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Torsional waves as one of the types of nonlinear elastic cylindrical displacement waves are analyzed theoretically within the framework of the five-constant Murnaghan model. The analysis is based on tools of the nonlinear theory of elasticity. Two variants of new nonlinear wave equations for torsional waves are derived taking into account cubicallyt nonlinear terms. The difference between the variants is in the different ways of allowing for the nonlinearities in the wave equation. The simpler variant is considered, and the evolution of torsional waves is analyzed theoretically and numerically. Special attention is paid to the boundary conditions and the transcendent equation classical for torsional waves. [ABSTRACT FROM AUTHOR]

The peculiarities of using the boundary conditions in the nonlinear problems of wave propagation are analyzed for media that deform elastically and have an internal or external boundary. The analysis is carried out for two types of waves: a Rayleigh surface wave and a torsional wave. The statement and wave analysis of the specified two waves in the linear (classical) approach are briefly described since the linear solutions are used as a first approximation in the nonlinear approach. Common to both types of waves (and, apparently, to other waves in media with boundaries) is a significant complication in the nonlinear approach of the boundary conditions due to the difference between the shape of the boundary before and after deformation (in the linear approach, the shape of the boundary does not change). Also, a common feature is the significant complication of the mathematical representation of the boundary conditions due to the additional nonlinear terms. The example of the Rayleigh surface wave shows that the procedure for solving the problem using nonlinear boundary conditions is difficult but possible. The example of a torsional wave reveals the fact that the use of the condition of absence of stresses on the boundary surface (assumption of a free boundary) may not be completely correct. [ABSTRACT FROM AUTHOR]

A method of determining the parameters of the standard three-constant rheological model is proposed. It is recommended to apply the model to the description of seismic waves in soil layers. The standard model is briefly described. Also, the essence of the method is outlined. A feature of this method is that it is sufficient to have one experimental creep curve of the soil layer to determine the three rheological parameters of the wave model. The effectiveness of the method is demonstrated for layers of sandy clay loam, silt loam, and silty clay. Also, the determined rheological parameters are used in an attempt to construct scenarios of evolution of the velocity and amplitude of an exponentially damped harmonic seismic shear wave for the three types of soil when the wave frequency or travel time change. [ABSTRACT FROM AUTHOR]

A new generalization of the method of constraints for displacement gradient occurring when studying a torsional displacement wave propagating in a nonlinear elastic material is proposed within the framework of the five-constant Murnaghan model. This method allows us to find an approximate solution of the recently proposed nonlinear wave equation and includes the constraints not only on the first partial derivatives of displacements, i.e., the smallness of the maximum amplitude of the wave relative to the wavelength, but also on the displacements, i.e., the real value of the maximum amplitude of the wave, and on the curvature of the wave profile. [ABSTRACT FROM AUTHOR]

New features of slow and fast modes of a plane wave in a composite material are analyzed. The composite is modeled by a linear structural model of elastic mixture. Quantitative estimates for wave modes in specific composites are proposed for the first time. The following four questions are answered: (i) Are there modes equally dispersive over the entire frequency range allowed for the mixture model? (ii) What is the difference between the phase velocities of the slow and fast modes in real materials? (iii) What are the frequency ranges in which the modes propagating in one component of the composite undergo in-phase and anti-phase oscillations? (iv) What are the frequency ranges in which particles of both composite components where one mode propagates undergo in-phase and anti-phase oscillations? For the computer analysis, we select eight composites with full sets of physical constants. The answers are based on three groups of 16 graphs of wave number versus frequency, phase velocity versus frequency, and amplitude versus frequency. [ABSTRACT FROM AUTHOR]

A nonlinear elastic cylindrical radial displacement wave is analyzed theoretically and numerically for an arbitrary solitary wave profile and initial wave profiles in the form of Friedlander and Macdonald functions. The five-constant Murnaghan model is used. Unlike the most profiles of nonlinear waves in materials that have periodical or single humps, these waves have no hump, decrease monotonically, and have concave downward profile. Both profiles are very similar, have the properties of solitary wave, and, therefore, can be studied using the nonlinear theory of elasticity. A comparison of the Macdonald and Friedlander profiles as the solutions of the linear wave equation for a cylindrical wave shows that if the Macdonald function is considered as the exact solution of this equation, then the Friedlander function can be considered an approximate solution of this equation because its graphical representation is similar to that of the Macdonald function. The evolution of waves is studied by the approximate method of limitation of displacement gradient taking into account the first two approximations. Formulas are theoretically obtained for an approximate representation of a solitary cylindrical wave and a concrete representation of this wave for the given Macdonald and Friedlander initial profiles. It is shown that the flection of the profiles changes when the waves propagate some distance but the behavior of the profiles (evolution scenarios) does not differ significantly from each other. Then within the framework of the problem stated, both profiles are interchangeable despite the fact that they are mathematically represented in different ways. [ABSTRACT FROM AUTHOR]

The distortion of a nonlinear elastic plane displacement wave of Friedlander profile typical for blast waves is analyzed theoretically and numerically using the five-constant Murnaghan model. Contrary to most nonlinear waves in materials that have periodic or single humps, this wave has no hump, is monotonically decreasing, and is concave down. The evolution of waves is studied using an approximate method with the first two approximations taken into account. Some essential distinctions of this wave are shown in detail theoretically and numerically: its atypical profile evolves in an atypical way. The following significant features of the Friedlander wave are shown: the profile becomes much (for materials with soft nonlinearity) or less (for materials with hard nonlinearity) steeper, still has no hump, and remains convex down, the maximum value of the profile increasing. [ABSTRACT FROM AUTHOR]

New extended information on the 12-volume edition Mechanics of Composites is offered in English. It includes the contents of each volume and is addressed to the English-language reader. These contents consist of the author's names, titles of volumes, and short summaries for each volume. Also, for each chapter, the author's names and titles of all chapters are given. This article aims to somewhat fill in the lack of information in English about Mechanics of Composites. [ABSTRACT FROM AUTHOR]

In order to identify analogies in the analysis procedures, two problems are described and commented on: the classical problem (problem O) on harmonic oscillations of two interconnected absolutely rigid bodies suspended on springs and the nonclassical problem (problem W) on the propagation of plane longitudinal waves in a two-phase elastic mixture. A number of analogies between these problems are developed, they are described in the form of six steps of comparative analysis of the problems O and W, each of the problems corresponds to a specific analogy. Attention was paid to the usefulness of analogies for the analysis of the problem of waves. The theory of two-phase mixtures can successfully use analogies from the corresponding problems of the theory of two interconnected oscillating systems. Hence the more general fact that the mechanism of mutual assistance in the oscillation theory discovered almost 100 years ago by academician Mandel'shtam has extended its influence to the theory of waves since then. [ABSTRACT FROM AUTHOR]

A nonlinear plane longitudinal elastic displacement wave is studied theoretically within the framework of the Murnaghan model for a harmonic initial profile. The main novelty is that the evolution of waves is analyzed by the developed approximate method of constraints on the displacement gradient within the framework of two-phase mixture theory. It is shown that the initially excited wave is divided into four modes, all modes are dispersed and distorted, and each mode wave is represented as a superposition of the first and second harmonics. The amplitude of the second harmonic depends on many parameters, including the direct dependence on time. This dependence means that the second harmonic will dominate over time. [ABSTRACT FROM AUTHOR]

The propagation of a nonlinearly elastic longitudinal plane displacement wave for a symmetric initial wave profile described by a Gaussian function and an asymmetric initial profile described by a Whittaker function is analyzed. The basic novelty is that the evolution of waves is analyzed by the approximate methods by taking into account the first three approximations. The harmonic wave is analyzed only to compare with the new results for the bell-shaped wave. Some significant differences between the evolutions of waves are shown. Common to these profiles is the distortion of the initial profile due to the nonlinear self-interaction of the wave. The bell-shaped (symmetrical profile) wave retains symmetry when moving in a nonlinearly elastic body. For some initial sets of parameters, this wave does not change the wavelength initially and only shows a tendency towards the formation of two humps instead of one when we take into account the second conditional harmonic (two bell-shaped waves form and adjoin each other and halve wavelength) and the sinking of the left and elevation of the right hump when we take into account the third harmonic. The asymmetric profile described by Whittaker function retains the wavelength and asymmetry when the second approximation of the second harmonic is taken into account, but the amplitude increases rapidly. With additional allowance for the third harmonic, two asymmetric humps are formed, the humps resemble the evolution of the symmetric profile when the second harmonic is taken into account. Common to the evolutions of the symmetric and asymmetric profiles is the distortion of the initial wave profile: the formation of two symmetric humps when the second harmonic is taken into account in the analysis of the Gaussian function and two asymmetric humps when the third harmonic is taken into account in the analysis of the Whittaker function. Taking the third harmonic into account for a symmetric profile makes the two humps asymmetrical for symmetric and asymmetric profiles, only in these two profiles, the asymmetry is different. [ABSTRACT FROM AUTHOR]

A nonlinear plane longitudinal elastic displacement wave is studied theoretically and numerically using the Murnaghan model for two forms of initial profile: harmonic and bell-shaped. A major novelty is that the evolution of waves is analyzed by approximate methods taking into account the first three approximations. The harmonic wave is analyzed only to compare with the new results for the bell-shaped wave. Some significant differences between the evolution of waves are shown. The initially symmetric profiles transform differently due to distortion: symmetrically (for the harmonic profile) and asymmetrically (for the bell-shaped profile). The third approximation introduces the fourth harmonic for the harmonic wave when this wave is analyzed by the method of successive approximations, while the bell-shaped wave is characterized in the third approximation differently when using the method of constraints on the displacement gradient. At relatively long distances from the beginning of the propagation, the one-hump bell-shaped wave transforms into a two-hump one. These humps adjoin each other halving their lengths. The third approximation allows us to observe new wave effects: the asymmetry of the left and right humps about their peaks and the asymmetry of the humps about each other; the lowering of the left hump and the rise of the right one. The results obtained are analyzed. [ABSTRACT FROM AUTHOR]

A theoretical attempt is proposed to explain the auxeticity of elastic materials by use of nonlinear models of elastic deformations for a wide range of strain values up to moderate level. Analytical expressions are obtained that correspond to three kinds of universal deformations (simple shear, uniaxial tension, omniaxial tension) within the framework of three models well-known in the nonlinear theory of elasticity: two-constant Neo-Hookean model, three-constant Mooney–Rivlin model, five-constant Murnaghan model. The most interesting novelty is that a sample of elastic material is deformed as a conventional material at small strains and as an auxetic at moderate strains. [ABSTRACT FROM AUTHOR]

New nonlinear wave equations are derived using the Murnaghan five-constant elastic potential. A feature of these equations is the following two assumptions: the elastic deformation process is physically nonlinear (geometric nonlinearity is neglected) and the deformation is geometrically axisymmetric and described by cylindrical coordinates. Therefore, the system of wave equations contains only two coupled equations. Such a statement allows us to use these new equations to analyze surface waves propagating along a circular cylindrical cavity in an elastic medium. Another feature of the nonlinear equations is that every equation includes the classical linear part. The nonlinear terms of the equations are quadratically nonlinear and contain twenty-three types of nonlinearities in the first equation and twenty-two types in the second equation. [ABSTRACT FROM AUTHOR]

A new variant of nonlinear wave equation is obtained for a solitary nonlinear cylindrical radial displacement wave to which an approximate problem-solving method tested against the problem on a plane longitudinal wave is applied. A numerical analysis is carried out for the wave initial profile in the form of the Macdonald function. About 30 variants of initial parameters are studied numerically, namely, three variants of materials (aluminum, copper, steel), three variants of the wave bottom, three variants of initial maximal amplitude, and one variant that unites two harmonics. For every variant a set of nine two-dimensional graphs “wave shape-travel distance” that shows the level of wave distortion is plotted. This profile turns out to be unusual from the point of view of profile shape. The profile shapes considered before (sinusoidal, bell-shaped, in the form of Whittaker and Hankel functions) changed substantially forming a plateau on the top and then two humps, manifesting in this way strong distortion. The shape of the Macdonald function is hardly distorted, the profile bottom increases slightly and only the profile maximum value increases considerably, changing the steepness of the profile left part. [ABSTRACT FROM AUTHOR]

This article is a continuation of the authors’ previous publication on the occasion of the 100th anniversary of the National Academy of Sciences of Ukraine and the S. P. Timoshenko Institute of Mechanics (1918-2018) and is meant as some addendum to the articles devoted to this anniversary. The most important books published by the S. P. Timoshenko Institute of Mechanics over the almost 100-year period are listed. The list includes preliminary information, generalized collective multi-volume monographs, classical monographs, textbooks, tutorials, and some other publications. In total, 468 books are listed, of which 247 are available in the Library of Congress. [ABSTRACT FROM AUTHOR]

The evolution of a vertically polarized plane transverse wave (SV-wave) propagating in a nonlinear elastic medium is analyzed. The deformation process is described by the Murnaghan model, where the cubic nonlinearity is taken into account. Two approximate approaches are used and the solutions of the corresponding nonlinear wave equations are found for the first two approximations. Numerical examples are shown and commented [ABSTRACT FROM AUTHOR]

Nonlinear plane longitudinal elastic waves with different profiles are studied using the Murnaghan model. The novelty is that the waves are analyzed using the same approximate method and the solutions of the nonlinear wave equations are similar in form. The distortion of the initial wave profile described by cosinusoidal, Gaussian, and Whittaker functions is described theoretically and numerically. About 80 variants of initial parameters are studied numerically: three analytical representations of the initial profile, three materials (aluminum, copper, steel), three wave lengths, three initial maximum amplitudes. For each variant, four (cosine) and five (Gauss, Whittaker) two-dimensional graphs of wave shape versus traveled distance are plotted to demonstrate the distortion of the wave profile [ABSTRACT FROM AUTHOR]

The problem of linear elasticity for free harmonic (periodic) and solitary bell-shaped (nonperiodic) waves in an isotropic half-space with stress-free plane boundary is considered. The half-space is made of either conventional (classical structural) or nonconventional (nonclassical auxetic) material. Two cases of wave damping are studied: rapid (surface wave) and periodic (nonsurface wave). The following conclusions on a free harmonic wave are drawn: a surface wave exists in materials of both classes, but the ratio of the wave velocity to the velocity of a transverse plane wave in auxetic materials is somewhat lower than in conventional materials; a nonsurface wave cannot be described by the approach applied to conventional materials, but can theoretically exist in auxetic materials where there are two wave velocities. For a solitary (bell-shaped) wave, the assumption that the wave velocity depends on the wave phase is substantiated and some constraint is imposed on the time of travel of the wave and the way the wave velocity varies with time. The following conclusions are drawn: a rapidly damped bell-shaped wave cannot be described by the approach for both classes of materials, whereas a periodically damped bell-shaped wave can be described [ABSTRACT FROM AUTHOR]

Elementary mechanical static tests that allow determining the physical constants (density, two Lame constants, three Murnaghan constants) of the nonlinear Murnaghan's hyperelastic material model are described. The theoretical method of analysis is based on the notion of universal deformation (simple shear, hydrostatic pressure, unidirectional tension/compression). The necessary theoretical formulas for Murnaghan's model are derived. Some additional features of these formulas are shown. For example, an analysis of simple shear shows that Murnaghan's model describes the classical nonlinear Pointing and Kelvin effects and an analysis of uniform and unidirectional tension/compression shows similar effects of nonlinear dependence of stresses on strain parameters. The proposed set of tests can be used for the nonlinear description of new classes of elastic materials, including metamaterials [ABSTRACT FROM AUTHOR]

Two types of solitary elastic waves are considered: a longitudinal plane displacement wave (longitudinal displacements along the abscissa axis of a Cartesian coordinate system) and a radial cylindrical displacement wave (displacements in the radial direction of a cylindrical coordinate system). The basic innovation is the use of nonlinear wave equations similar in form to describe these waves and the use of the same approximate method to analyze these equations. The distortion of the wave profile described by Whittaker (plane wave) or Macdonald (cylindrical wave) functions is described theoretically [ABSTRACT FROM AUTHOR]

The classical, quite abstract constraint | u | < 1 for elastic materials and a number of possible mathematical and physical constraints for displacement gradients are discussed Keywords: elastic material, nonlinear elasticity, constraints, displacement gradient [ABSTRACT FROM AUTHOR]

Linear and nonlinear equations describing the propagation of a surface wave along the free flat boundary of an elastic half-space that is in an antiplane strain state are analyzed. The nonlinearity, both geometrical and physical, is represented by a five-constant Murnaghan potential. Four cases of surface waves are considered: harmonic and simple waves in linear and nonlinear cases. It is shown that there is a contradiction between the initial assumptions and the final result in all the cases. This means that such a surface wave cannot be described in these cases and, thus, is impossible. [ABSTRACT FROM AUTHOR]

The perturbation method is applied to solve the problem of the propagation of a plane longitudinal harmonic wave in a hyperelastic material described by the classical Murnaghan model. The exact expression of the second-order solution in terms of Hankel functions of zero and first order and their products is derived. A simplification of the expression is considered [ABSTRACT FROM AUTHOR]

New nonlinear wave equations describing the propagation of a surface wave along the interface between two half-spaces with different densities and elastic properties (Stoneley wave) are proposed. Nonlinearity is introduced by the five-constant Murnaghan potential, which includes both geometrical and physical nonlinearities. The nonlinear equations are solved in two iterations of the method of successive approximations. The solution includes second harmonics [ABSTRACT FROM AUTHOR]

The classical problem of Love waves with the additional assumption of nonlinear deformation is considered. The Murnaghan model is used. A new nonlinear wave equation for displacements that has a linear part and a nonlinear part consisting of only third- and fifth-order terms is derived. In the case of physical nonlinearity alone, the solution of the new nonlinear equation subject to nonlinear boundary conditions is obtained using the first two approximations of the method of successive approximations. A new nonlinear equation for determining the wave number is derived. It demonstrates that the change in the wave length while the frequency remains constant is a new factor that distorts the initial wave profile [ABSTRACT FROM AUTHOR]

New two-dimensional nonlinear wave equations for Murnaghan materials are proposed. Four lines of simplifying the Murnaghan potential are considered. Based on the simplified Murnaghan potentials, sixteen submodels (models of different levels) can be constructed. For the most typical submodels, new systems of nonlinear wave equations are presented [ABSTRACT FROM AUTHOR]

This article is prepared on the occasion of awarding Professor A.N. Guz the ICCES Lifetime Achievement Medal and was read as a lecture at the International Conference on Computational and Experimental Engineering and Sciences (ICCES-12), Greece, Crete, April 30-May 4, 2012. Four important mile-stones in the scientific life of A. N. Guz are shown and discussed: defense of doctor of sciences dissertation, forming of new scientific areas and scientific school, directorship at the S. P. Timoshenko Institute of Mechanics, preparation of many monographs, which can be classified as the first ones in the world's scientific literature [ABSTRACT FROM AUTHOR]

Features of applying bibliometric indicators for scientific journals and scientists are discussed using, as examples, scientists of the S. P. Timoshenko Institute of Mechanics and the journal Prikladnaya Mekhanika (International Applied Mechanics), which is published by the institute in Russian and by Springer in English. Old and new scientific databases are described and commented on. Consideration is given to citation as the most popular parameter for bibliometric indicators, the Hirsch and Egghe indices as criteria for the evaluation of scientists, the Hirsch index, Impact-Factor, SJR, SNIP, and RIP as criteria for the evaluation of scientific journals, and a new approach to evaluation based on full-text article requests. In 1991–2011, Prikladnaya Mekhanika (International Applied Mechanics) had highest indicators among all Ukrainian scientific journals: Impact-Factor = 1.740 in 2005, SJR = 0.240 in 2006, RIP = 1.76 in 2006, SNIP = 2.45 in 2011 [ABSTRACT FROM AUTHOR]

The information on the six-volume series Uspekhi Mekhaniki: Advances in Mechanics is generalized. Examples of the recognition of the series by world's leading research institutions and scientists are given. Each volume of the series is briefly characterized [ABSTRACT FROM AUTHOR]

A Rayleigh wave propagating along the boundary surface of an elastic half-space whose nonlinear deformation is described by the Murnaghan model is analyzed. Three simple equations of nonlinear motion for displacement and six new nonlinear wave equations for potentials are proposed. New approximate (first two approximations) solutions are obtained and discussed. It is shown that the second approximation includes the second harmonics of both traveling harmonic wave and its amplitude decreasing with depth and nonlinearly depends on the initial amplitude of the Rayleigh wave. The geometrically linear and nonlinear boundary conditions are written, and their difference is shown. Their role in the analysis of Rayleigh wave is discussed. A new nonlinear equation for the Rayleigh wave number is derived and analyzed [ABSTRACT FROM AUTHOR]

Two new tendencies in the integration of the journal Prikladnaya Mekhanika ( International Applied Mechanics) into the world's scientific community are discussed. One tendency is that representatives of the world's scientific community publish their articles in the journal. The other tendency is positioning of this journal in the world's scientific information environment. The number of full-text article requests as per the document Springer-the Language of Science: International Applied Mechanics, Publisher's Report, July 1 (2011) is discussed.Anew publication evaluation criterion based on this metric is offered [ABSTRACT FROM AUTHOR]

The generation of the first, second, fourth, and eighth harmonics of a harmonic longitudinal plane wave propagating in quadratic nonlinear materials described by the classical Murnaghan model is numerically modeled. This situation was also analyzed analytically. The materials are fibrous composites with micro- and nanoscale structure. Using such materials introduces additional real restrictions on the main parameters and allows simulating various real situations: from the generation of all harmonics for feasible distances and times to the generation of the second harmonics for feasible distances and times. The contribution of each approximation to the overall wave pattern is analyzed. It is shown that these approximations affect the prediction of the evolution of the initial wave profile: first there is a tendency to the generation of the second harmonic which then transforms into a tendency to the generation of the fourth and eight harmonics [ABSTRACT FROM AUTHOR]

The perturbation method (small-parameter method) is used to analyze the propagation of a cylindrical wave in a quadratic nonlinear hyperelastic material described by the classical Murnaghan model. The exact representation of the first-order solution in terms of squared Hankel functions of zero and first orders and their product is derived. A simplification of the new solution is considered [ABSTRACT FROM AUTHOR]

Structurally complex nanocomposites (their fillers have complex shape, which complicates the theoretical analysis of these composites) are considered. Nanotubes of quite complex shape that are very difficult to theoretically describe and analyze are exemplified. Fibrous and particulate composites reinforced with bristled nanofibers and bristled knedel-like nanogranules, respectively, are described and analyzed theoretically. Theoretical approaches to studying nanocomposites with large-scale and small-scale bendings of nanotubes are outlined [ABSTRACT FROM AUTHOR]

The nonlinear equations that underlie the analysis of classical Rayleigh waves are derived for the two-dimensional case of nonlinear elastic deformation described by the Murnaghan model. In addition to the case of presence of both geometrical and physical nonlinearities, two special cases are considered where one only type of nonlinearity is taken into account. It is shown that unlike the one-dimensional problems for plane waves where only three types of nonlinear interaction should be allowed for, the two-dimensional problems should include 24 types of nonlinear interaction. In the case of geometrical nonlinearity alone, a preliminary analysis of the nonlinear equations is carried out. Second-order equations are derived. The second approximation includes the second harmonics of the wave itself and its attenuating amplitude and is nonlinearly dependent on the initial amplitude of the Rayleigh wave and linearly increasing with the distance traveled by the wave [ABSTRACT FROM AUTHOR]

general idea of the mechanics of nanocomposites that allows formulating a system of approaches and methods of analysis in this area is given. The place of mechanics in materials research and the structural levels that divide mechanics into macromechanics, mesomechanics, micromechanics, and nanomechanics are discussed. A brief historical sketch of the nanomaterial technology is presented. Examples of different nanotechnologies and nanomaterials are given. Typical nanomaterials and their properties are described. Matrices and reinforcements of nanocomposite materials as well as their properties are considered separately. A classification of nanocomposites is proposed. Special attention is given to modeling in the structural mechanics of nanocomposites, the principles of continualization and homogenization, edge and near-surface effects, validity limits of the continuum approach, and two-sided estimates. A discussion is given of two basic models within the framework of the basic approach as a set of concepts, models, and problem statements and of the development of methods adequately describing mechanical phenomena in nanocomposites. The presented material is mainly taken from the book A. N. Guz, J. J. Rushchitsky, and I. A. Guz, Introduction to the Mechanics of Nanocomposites [in Russian], S. P. Timoshenko Inst. Mech., Kyiv (2010) [ABSTRACT FROM AUTHOR]

The perturbation (small-parameter) method is used to obtain the first three approximations for the problem of a harmonic longitudinal plane wave propagating in a quadratic nonlinear hyperelastic material described by the classical Murnaghan model. The subsequent approximations are discussed. The contribution of each approximation to the overall wave pattern is analyzed. It is shown that the third approximation corrects the prediction of the evolution of the initial wave profile. Which of the harmonics dominates depends on the distance traveled by the wave: the second harmonic is generated first, then it transforms into the fourth harmonic, and finally, as the distance increases, the eighth harmonic shows [ABSTRACT FROM AUTHOR]

general Love solution for the inhomogeneous linear transversely isotropic theory of elasticity with the elastic constants dependent on the coordinate r is proposed. The axisymmetric case is analyzed and cylindrical coordinates are used. The key steps of deriving the classical Love solution are described for further use of the derivation procedure. The procedure of generalizing the Love solutions to the inhomogeneous theory of elasticity is detailed. This is the fifth publication in the series on general solutions in the inhomogeneous theory of elasticity. The new results obtained are promising for the modern theory of functionally graded materials [ABSTRACT FROM AUTHOR]

general Love solution for the inhomogeneous linear isotropic theory of elasticity with the elastic constants dependent on the coordinate r is proposed. The axisymmetric case is analyzed and cylindrical coordinates are used. This is the fourth publication in the series on general solutions in the inhomogeneous theory of elasticity. The new results are promising for the modern theory of functionally graded materials. The key steps of deriving the Love solutions are described for further use of the derivation procedure. The procedure of generalizing the Love solutions to the inhomogeneous theory of elasticity is detailed. The results obtained are discussed [ABSTRACT FROM AUTHOR]

general Love solution for the inhomogeneous transversely isotropic theory of elasticity with the elastic constants dependent on the coordinate z is proposed. This result may be considered as a generalization of the Love solutions we recently derived for the inhomogeneous isotropic theory of elasticity. The key steps of deriving the Love solution for the classical linear homogeneous transversely isotropic theory of elasticity are described for further use of the derivation procedure, which is then generalized to the inhomogeneous transversely isotropic case. Some particular cases of inhomogeneity traditionally used in the theory of elasticity are also examined. The significance of the derived solutions and their importance for the modeling of functionally graded materials are briefly discussed [ABSTRACT FROM AUTHOR]

The general Hoyle–Youngdahl and Love solutions in the three-dimensional theory of inhomogeneous linear elastic materials are proposed. Following a brief historical outline of various general solutions existing in the classical linear elasticity of homogeneous isotropic media, key steps of the derivation of the Hoyle–Youngdahl and Love solutions are presented. The procedure is then generalized to the case of inhomogeneous elastic materials with elastic constants depending on the z-coordinate. The significance of the solutions and their relevance to modeling of functionally graded materials is discussed in brief [ABSTRACT FROM AUTHOR]

We present fragments of the theory of nanotransistors concerning general information about transistors, models of nanocomposite materials, effects of nonlinear interaction of waves, and a theoretical analysis of the interaction of cubically nonlinear elastic plane harmonic waves in materials whose nonlinear properties are described by the Murnaghan potential. Using the method of slowly varying amplitudes, we investigate the interaction of two harmonic vertical transverse plane waves. Shortened and evolution equations, and Manley-Rowe relations, are obtained. We analyze analytically and numerically the mechanism of repumping of the energy of a strong pumping wave that propagates at a frequency of ω to a weak signal wave propagating at a frequency of 3ω . The described mechanism of switching of hypersonic waves in a nonlinearly elastic nanomaterial is similar to the mechanism of switching observed in optical and other transistors. [ABSTRACT FROM AUTHOR]

The paper analyzes the level of coverage and citation of publications by mechanicians of the National Academy of Sciences of Ukraine (NASU) in the Scopus database. Two groups of mechanicians are considered. One group includes 66 doctors of sciences of the S. P. Timoshenko Institute of Mechanics as representatives of the oldest institute of the NASU. The other group includes 34 members (academicians and corresponding members) of the Division of Mechanics of the NASU as representatives of the authoritative community of mechanicians in Ukraine. The results are presented for each scientist in the form of two indices—the total number of publications accessible in the database as the level of coverage of the scientist’s publications in this database and the h-index as the citation level of these publications. This paper may be considered to continue the papers [–] published in Prikladnaya Mekhanika (International Applied Mechanics) in 2005–2009 [ABSTRACT FROM AUTHOR]

The development of the classical Signorini nonlinear elastic model is continued. Recent year’s published results on a recently developed area of the theory of nonlinear waves are outlined from a unified position and analyzed. The paper consists of six sections: explanation of the features of the class of waves under consideration; detailed description of the Signorini model; general formulation of wave-propagation problems based on the Signorini potential; analysis of results on plane and cylindrical waves obtained with the Signorini model; comparison of these results with those obtained with the Murnaghan model; discussion of the possible lines for the development of the research. [ABSTRACT FROM AUTHOR]

The paper performs a citation analysis of publications of mechanicians of the National Academy of Sciences of Ukraine (NASU) based on information tools developed by the Thomson Reuters Institute for Scientific Information. Two groups of mechanicians are considered: representatives of the S. P. Timoshenko Institute of Mechanics of the NASU (NASU members, heads of departments) and members (academicians) of the NASU Division of Mechanics. Three elements of the Citation Report (Results Found, Citation Index (Sum of the Times Cited), h-index) are presented for each scientist. This paper may be considered as a follow-up on the papers [–] published by Prikladnaya Mekhanika ( International Applied Mechanics) in 2005–2009 [ABSTRACT FROM AUTHOR]

The paper discusses the evaluation of scientific journals based on the Scopus database, information tools, and criteria. The SJR (SCImago Journal Rank) as the main criterion used by Scopus to evaluate scientific journals is considered. The Scopus and ISI systems are compared using information on the journal Prikladnaya Mekhanika ( International Applied Mechanics), a number of world-known journals on mechanics, and some journals on natural sciences issued by the National Academy of Sciences of Ukraine. Some comments and proposals are formulated. This paper may be considered as a follow up on papers published in Prikladnaya Mekhanika ( International Applied Mechanics) in 2005–2009 [ABSTRACT FROM AUTHOR]

The paper is concerned with the problem of evaluation of scientific publications as a part of the general problem of scientific information environment. A discussion on objective citation (entitled “Proposal from the Timoshenko Institute” and took place on the Internet in July 2007) is reviewed. New criteria (h-index, g-index) are discussed. A recent discussion by the mathematician community on the evaluation of scientific publications is presented. Some comments and proposals are formulated [ABSTRACT FROM AUTHOR]

The perturbation (small-parameter) method is used to analyze the propagation of a harmonic longitudinal plane wave in a quadratic nonlinear hyperelastic material described by the classical Murnaghan model. The three first approximations are obtained, and the contribution of each of them into the wave pattern is analyzed. It is shown that the third approximation somewhat improves the prediction of the evolution of the initial waveprofile: the tendency to generate the second harmonic goes over into the tendency to generate the fourth harmonic [ABSTRACT FROM AUTHOR]

A summary on transistors and some facts on nanocomposite materials and their classical models are provided. New models used here for computer simulation are described. Results from a theoretical study of the interaction of cubic nonlinear harmonic elastic plane waves in a Murnaghan material are presented. The interaction of two harmonic waves is analyzed using the method of slowly varying amplitudes. The mechanism of energy pumping from a strong pump wave to a weak signal wave is examined. The theoretical and numerical analyses conducted suggest that in theory, a nanocomposite material may be used to create a transistor that would work with hypersonic waves and have a speed in the nanosecond range [ABSTRACT FROM AUTHOR]