Motion of a nonlinear viscoelastic liquid in cylindrical channels of triangular cross section

The problem of the nonrectilinear steady-state flow of a nonlinear viscoelastic liquid in cylindrical channels is considered. It is established that in channels whose cross sections form an equilateral triangle or an isosceles right-angled triangle there are six transverse currents (eddies) in a plane perpendicular to the main longitudinal flow. In cylinders with cross sections in the form of an arbitrary triangle there may be four or six eddies, depending on the shape of the triangle.     

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.     

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.     

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.     

Averaging of acoustic equation for partially perforated viscoelastic material with channels filled by a liquid

Acoustic equations for combined media consisting of partially perforated viscoelastic material and viscous incompressible liquid filling pores are considered. An averaged model is constructed for the model under consideration, and boundary conditions connecting equations of the obtained averaged model on the boundary between solid viscoelastic material and porous viscoelastic material filled by a viscous incompressible liquid are found. The convergence of limit problems to the solution of corresponding averaged problem with respect to the norm of the space L ² is proved.     

Nonlinear free vibration analysis of SSMFG cylindrical shells resting on nonlinear viscoelastic foundation in thermal environment

In this paper, a semi-analytical method for the free vibration behavior of spiral stiffened multilayer functionally graded (SSMFG) cylindrical shells under the thermal environment is investigated. The distribution of linear and uniform temperature along the direction of thickness is assumed. The structure is embedded within a generalized nonlinear viscoelastic foundation, which is composed of a two-parameter Winkler-Pasternak foundation augmented by a Kelvin-Voigt viscoelastic model with a nonlinear cubic stiffness. The cylindrical shell has three layers consist of ceramic, FGM, and metal in two cases. In the first model i.e. Ceramic-FGM-Metal (CFM), the exterior layer of the cylindrical shell is rich ceramic while the interior layer is rich metal and the functionally graded material is located between these layers and the material distribution is in reverse order in the second model i.e. Metal-FGM-Ceramic (MFC). The material constitutive of the stiffeners is continuously changed through the thickness. Using the Galerkin method based on the von Kármán equations and the smeared stiffeners technique, the problem of nonlinear vibration has been solved. In order to find the nonlinear vibration responses, the fourth order Runge–Kutta method is utilized. The results show that the different angles of stiffeners and nonlinear elastic foundation parameters have a strong effect on the vibration behaviors of the SSMFG cylindrical shells. Also, the results illustrate that the vibration amplitude and the natural frequency for CFM and MFC shells with the first longitudinal and third transversal modes (m = 1, n = 3) with the stiffeners angle θ = 30°, β = 60° and θ = β = 30° is less than and more than others, respectively.     

Forced nonlinear vibrations of a viscoelastic body

An approximate solution of the problem of the forced, geometrically nonlinear vibrations of an arbitrary viscoelastic body is found in the form of an expansion in eigenfunctions of the corresponding linear elastic problem. With the aid of the virtual displacement principle the problem is reduced to a system of nonlinear integro-differential equations whose periodic solution is constructed by the small-parameter method.     

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.     

Dynamic torsion of viscoelastic cylindrical rods

An exact solution of the problem of the propagation of torsional waves in semiinfinite and finite circular cylinders is obtained within the framework of the linear theory of viscoelasticity. Concrete examples are discussed, and estimates are given for the stresses near the wave front. All the solutions are obtained in series; it is shown that these series converge absolutely for any finite time.     

Polymer flow in cylindrical channels

The author examines the problem of flow of a polymer melt in a cylindrical channel of arbitrary cross section. It is assumed that the polymer is an isotropic viscoelastic medium. All the coefficients of the equation of state obtained for the flow in question are functions of the second invariant of the strain rate tensor only and can be determined experimentally in simple types of flow. A perturbation method is proposed for the solution of specific problems, the Dirichlet problem for Poisson's equation being solved in each perturbation step.Mekhanika Polimerov, Vol. 2, No. 3, pp. 421–428, 1966     

Global attractor for a nonlinear viscoelastic model

In this paper we establish the existence of global attractors of a semiflow and a semigroup for a nonlinear 1-d viscoelasticity in two frameworks. We exploit the properties of the analytic semigroup to show the compactness for the semiflow and semigroup generated by the weak global solutions.     

Calculation of nonlinear vibrations of a viscoelastic bar

The problem of forced nonlinear vibrations of a viscoelastic bar is reduced by the Bubnov—Galerkin method to a nonlinear integro-differential equation. Transverse vibrations with small amplitude are considered, and therefore the approximate solution is constructed by the small-parameter method.     

Study of oscillations in a viscoelastic cylindrical shell in an elastic medium

An equation was obtained and solved for oscillations in a viscoelastic cylindrical shell located in the ground. A numerical example is examined.Moscow Electronic Engineering Institute. Translated from Mekhanika Polimerov, No. 1, pp. 178–181, January–February, 1974.     

Transient contraction flow of a nonlinear viscoelastic fluid

The unsteady behavior of a Phan-Thien-Tanner fluid in a pressure driven contraction flow is investigated. Calculations are performed using the log-conformation reformulation and block coupled pressure correction. Studies are carried out for the Deborah number De of the process and the model's extension parameter α. It is shown that for very small and very large De the fluid responds newtonian whereas for moderate De damped oscillations of the volume flux can be observed. The studies for α show that the flow is shear dominant despite the extensional flow character of contractions. (© 2016 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)     

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.     

Strength of a viscoelastic liquid in quasistatic three-dimensional tension

Conclusions 1. An apparatus has been built with which experiments could be performed yielding, with a minimal spread of values, the quasistatic bulk strength of a liquid specimen.2. It has been established that the concentration of a polymer liquid does not significantly affect the experimental values of the liquid resistance to rupture. The strength of a viscous polymer liquid specimen is much lower than that of its low-viscosity solute.Institute of Polymer Mechanics, Academy of Sciences of the Latvian SSR, Riga. Translated from Mekhanika Polimerov, No. 3, pp. 525–530, May–June, 1978.     

Vibrations of a shock-absorbing device on a nonlinear viscoelastic base

A method of calculating a viscoelastic shock-absorbing device or structure by the method of averaging systems of integro-differential equations is considered. The principal quadratic theory of hereditary viscoelasticity is used as the physical relationship between forces and displacements of the shock-absorbing base or structure.Moscow Institute of Electronic Machine Construction. Translated from Mekhanika Polimerov, No. 4, pp. 730–737, July–August, 1972.