Temperature stresses in a long hollow viscoelastic cylinder with variable inner boundary

As distinct from existing solutions for the state of stress and strain, in addition to the stresses created by internal pressure acting on the moving inner surface, the thermal stresses created by a temperature field are also taken into account. A solution is obtained using tabulated singular kernels of the hereditary theory of viscoelasticity.Moscow Lomonosov State University. Translated from Mekhanika Polimerov, Vol. 5, No. 2, pp. 219–226, March–April, 1969.     

On the influence of the viscoelastic properties of a material on the stressed state of a cylinder under diffusion saturation

We study the influence of relaxation effects on the stress-strain state of a cylinder when it is being diffusion saturated. The study is conducted for solid circular cylinders whose viscoelastic properties are described by various rheological models (those of Maxwell, Foigt, Lesersich, and Koltunov). We carry out an analysis of the stresses and give a comparison of the results for the materials under consideration.Translated fromMatematicheskie Melody i Fiziko-Mekhanicheskie Polya, Issue 31, 1990, pp. 41–44.     

3D Analyses of the symmetric local stability loss of the circular hollow cylinder made from viscoelastic composite material

The 3D approach was employed for investigations of the symmetric local stability loss of the circular hollow cylinder made from the viscoelastic composite materials. This approach is based on investigations of the development of the initial rotationally symmetric infinitesimal local imperfections of the circular hollow cylinder within the scope of 3D geometrically nonlinear field equations of the theory of viscoelasticity for anisotropic bodies. The numerical results of the critical force and critical time are presented and discussed. For comparison and estimation of the accuracy of the results given by the 3D approach, the same problem is also solved by using various approximate shell theories. The viscoelasticity properties of the plate material are described by the fractional–exponential operator. The numerical results and their discussion are presented for the case where the cylinder is made of a uni-directional fibrous viscoelastic composite material. In particular, it is established that the difference between the critical times obtained by employing 3D and third order refined shell theories becomes more non-negligible if the values of the external compressive force are close to the critical compressive force which is obtained at t = ∞ (t denotes a time).     

New approximate solutions of the problem of the thermomechanics of a hollow cylinder with a material of variable properties

We use the method of equivalent sources to obtain approximate solutions of an unrestricted quasistatic axisymmetric problem of the thermomechanics of a long hollow cylinder with ends fastened and materials whose properties depend on the temperature. We perform a comparative analysis of the results with the solutions obtained by the method of perturbations and the method of finite differences.Translated fromMatematicheskie Metody i Fiziko-Mekhanicheskie Polya, Issue 27, 1988, pp. 71–74.     

On the plane non-stationary heat transfer in two-phase hollow cylinder with radially graded material properties

This consideration concerns heat transfer in two-component composite with a deterministic microstructure, which is -periodic along the angular axis and has slowly varying effective properties in the radial direction (Fig.1). Therefore, we deal here with a special case of functionally graded materials, FGM, c.f. Suresh, Mortensen (1998). The main aim of this consideration is to capture effect of the discontinuous boundary conditions on the thermal field. (© 2010 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)     

One-dimensional viscoelastic fluid model where viscosity and normal stress coefficients depend on the shear rate

We study the unsteady motion of a viscoelastic fluid modeled by a second-order fluid where normal stress coefficients and viscosity depend on the shear rate by using a power-law model. To study this problem, we use the one-dimensional nine-director Cosserat theory approach which reduces the exact three-dimensional equations to a system depending only on time and on a single spatial variable. Integrating the equation of conservation of linear momentum over the tube cross-section, with the velocity field approximated by the Cosserat theory, we obtain a one-dimensional system. The velocity field approximation satisfies both the incompressibility condition and the kinematic boundary condition exactly. From this one-dimensional system we obtain the relationship between average pressure and volume flow rate over a finite section of the tube with constant and variable radius. Also, we obtain the correspondent equation for the wall shear stress which enters directly in the formulation as a dependent variable. Attention is focused on some numerical simulation of unsteady/steady flows for average pressure, wall shear stress and on the analysis of perturbed flows.     

Deformation of a heavy viscoelastic cylinder supported on a rigid plate

Plane strain of a viscoelastic cylinder supported arcwise on a rigid plate is considered. By means of Laplace transformation the viscoelastic problem is reduced to the perfectly elastic problem. The elastic solution is found by methods of complex variables by means of the stress function. Inverse transformation is carried out by the method of Il'yushin approximations. the first approximation of the stated problems is found in the method of approximations.     

The problem of a viscoelastic cylinder rolling on a rigid half-space

The problem of a viscoelastic cylinder rolling on a rigid base, propelled by a line force acting at its centre, is solved in the noninertial approximation. The method used is based on a decomposition of hereditary integrals developed by the authors in previous work, and on the viscoelastic Kolosov-Muskhelishvili equations which are used to generate a Hilbert problem. In this formulation, the problem reduces to a nonsingular integral equation in space and time, which simplifies under steady-state conditions and for exponential decay materials, to algebraic form. There are also two subsidiary conditions.In the case of a standard linear model, explicit analytic results and numerical examples are given for the pressure function, for surface displacements, and also for hysteretic friction.     

State of stress of flexible viscoelastic plates with an opening

The problem of the state of stress of flexible plates with an opening is investigated with allowance for the viscoelastic properties of the material. The basic equations and the corresponding boundary conditions are formulated. The boundary value problem is solved by numerical integration. The effect of the creep properties of the material on the stress redistribution in the plate is investigated with reference to polymethyl methacrylate. It is shown that the angle of rotation, the ring moment, and the ring forces at the edge of the opening vary with time and as a function of the load.Institute of Mechanics, Academy of Sciences of the Ukrainian SSR, Kiev. Translated from Mekhanika Polimerov, No. 4, pp. 708–713, July–August, 1971.     

Modelling of viscoelastic material behaviour close to the glass transition temperature

In this contribution we investigate the mechanical behaviour of polyurethane over a range of different but constant temperatures from the glass to the viscoelastic state. Therefore uniaxial tension tests are performed on dogbone specimens under different isothermal conditions. In this manner an experimental data set is provided. As a theoretical basis we present the well known thermomechanically coupled one dimensional linear viscoelastic material model which is able to display the experimentally observed material behaviour. For this we adopt temperature dependent relaxation times. The introduced model parameters are identified via a standard parameter identification tool. Finally, the experimental results are compared with the ones of simulations of the identified model parameters. (© 2009 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Exact solution of thermal stress problem of an inhomogeneous hygrothermal piezoelectric hollow cylinder

The closed-form exact solution for the hygrothermal response of inhomogeneous piezoelectric hollow cylinders is obtained. The interaction of electric potentials, electric displacement and elastic deformations is presented. The present cylinder is subjected to both a mechanical load and an electric potential. The material properties coefficients of the present cylinder are assumed to be changed in the radial direction by different distribution forms. The field quantities like displacement, stresses and electric potentials in the inhomogeneous piezoelectric cylinders are determined. The significant of influences of material inhomogeneity, initial temperature, final moisture, and the load and electric ratios in the field quantities are investigated. The concluding remarks and suitable discussions are made.     

Vibrations of a viscoelastic cylinder with an elastic shell

The nonlinear vibrations of a viscoelastic cylinder with an elastic shell subjected to two harmonic forces are investigated using the averaging scheme described in [3, 4]. Nonresonance, resonance, and subharmonic vibrations are examined. It is shown that the presence of viscosity in the system leads to a single stationary equilibrium position for which the stability conditions are given.V. I. Lenin Tashkent State University. Translated from Mekhanika Polimerov, No. 4, pp. 691–697, July–August, 1973.     

Singular Sturm-Liouville problems whose coefficients depend rationally on the eigenvalue parameter

Let −Dω(·,z)D+q be a differential operator in L²(0,∞) whose leading coefficient contains the eigenvalue parameter z. For the case that ω(·,z) has the particular form

     

Action of a flat stamp on a half-plane of viscoelastic material

A plane problem concerning the action of a flat stamp on a reinforced, linearly viscoelastic medium is considered. One of the main axes of elasticity is parallel to the boundary of the half-plane. The reinforcing material is supposed to be perfectly elastic, and the matrix material linearly viscoelastic. The solution of the problem is based on the assumption that up to the moment of application of the forces, the medium is stress-free and at rest. The formulation of the problem is given, and a method of solution presented. A numerical example is offered.Mekhanika Polimerov, Vol. 2, No. 5, pp. 688–692, 1966     

On the longitudinal wave propagation in a viscoelastic cylinder

Résumé L'auteur étudie le calcul des déplacements d'un matériau visco-élastique linéaire dans un cylindre d'étendue finie qui sont produits par des oscillations longitudinales. Il montre qu'avec une approximation pour le cas des basses fréquences, on arrive au même résultat que celui obtenu de façon rigoureuse par un autre auteur. De plus, il montre que cette méthode peut être utilisée dans la region de hautes fréquences.