A study of the life of alkyd coatings

The effect of the conditions of formation and aging on the life of alkyd coatings is studied. It is shown that the life of alkyd coatings aged under various conditions can be expressed by the general equation =Ae^–ax The relationship between the life of alkyd coatings and curing temperature is linear. It is observed that the conditions of aging have no effect on the rupture energy or ₀, but cause a substantial change in the distribution of the lines =f(1/T_f). Cross-linkage of alkyd coatings due to the action of heat, light, and moisture, under various conditions of aging, is accompanied by an increase in rupture energy with increase in the internal stresses.Mekhanika Polimerov, Vol. 1, No. 3, pp. 68–76, 1965     

Study of the prefracture states of rigid polymers 1. Forced high-elastic deformation

It is shown that in the process of extension specimens of a rigid unoriented polymer — polyethylene terephthalate — go over into the oriented state before failure. Various cases of transition to the oriented state are considered: with the formation of a neck and deformation bands, with and without loss of continuity. The degree of molecular orientation of the specimens and their fracture conditions are estimated.A. F. Ioffe Physicotechnical Institute, Academy of Sciences of the USSR, Leningrad. Translated from Mekhanika Polimerov, No. 1, pp. 8–14, January–February, 1976.     

Solvability of the Dirichlet problem for second-order elliptic equations

In our preceding papers, we obtained necessary and sufficient conditions for the existence of an (n?1)-dimensionally continuous solution of the Dirichlet problem in a bounded domain Q ? ? _n under natural restrictions imposed on the coefficients of the general second-order elliptic equation, but these conditions were formulated in terms of an auxiliary operator equation in a special Hilbert space and are difficult to verify. We here obtain necessary and sufficient conditions for the problem solvability in terms of the initial problem for a somewhat narrower class of right-hand sides of the equation and also prove that the obtained conditions become the solvability conditions in the space W ₂ ¹ (Q) under the additional requirement that the boundary function belongs to the space W ₂ ^1/2 (?Q).     

The eigenvalues of the Laplacian on locally finite networks

We consider the continuous Laplacian on an infinite locally finite network with equal edge lengths under natural transition conditions as continuity at the ramification nodes and classical Kirchhoff conditions at all vertices. It is shown that eigenvalues of the Laplacian in a L^∞-setting are closely related to those of the adjacency and transition operator of the network. In this way the point spectrum is determined completely in terms of combinatorial quantities and properties of the underlying graph as in the finite case [2]. Moreover, the occurrence of infinite geometric multiplicity on trees and some periodic graphs is investigated.     

Variational derivatives and p-gradients of functionals on spaces of continuously differentiable functions

The purpose of this paper is to introduce and study a new type of derivative – the variational gradient – for a functional on Cⁿ[a, b]. Local and global versions of this concept are analyzed. This notion provides a natural approach to variational derivatives on Cⁿ[a, b] under rather mild smoothness assumptions on the functional. When applied in the context of the Calculus of Variations, the notion of the variational gradient captures the natural boundary conditions (as well as the Euler-Lagrange equations) under weaker smoothness assumptions than those usually required using Gǎteaux variations. Conditions are established for the existence of the variational derivative and an integral representation for the Gǎteaux variation in terms of the variational derivative is derived. Conditions for the variational derivative to be differentiable are also established.     

Global Hopf bifurcation of differential equations with threshold type state-dependent delay

We develop global Hopf bifurcation theory of differential equations with state-dependent delay using the S¹$S^1$-equivariant degree and investigate a two-degree-of-freedom mechanical model of turning processes. For the model of turning processes we show that the extreme points of each vibration component of the non-constant periodic solutions can be embedded into a manifold with explicit algebraic expression. This observation enables us to establish analytical upper and lower bounds of the amplitudes of the periodic solutions in terms of the system parameters and to exclude certain periods. Using the achieved global bifurcation theory we reveal that if the relative frequency between the natural frequency and the turning frequency varies in a certain interval, then generically every bifurcated continuum of periodic solutions must terminate at a bifurcation point. This termination means that the underlying system with parameters in the stability region near the vertical asymptotes of the stability lobes is less subject to chatter. In the process, several sufficient conditions for the non-existence of non-constant periodic solutions are also obtained.     

Variation of prestress in filament-wound glass-reinforced plastics

The authors examine the process of winding prestressed parts from oriented glass-reinforced plastics. It is shown that the essential anisotropy of the properties of these materials in responsible for variation of the specified prestress. The law of distribution of the tensile forces is investigated in the linear-elastic approximation for the case of a ring wound onto a rigid mandrel. A method of calculation is proposed that permits the change in prestress to be estimated and gives the critical number of turns beyond which the pressure on the mandrel ceases to increase.Mekhanika Polimerov, Vol. 2, No. 2, pp. 278–284, 1966     

Limit laws of entrance times for homeomorphisms of the circle

Given a homeomorphismf of the circle with irrational rotation number and a descending chain of renormalization intervalsj _n off, we consider for each interval the point process obtained by marking the times for the orbit of a point in the circle to enterJ _n. Assuming the point is randomly chosen by the unique invariant probability measure off, we obtain necessary and sufficient conditions which guarantee convergence in law of the corresponding point process and we describe all the limiting processes. These conditions are given in terms of the convergent subsequences of the orbit of the rotation number off under the Gauss transformation and under a certain realization of its natural extension. We also consider the case when the point is randomly chosen according to Lebesgue measure,f being a diffeomorphism which isC ¹-conjugate to a rotation, and we show that the same necessary and sufficient conditions guarantee convergence in this case.     

Gaussian quasimartingales

Summary Necessary and sufficient conditions in terms of the mean function and covariance are obtained for a separable Gaussian process to have paths of bounded variation, absolutely continuous or continuous singular. If almost all paths are of bounded variation, the L ² expansion of the Gaussian process is shown to converge in the total variation norm. One then obtains a decomposition of the paths of a Gaussian quasimartingale into a martingale and a predictable process of bounded variation paths such that these components are jointly Gaussian; the martingale component is decomposed into two processes, one consisting of (fixed) jumps and the other a continuous path martingale, and the bounded variation component is decomposed into three processes, one consisting of (fixed) jumps, another with absolutely continuous paths and the third with continuous singular paths. All components are jointly Gaussian. Uniqueness of the decompositions is also established.This work was partially supported by the National Science Foundation.     

Affine minimal hypersurfaces of rotation

We give a complete list of affine minimal surfaces inA ³ with Euclidean rotational symmetry, completing the treatise given in [1] and prove that these surfaces have maximal affine surface area within the class of all affine surfaces of rotation satisfying suitable boundary conditions. Besides we show that for rotationally symmetric locally strongly convex affine minimal hypersurfaces inA ⁿ ,n4, the second variation of the affine surface area is negative definite under certain conditions on the meridian.     

Concerning the strength and fracture of thermally aged polycarbonate

The change in the strength, fractography, and supermolecular structure of polycarbonate after thermal aging has been experimentally investigated. It is shown that the fall in the strength of the polycarbonate after aging (T 160°C) is chiefly related with the formation of dangerous defects as a result of the destruction of the supermolecular structure at the surface of the block. It is noted that under the same conditions there is some ordering of the supermolecular structure of the polycarbonate at depths of 150 µ or more, but this has practically no effect on the strength characteristics.Institute of Physicotechnical Problems of Energetics, Academy of Sciences of the Lithuanian SSR, Kaunas. Translated from Mekhanika Polimerov, No. 5, pp. 951–952, September–October, 1971.     

Infrared absorption spectra of some lanthanide acetylacetonate complexes

The infrared absorption spectra of 12 lanthanide acetylacetonate complexes were measured in the region 400–2000 cm^?1 and discussed. Assignments of the bands especially those due to metal-oxygen (M—O), C=O and C=C stretching vibration is given. It is found that the band at 530 ± 5 cm^?1 is due mainly to Ln—O stretching vibration. In the carbonyl region, it is confirmed that the band at lower frequency is a C=C stretching vibration while that at higher frequency is due to C=O stretching vibration. Integral intensities for the M—O, C=O and C=C stretching vibrations were calculated in KB₁ and CHCl₃ solutions. The variation of the intensities of the M—O bands witn complexed cation were discussed in terms of crystal field stabilization energy (CFSE).     

Bending and vibration of an electrostatically actuated circular microplate in presence of Casimir force

The pull-in instability and the vibration for a prestressed circular electrostatically actuated microplate are investigated in consideration of the Casimir force. Based on von Kármán’s nonlinear bending theory of thin plates, the governing equations for the whole analysis are decomposed into two two-point boundary value problems. For static deformation of the plate, the geometric nonlinearity is involved and the pull-in parameters are obtained by using the shooting method through taking the applied voltage or Casimir parameter as an unknown. This algorithm is also used to study the small amplitude free vibration about the predeformed bending configuration following an assumed harmonic time mode, and the variation of the prestress and Casimir parameters dependent fundamental natural frequency with the applied voltage is presented. Several case studies are compared with available published simulations to confirm the proposed method. The influences of various parameters, such as the initial gap-thickness ratio, Casimir effect, prestress on the pull-in instability behavior and the natural frequency are examined.     

Effect of production technology upon the supramolecular structure of crystalline polymers

The supramolecular structure and some other properties (density, microhardness) of high-density polyethylene and polycaprolactam specimens, molded under various conditions and aged for periods up to five months, have been studied.The change in the nature of the supramolecular structure and properties of the tested materials was determined in relation to molding conditions and aging time. It was found that the properties of these materials are determined by their supramolecular structure.Mekhanika Polimerov, Vol. 1, No. 2, pp. 9–14, 1965     

A modified dual scheme for solving an elastic crack problem

A dual scheme for solving a crack problem in terms of displacements is considered. The dual solution method is based on a modified Lagrange functional. The convergence of the method is investigated under a natural assumption of H ¹-regularity of the solution to the crack problem. A duality relation for the primal and dual problems is proposed.     

Effect of heat treatment on the static and fatigue strength of polycaproamide

The changes in strength and the polymorphous transformations which occur during the aging in air of polycaproamide heat-treated under various conditions were investigated. It was shown that the strength after prolonged aging in air with normal relative humidity depends on the structural changes occurring in the heat-treatment process. The structural changes lead to changes in fatigue strength and also in the mechanism of the breakdown of polycaproamide on aging.Kaunas Polytechnic Institute. Translated from Mekhanika Polimerov, No. 1, pp. 59–62, January–February, 1972.     

Investigation of the supermolecular structure of polyformaldehyde in an injection-molded block

The process of variation of the spherulitic and "superspherulitic" structure in an injection-molded block of polyformaldehyde has been investigated as a function of the molding conditions with allowance for the structural inhomogeneity of the block. The molding conditions corresponding to the formation of "superspherulitic" structures have been determined. The thermal stability of these structures has been investigated.Mekhanika Polimerov, Vol. 4, No. 3, pp. 394–401, 1968     

Thermal deformation of oriented irradiated polyethylene and ethylene-propylene copolymer under uniaxial tensile load

The deformation of preoriented irradiated polyethylene and ethylenepropylene copolymer has been investigated under conditions of multiple heating above the melting point of the crystals and subsequent cooling with application of a constant uniaxial tensile load. The specimens are found to shorten during heating and to lengthen during cooling. However, this process is not reversible and irreversible elongation of the specimen occurs during each temperature cycle (heating and cooling).Mekhanika Polimerov. Vol. 3, No. 3, pp. 392–394, 1967     

Preservation of reliability classes under the formation of coherent systems

The preservation of reliability aging classes under the formation of coherent systems is a relevant topic in reliability theory. Thus, it is well known that the new better than used class is preserved under the formation of coherent systems with independent components. However, surprisingly, the increasing failure rate class is not preserved in the independent and identically distributed case, that is, the components may have the (negative) aging increasing failure rate property, but the system does not have this property. In this paper, we study conditions for the preservation of the main reliability classes under the formation of general coherent systems. These results can be applied both for systems with independent or dependent components. We consider both the case of systems with identically distributed components and the case of systems with components having different distributions. Copyright © 2013 John Wiley & Sons, Ltd.     

The dynamic properties of polyethylene and an acrylonitrile — Butadiene — Styrene material in a broad range of temperature and strain-rate variation

Conclusions The mechanical properties of an acrylonitrile-butadiene-styrene material and polyethylenes of densities =0.92 and 0.96 g/cm³ are studied within the temperature range of from 100 to –196°C and at strain rates of from 10^–3 to 1.3 · 10³ sec^–1. It is observed that under low-temperature and high-strain-rate conditions, the laws governing the mechanical properties of the acrylonitrile-butadiene-styrene material and polyethylenes are similar. Regions of strain rates and temperatures are found for which the behavior of the test materials is in good agreement with the Ree-Eyring equation, and, consequently, conforms to a temperature-time analogy. No embrittlement of the polyethylene is observed during tests at strain rates to 1.3 · 10³ sec^–1 and temperatures down to –196°C. In approximating these values of and T, the mechanical properties of polyethylenes will cease to be dependent on initial density.Institute of Polymer Mechanics, Academy of Sciences of the Latvian SSR, Riga. Translated from Mekhanika Polimerov, No. 6, 1027–1033, November–December, 1978.