, pp. 1082–1086, November–December, 1970.     

Forced axisymmetric oscillations of a viscoelastic cylindrical shell

The variational problem of forced oscillations of a cylindrical shell is reduced to a system of linear integrodifferential equations for which a periodic solution is constructed.Moscow Institute of Electronic Machinery. Translated from Mekhanika Polimerov, No. 6, pp. 1111–1114, November–December, 1975.