Solution of some dynamic problems of viscoelasticity theory by the averaging method

Damping of longitudinal vibrations of a viscoelastic bar and transverse vibrations of a freely supported orthotropic plate is investigated by the averaging method. The problem of the forced movement of a viscoelastic cylinder enclosed in a thin elastic shell under the effect of an arbitrarily time-varying internal pressure is studied.Institute of Cybernetics at the Computer Center Academy of Sciences of the Uzbek SSR, Tashkent. Translated from Mekhanika Polimerov, No. 2, pp. 246–252, March–April, 1970.     

Speed-optimized control of heating of a thermoelastic plate with the help of internal heat sources

Speed-optimized control of the heating of a plate with restrictions on the thermal stresses is constructed as a junction of the distribution of internal heat sources by the method of the inverse problem of heat conduction.Translated from Matematicheskie Methody i Fiziko-mekhanicheskie Polya, No. 26, pp. 55–59, 1987.     

Factors in the adhesion strength of polymers toward a solid substrate

The true adhesion is looked upon as the sum of the experimentally determined strength of the glued area, internal stresses, and unaccountable technological losses (unrealized contacts). It has been established that the internal stresses do not depend on the value of the adhesion strength.Translated from Mekhanika Polimerov, No. 2, pp. 356–359, March–April, 1976.     

Stress on the interatomic bonds near the surface of a polymer

The stresses on the interatomic bonds in the interior and at the surface of polyethylene terephthalate film in uniaxial tension have been determined by means of infrared transmission and reflection spectroscopy. The stresses are found using the shift in the frequency of the atomic vibrations produced by the application of a mechanical load. It is shown that the stresses on some bonds in the specimen reach 700 kgf/mm², i.e., approach their theoretical strength. The concentration of these bonds in a surface layer 1 µ thick is approximately an order greater than the concentration in the interior of the specimen.A. F. Ioffe Physicotechnical Institute, Academy of Sciences of the USSR, Leningrad. Translated from Mekhanika Polimerov, No. 3, pp. 512–514, May–June, 1976.     

Refined analysis of the harmonic vibrations of disk-shaped orthotropic plates

On the basis of the refined three-dimensional theory the article solves the problem of vibrations of a thick orthotropic plate. Expansions according to homogeneous solutions of exponential type are used. The article presents the results of calculations of the stresses on the circumference of a circular and an elliptical disk.Translated from Teoreticheskaya i Prikladnaya Mekhanika, No. 18, pp. 98–101, 1987.     

Bending of a rectangular orthotropic glass-reinforced plastic plate under a transverse load

The Bubnov-Galerkin method is used to solve the problem of the bending of a clamped flexible orthotropic plate. An equation relating the deflection and the load is obtained. An experiment on a plate made of polyester plastic reinforced with satin-weave glass fabric is described. It is shown that within certain limits the deflections at the center of the plate and the combined stresses along the clamped edges are in good agreement with the theoretical values. The limits of applicability of the first-approximation formulas are investigated.All-Union Scientific-Research Institute of Railroad Transport, Ural Division, Sverlovsk. Translated from Mekhanika Polimerov, No. 4, pp. 674–679, July–August, 1969.     

Effect of fillers and solvents on the properties of polystyrene coatings

The mechanism of coating formation from solutions of atactic polystyrene in xylene and carbon tetrachloride has been investigated. It has been established that, as the filler content increases, in coatings formed from polystyrene solutions containing an evaporating solvent the growth of the internal stresses and the thermophysical characteristics is characterized by similarity of slope, as distinct from the case of coatings obtained from systems containing a polymerizing solvent. It is shown that the nature of the solvent has an important effect on the character of the interaction at the polymer—filler interface and on the structure and properties of the coatings.Kucherenko Central Scientific-Research Institute of Structural Design. Institute of Physical Chemistry, AS USSR, Moscow. Translated from Mekhanika Polimerov, Vol. 4, No. 6, pp. 1127–1129, November–December, 1968.     

The influence of coupled diffusion of heat and moisture on the state of stress in a plate

The fundamental results of previous reports on the coupling of the processes of diffusion of heat and moisture in solids are reviewed. The influence of the coupling on diffusion into an infinite plate from both its surfaces is discussed with the aim of clarifying what can and cannot be learned from such experiments. The nonuniformity of temperature and moisture content tends to cause nonuniform deformation. The stresses set up are computed for a homogeneous, isotropic plate. These self-equilibrating stresses first increase with time and then die out. For some combinations of material constants, the stresses undergo a reversal. For example, in some cases the surface stresses initially become compressive as moisture begins diffusing into the plate. Subsequently, as the interior of the plate increases in temperature due to the coupling effect, the surface stresses become tensile before eventually subsiding to zeroPublished in Mekhanika Kompozitnykh Materialov, No. 1, pp. 53–61, January–February, 1980.     

Bending of a thin cantilevered orthotropic plate with a concentrated load at the free edge

The problem of a thin rectangular cantilevered plate of constant thickness with a concentrated load in the center of the free edge is considered. The plate is assumed to be orthotropic, the fixed edge coinciding with the principal direction of elasticity. An equation is obtained for the normal stresses at an arbitrary point on the plate. The theoretical results are compared with experiment.A. A. Zhdanov Gor'kii Polytechnic Institute. Translated from Mekhanika Polimerov, Vol. 4, No. 4, pp. 739–741, July–August, 1968.     

Various methods of determining the natural frequencies and damping of composite cantilever plates. 1. Exact solution for the binomial model of deformation

On the basis of the classical theory of thin anisotropic laminated plates the article analyzes the free vibrations of rectangular cantilever plates made of fibrous composites. The application of Kantorovich's method for the binomial representation of the shape of the elastic surface of a plate yielded for two unknown functions a system of two connected differential equations and the corresponding boundary conditions at the place of constraint and at the free edge. The exact solution for the frequencies and forms of the free vibrations was found with the use of Laplace transformation with respect to the space variable. The magnitudes of several first dimensionless frequencies of the bending and torsional vibrations of the plate were calculated for a wide range of change of two dimensionless complexes, with the dimensions of the plate and the anisotropy of the elastic properties of the material taken into account. The article shows that with torsional vibrations the warping constraint at the fixed end explains the apparent dependence of the shear modulus of the composite on the length of the specimen that had been discovered earlier on in experiments with a torsional pendulum. It examines the interaction and transformation of the second bending mode and of the first torsional mode of the vibrations. It analyzes the asymptotics of the dimensionless frequencies when the length of the plate is increased, and it shows that taking into account the bending-torsion interaction in strongly anisotropic materials type unidirectional carbon reinforced plastic can reduce substantially the frequencies of the bending vibrations but has no effect (within the framework of the binomial model) on the frequencies of the torsional vibrations.Institute of Engineering Science Russian Academy of Sciences, St. Petersburg, Russia. St. Petersburg State University, Russia. Translated from Mekhanika Kompozitnykh Materialov, Vol. 32, No. 6, pp. 759–769, November–December, 1996.     

An asymptotic calculation of the vibrations of a viscoelastic cylinder with a slowly varying internal boundary

The vibrational problem is considered for a long hollow viscoelastic cylinder with a variable internal boundary, this being enclosed in an elastic shell. An asymptotic method based on averaging is used to find the resonant vibrations in response to a small uniformly distributed internal pressure that varies periodically with time. The calculation is carried through to quadrature working formulas.Moscow Institute of Electric Machine Construction. Translated from Mekhanika Polimerov, No. 5, pp. 935–939, September–October, 1973.     

Stress analysis for a rectangular thick plate of a composite material with a spatially locally curved structure under forced vibration

Natural and forced vibrations of a thick rectangular plate fabricated from a composite material with a spatially locally curved structure are investigated with the use of exact three-dimensional equations of motion of the theory of elastic anisotropic bodies. The investigations are carried out within the framework of the continuum approach developed by Akbarov and Guz. It is supposed that the plate is clamped at all its edges and is loaded on the upper face with uniformly distributed normal forces periodically changing with time. The influence of the parameters of local curving on the fundamental frequency of the plate and on the distribution of the normal stress acting in the thickness direction under forced vibration is studied. The corresponding boundary-value problems are solved numerically by employing the three-dimensional FEM modelling.Russian translation published in Mekhanika Kompozitnykh Materialov, Vol. 40, No. 6, pp. 779–790, November–December, 2004.     

Electroelastic thickness vibrations of a quartz SC-cut plate

Analytic solutions are obtained of the boundary value problem of steady motions of a thick piezocrystalline SC-cut quartz plate describing thickness modes of harmonic elastic vibrations. The plate endfaces have no electrodes and adjoin a vacuum or a rarefied gas. The measure of the difference between the found values of the five lowest eigenfrequencies of the thickness vibrations of a plate without electrodes and the values of the corresponding frequencies of a plate whose endfaces are covered by massive short-circuited electrodes is determined.Translated from Teoreticheskaya i Prikladnaya Mekhanika, No. 19, pp. 83–85, 1988.     

On the stress distribution in a rectangular thick plate of a composite material with curved structure under forced vibration

The stress distribution in a rectangular plate of a multilayer composite material with a periodically curved structure under forced vibration is studied. It is assumed that the plate is hinge supported at opposite sides. The investigation is carried out within the exact three-dimensional linear theory of elasticity. The mechanical relationships of the plate material are described by the continuum theory of Akbarov and Guz'. The numerical results obtained by the finite element method show that even in low-frequency dynamic loading of the plate the extreme values of stresses, which appear as a result of the curving in the plate structure, considerably exceed those in the corresponding static loading.Institute of Mathematics and Mechanics, Academy of Sciences of Azerbaijan, Baku, Azerbaijan. Translated from Mekhanika Kompozitnykh Materialov, Vol. 35, No. 4, pp. 447–454, July–August, 1999.     

Effect of the conditions of formation of glued joints on their thermophysical properties

A correlation has been experimentally established between the thermal resistance of adhesive films and the internal stresses that develop during the curing process. During cure the thermal resistance varies in parallel with the internal stresses. It is assumed that the development of thermal resistance is determined by the tension produced in the film by the development of the internal stresses.Voronezh Forest Engineering Institute. Translated from Mekhanika Polimerov, No. 4, pp. 754–756, July–August, 1973.     

Forced vibrations of a multiply connected isotropic plate

On the basis of A. I. Aleksandrovich's investigations the present authors worked out an approximate method of solving problems of forced flexural vibrations of a multiply connected isotropic plate. For an elliptic plate with circular holes numerical results are presented.Translated from Teoreticheskaya i Prikladnaya Mekhanika, No. 18, pp. 105–111, 1987.     

Effect of internal stresses on the wear resistance of epoxy coatings

The results of wear tests on ED-5 epoxy coatings are used to derive a relation between internal stresses, modulus of elasticity, and wear resistance. During wear the internal tensile stresses diminish, the rate of decrease depending on the initial stress state, the material of the abrading body, and the test conditions. The thickness of the coating affects wear resistance up to a certain value; for ED-5 the limiting thickness is 500 microns.Mekhanika Polimerov, Vol. 1, No. 2, pp. 123–128, 1965     

Concentration of electroelastic fields in a composite piezoceramic plate with a hole intersecting the interface of materials

A plane problem of electroelasticity is considered for an infinite compound plate with a hole located in both constituents of the plate. The corresponding boundary value problems is reduced to a system of singular integral equations of second kind, which is solved in numerical quadratures. Calculation results are presented that describe the concentration of electroelastic fields near the hole upon action at infinity of the vectors of mechanical stresses and electric field strength.Translated from Mekhanika Kompozitnykh Materialov, Vol. 35, No. 3, pp. 359–366, May–June, 1999.     

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.     

An approach to studying nonsteady-state vibrations of a finite length cylinder

A method is given for analyzing the nonsteady-state vibrations of a finite length cylinder based on using Laplace transforms and approaches developed previously for determining the vibration natural frequencies and forms. A numerical method is demonstrated for determining residues with reference to expressions for displacements and stresses. Quantitative estimates are given for stresses in a cylinder for a specific principle of the change in load with time and features of the time-dependent behavior of displacements in relation to the magnitude of the area of loading at the end are studied.Translated from Teoreticheskaya i Prikladnaya Mekhanika, No. 18, pp. 129–133, 1987.