Effect of certain factors on the vibrations of polymers

The authors' work on the effect of various factors on the vibrations of the polymer chain is reviewed. A method of calculating chain vibrations is briefly described, an expression is given for the strain energy of a polymer molecule in the nonlinear approximation, the frequency shift of the vibrations of a molecule under load is calculated and discussed, the effect of intermolecular interaction in the polymer crystal and the disorder of the chain on the vibration spectrum is taken into account, and the change in the intensity of the normal vibrations when the chain is loaded and the effect of anharmonicity on the band width are investigated. In conclusion, the stress distribution over the interatomic bonds is estimated.A. F. Ioffe Physico-Technical Institute, Academy of Sciences of the USSR, Leningrad. Translated from Mekhanika Polimerov, No. 1, pp. 33–46, January–February, 1975.     

Effect of loading history on the free vibrations of an elastic-hereditary oscillator

The effect of the dynamic loading history on the free vibrations of an elastic-hereditary oscillator is examined. The response of the material is described by an integral relation of the heriditary type with an exponential-fractional relaxation kernel. An integrooperator representation of the starting equation makes it possible to obtain a closed solution to the problem of free vibrations of an elastic-heriditary oscillator for certain specific loading histories. The results are illustrated with reference to polyamide (kapron).Mekhanika Polimerov, Vol. 4, No. 2, pp. 222–226, 1968     

Effect of hydrostatic pressure combined with uniaxial tension on certain physical properties of polymers

The residual changes in the density and swelling properties of high-density polyethylene, teflon, PVC, and ebonite after extension under hydrostatic pressure have been investigated. It is shown that in this case the density of all the materials tested is higher and the swelling lower than in the case of uniaxial tension alone. This effect of hydrostatic pressure is attributable to the creation of favorable conditions for the healing of cracks formed in the deformation process.Mekhanika Polimerov, Vol. 3, No. 6, pp. 1018–1023, 1967     

Effect of loading on intensity of fracture and deformation of polymers

An expression is proposed for the activation energy U = U₀ –a + b², by means of which it is possible qualitatively to describe the various cases of the kinetics of deformation and rupture in polymers.Scientific-Research Institute of Plastics, Moscow. Translated from Mekhanika Polimerov, No. 2, pp. 366–368, March–April, 1972.     

Rotating response on the vibrations of functionally graded zigzag and chiral single walled carbon nanotubes

This study deals with the vibration analysis of zigzag and chiral rotating functionally graded carbon nanotubes (FG-CNT) invoking Love's shell theory using wave propagation approach. The frequency equation is formed in the eigenvalue form. It has been shown that with the increase of angular speed, frequencies of forwarding curve decrease and backward curve increase. The phenomena of frequency versus length-and height-to-radius ratios are noted as decreasing and increasing, respectively, for rotating CNTs. The backward and forward frequency curves of clamped-free are lower throughout the computation than the clamped-clamped zigzag and chiral carbon nanotube depending upon the rotating speed. MATLAB software is used to calculate the rotating (backward and forward) frequencies of SWCNTs and the frequency peaks in the present results show excellent stability across a wide range of parameters. Using geometrical and material parameters, the vibration results are given in tabular and graphical form. It is thus desirable to produce more precise estimations of the vibrational frequencies of CNTs. The present results are compared with earlier literature using simply supported boundary conditions and show a good coincidence.     

Steady-state vibrations of a compound isotropic cylinder under a plane strain

We solve the problem of two-dimensional strain of a compound isotropic cylinder deformed by distributed pulsing forces. We study the influence of the geometric and elastic characteristics of the layers on the magnitude of the stresses and the lowest natural frequency of radial-symmetric vibrations of a three-component cylinder. Two figures Bibliography: 3 titles Translated fromTeoreticheskaya i Prikladnaya Mekhanika, No. 25, 1995, pp. 103–108.     

Durability of polymers as a function of loading regime during repeated loading with a small number of cycles

Specimens of oriented polycaproamide and unoriented polymethyl methacrylate subjected to uniaxial extension were used to study durability as a function of the number of loading cycles and the intervals between them in different segments of the creep curve. It was shown that the deformation hardening during the initial segment of the creep curve governs the ability of the specimen to withstand subsequent loading cycles. With a relatively low loading rate, deloading-loading cycles during the initial segment of the creep curve lead primarily to an increase in local stresses. During the second stage, repeated loading causes principally an increase in local heating. The interval between loading cycles has only a weak influence on durability.A. F. Ioffe Physicotechnical Institute, Academy of Sciences of the USSR, Leningrad. Translated from Mekhanika Polimerov, No. 2, pp. 252–256, March–April, 1972.     

On unbounded trajectories of a certain quadratic mapping of the plane

Unbounded trajectories of the mapping F(x, y) = (xy, (x-2)²) are studied. Translated from Sovremennaya Matematika i Ee Prilozheniya (Contemporary Mathematics and Its Applications), Vol. 53, Suzdal Conference-2006, Part 1, 2008.     

Effect of vertical vibrations on a two-layer system with a deformable interface

The effect of single- and two-frequency vibrations on the behavior of a system consisting of two homogeneous viscous fluids bounded by rigid walls is analyzed. It is assumed that the system as a whole is under vertical vibrations obeying a certain law. An eigenvalue problem is obtained in order to analyze the stability of the relative equilibrium. The case of finite frequencies and arbitrary modulation amplitudes is treated along with the case of high frequencies and small modulation amplitudes. In the former case, the parametric resonance domains are examined depending on the parameters of the system. In the latter case, the high-frequency vibration is shown to create effective surface tension, thus flattening the interface, and can suppress instability when the heavy fluid is over the light one.     

Solvability of a certain problem on the plane motion of two viscous incompressible fluids with free noncompact boundaries

The solvability of a certain two-dimensional boundary-value problem for the system of the Navier-Stokes equations, describing the steady (partially common) motion of two heavy viscous incompressible capillary fluids with free noncompact boundaries, is proved.Translated from Zapiski Nauchnykh Seminarov Leningradskogo Otdeleniya Matematicheskogo Instituta im. V. A. Steklova AN SSSR, Vol. 163, pp. 146–153, 1987.     

Rigidity of certain finite group actions on the complex projective plane

Partially supported by NSERC grant A4000     

Effect of ultrasonic vibrations on the flow of a viscoelastic liquid

The rheological characteristics of a viscoelastic liquid flow, on which finite-amplitude ultrasonic shear vibrations have been superimposed, are investigated. It is shown that at periodic deformation amplitudes of 5 µ or more there is a thixotropic reduction of the viscosity and elasticity of the system owing to the destruction of certain types of structural bonds. The experimental apparatus is described.Moscow Institute of Chemical Machine Building. Translated from Mekhanika Polimerov, No. 6, pp. 1097–1099, November–December, 1971.     

Simulation of thermo-mechanical loading processes on amorphous thermoplastic polymers

A constitutive model for the thermo-mechanical behavior of amorphous thermoplastic polymers is presented that accounts for the dependence of the macromolecular network and entropic hardening on large temperature changes. (© 2010 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)