publications

2021

1. 

   Ritz method

   N. Zhivotenko

   Oct 2021

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   Calculus of variations is a mathematical discipline devoted to finding extreme (largest and smallest) values of functionals – variables that depend on the choice of one or more functions. Calculus of variations is a natural development of the chapter of mathematical analysis devoted to the problem of finding the extremums of functions. The emergence and development of the calculus of variations is closely related to the problems of mechanics, physics and other technical sciences. Methods of calculus of variations are widely used in various fields of mathematics. For example, in differential geometry, geodesic lines and minimal surfaces are searched with their help. In physics, the variational method is one of the most powerful tools for obtaining equations of motion, both for discrete and distributed systems, including for physical fields. The methods of calculus of variations are also applicable in statics. There are two main types of methods for solving variational problems. The first type includes methods that reduce the original problem to solving differential equations. The alternative is the so-called direct methods. These methods somehow solve the original problem of finding a function in a given class that would deliver an extreme value to a given functional. One of the most popular methods of this class is the Ritz method.

2017

1. 

   Numerical modeling deflected mode in the typical construction of small-size spacecrafts from the composite material with rational reinforcement

   N. Zhivotenko, E. Eremina, and A. Sergeeva

   Innovative Development Dec 2017

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   Rationally reinforced products from composite materials are of huge interest to application designing of small-size spacecrafts. Results of numerical modeling of the deflected mode of a standard construction of the small-size spacecraft are presented in this work. It is represented that the weight efficiency of rationally reinforced composites is three times higher than at traditional aluminum alloys.

2016

1. 

   Crossover from an ordinary ferroelectric to a relaxor ferroelectric in Sr₍₂₊ₓ₎Bi₍₄₋ₓ₎Ti₍₅₋ₓ₎NbₓO₁₈

   S. Gridnev, N. Tolstykh, N. Zhivotenko, and 1 more author

   Bulletin of the Russian Academy of Sciences Physics Oct 2016

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   Sr₍₂₊ₓ₎Bi₍₄₋ₓ₎Ti₍₅₋ₓ₎NbₓO₁₈ materials with x = 0.2, 0.4, 0.6, 0.8, and 1 are synthesized. Investigations of the dielectric constant of the samples reveal an increase in the blurring of the phase transition as the share of titanium ions substituted for niobium ions grows. The Burns temperature and the temperature corresponding to the dielectric permittivity maximum are determined for all of the above compositions. Crossover from a normal ferroelectric to a relaxor ferroelectric in Sr₍₂₊ₓ₎Bi₍₄₋ₓ₎Ti₍₅₋ₓ₎NbₓO₁₈ samples is observed.

2015

1. 

   Phase transitions in a family of new ferroelectric materials with a layered aurivillius structure

   S. Gridnev, N. Zhivotenko, A. Bocharov, and 1 more author

   Sep 2015

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   The purpose of this research is the synthesis of new layered ferroelectrics, with the general formula Sr₍₂₊ₓ₎Bi₍₄₋ₓ₎Ti₍₅₋ₓ₎NbₓO₁₈ where 0 ≤ x ≤ 1 with the structure of Aurivillius Phases (AP), and the establishment of regularities of the influence of the chemical composition and the degree of structural disorder on the physical properties of these materials.

2. 

   Crossover normal to relaxor ferroelectric in Sr₍₂₊ₓ₎Bi₍₄₋ₓ₎Ti₍₅₋ₓ₎NbₓO₁₈

   S. Gridnev, N. Tolstykh, N. Zhivotenko, and 1 more author

   Sep 2015

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   Investigation of the influence of substitution of titanium cations Ti⁴⁺ for niobium cations Nb⁵⁺ on the occurrence of relaxor properties of layered perovskite with the structure of Aurivillius Phases Sr₍₂₊ₓ₎Bi₍₄₋ₓ₎Ti₍₅₋ₓ₎NbₓO₁₈, as well as the smearing of the phase transition in this material. The study was carried out for 0 ≤ x ≤ 1 with a step of 0.2.

3. 

   Relaxor behavior of layered perovskite Sr₂.₈Bi₃.₂Ti₄.₂Nb₀.₈O₁₈

   S. Gridnev, N. Tolstykh, A. Bocharov, and 1 more author

   Sep 2015

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   The studies of the dielectric properties of the obtained samples revealed the frequency dispersion and significant smearing of the peak of the real part of the permittivity and the dielectric loss tangent, which indicates the relaxor behavior of the material Sr₂.₈Bi₃.₂Ti₄.₂Nb₀.₈O₁₈, which is not characteristic of pure Sr₂Bi₄Ti₅O₁₈ (without substitution of Ti⁴⁺ for Nb⁵⁺).

2014

1. 

   Preparation and dielectric properties of (x)BiLi₀.₅Sb₀.₅O₃ — (1-x)Na₀.₅Bi₀.₅TiO₃ solid solution

   N. Zhivotenko, N. Tolstykh, S. Gridnev, and 1 more author

   Vestnik Voronezhskogo Gosudarstvennogo Tehnicheskogo Universiteta Dec 2014

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   According to the standard ceramic technology obtained solid solution (x)BiLi₀.₅Sb₀.₅O₃ — (1-x)Na₀.₅Bi₀.₅TiO₃. In the temperature range from 23 to 500 °C studied the temperature dependence of the real part of permittivity ε’ and tan(δ) at frequencies of 1 to 1,000 kHz in a weak measuring field of about 10 V/cm, which bind to the presence in these samples of the structural phase transition characteristic of the NBT of the ferroelectric rhombohedral phase to the tetragonal paraelectric phase. This phase transition is a highly time - blurred because in a wide range of temperatures and exhibits the characteristics of a relaxor transition, as evidenced by the variance ε’ and tan(δ) measured at different frequencies.

2. 

   Mechanical characteristics of laminated metal-polymer composite SIAL-2-1

   N. Zhivotenko

   Oct 2014

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   The rapid development of the aerospace industry worldwide, since the 1950s, has created a need for new materials for emerging high-tech products, since many of the requirements for traditional materials (metal alloys) could not be achieved. Light, high temperature resistant materials were required, which would have high mechanical characteristics and could be used in outer space. This led to the creation of metal-polymer composite materials and, in particular, laminated metal-polymer composites (for example aluminum/fiberglass - SIAL). Therefore, studies of the strength properties of SIAL’s are very relevant, which is what this work is devoted to.