### Rubric: "01.02.00 Mechanics"

#### 539.3 Modeling of the dynamic stability of a cylindrical shell under the axial compressive load

##### Dubrovin V. M. (Bauman Moscow State Technical University), Butina T. A. (Bauman Moscow State Technical University)

doi: 10.18698/2309-3684-2015-2-4657

The article describes a method for calculating the dynamic stability of cylindrical shell under axial compressive time-varying load. The case of linearly varying load was con-sidered as an example.

Dubrovin V., Butina T. Modeling of the dynamic stability of a cylindrical shell under the axial compressive load. Маthematical Modeling and Coтputational Methods, 2015, №2 (6), pp. 46-57

#### 629.1.028 Mathematical model of movement of the multi-wheeled vehicles with torsional flexible bearing system

##### Zhileykin M. M. (Bauman Moscow State Technical University), Sarach E. B. (Bauman Moscow State Technical University)

doi: 10.18698/2309-3684-2015-3-1740

Within the framework of solving the problem of active control of the elastic and damping elements of multi-wheeled vehicle (MWV) suspension brackets investigating the properties of suspension bracket families designed both for different travels and for different loading is of great importance. Their kinematic schemes can be also rather various. It is not feasible to collect the required amount of information for families of vehicles of different design and operating characteristics. Performing a full analytical study to determine the appropriate characteristics is not possible. This problem could be successfully solved only by simulation. A mathematical model of the MWV motion is developed. The characteristic feature of the model is that the vehicle speed is not set forcedly, but it is generated by the interaction of the rotating wheeled propellers with the supporting base. It results in high accuracy in modeling real processes of MWV moving along an uneven road. The developed model can be applied to research various laws of multi-wheeled vehicle suspension bracket control.

Zhileykin M., Sarach E. Mathematical model of movement of the multi-wheeled vehicles with torsional flexible bearing system. Маthematical Modeling and Coтputational Methods, 2015, №3 (7), pp. 17-40

#### 539.3 Simulation of dynamic stability of a cylindrical shell under cyclic axial impact

##### Dubrovin V. M. (Bauman Moscow State Technical University), Butina T. A. (Bauman Moscow State Technical University)

doi: 10.18698/2309-3684-2016-3-2432

In this article we suggest a method for calculating the dynamic stability of a cylindrical shell with its axial compressive time-varying load, and cyclic axial load, which varies according to a certain law. As an example, we consider the axial load, changing linearly and the cyclic load, which varies according to the harmonic law. To show the cyclic load, we use Ince — Strutt diagram, defining the stable and unstable regions of the shell fluctuations.

Dubrovin V., Butina T. Simulation of dynamic stability of a cylindrical shell under cyclic axial impact. Маthematical Modeling and Coтputational Methods, 2016, №3 (11), pp. 24-32

#### 551.521 Simulation of atmospheric parameters of two-dimensional fields in problems of laser remote sensing

##### Ivanov S. E. (Bauman Moscow State Technical University), Gorodnichev V. A. (Bauman Moscow State Technical University), Belov M. L. (Bauman Moscow State Technical University), Mikhaylovskaya M. B. (Bauman Moscow State Technical University)

doi: 10.18698/2309-3684-2015-4-110121

The objective of this research is to examine the problem of simulating two-dimensional fields of atmospheric backscattering aerosol coefficient and speed of atmospheric wind. The problem is essential for mathematical simulation of laser remote sensing systems and laser location systems. For wind correlation lidar we selected optimal simulation parameters with regard to simulation time and conformity of atmospheric field parameters and their statistical characteristics with set-up statistical characteristics. The findings of the research illustrate that for small sized atmospheric irregularities it is more effective to use the forming filter method, but for large sized atmospheric irregularities the spectral method is the most effective simulation method.

Ivanov S., Gorodnichev V., Belov M., Mikhaylovskaya M. Simulation of atmospheric parameters of two-dimensional fields in problems of laser remote sensing. Маthematical Modeling and Coтputational Methods, 2015, №4 (8), pp. 110-121

#### 539.3 Theory of plates based on the method of asymptotic decompositions

##### Sheshenin S. V. (Lomonosov Moscow State University), Skoptsov K. A. (Lomonosov Moscow State University)

doi: 10.18698/2309-3684-2014-2-4961

The paper presents comparison of asymptotic analysis of a composite plate lateral bending under the impact of surface load against classical theories of thin and thick plates. Layers of the plate are assumed to be homogeneous linear elastic orthotropic materials.

Sheshenin S., Skoptsov K. Theory of plates based on the method of asymptotic decompositions. Маthematical Modeling and Coтputational Methods, 2014, №2 (2), pp. 49-61

#### 519.248 Progressively censored sample comparison - numerical methods for homogeneity statistic distributions and study of communication parameters estimating by Monte Carlo method

##### Timonin V. I. (Bauman Moscow State Technical University), Tyannikova N. D. (Bauman Moscow State Technical University)

doi: 10.18698/2309-3684-2015-3-89100

This paper considers the problem of function estimating for times to failure translation from one mode to another. This problem arises, for example, when there is data on failures of products in vitro tests and you need to estimate the reliability of the same type products with actual test conditions. For simplicity, we consider the case where MTBF have linear relation. The proposed method is based on minimizing the Kolmogorov-Smirnov statistic, which is used to test the homogeneity of two progressively censored samples. A special feature of the proposed statisticis using the Kaplan-Meier estimates of the reliability function for each sample. Provided conjecture homogeneity of two samples, the distribution of statistics does not depend on the type of distribution of failures. This paper proposes a method for calculating the exact distributions of these statistics. Tables of exact distributions probabilities are presented for a wide range of possible values of the volumes of samples. By means of statistical modeling a table of acceleration factor values is calculated and its histograms are presented.
Keywords: non-parametric statistics, the Kolmogorov-Smirnov test, Kaplan-Meier estimate, progressive censoring.

Timonin V., Tyannikova N. Progressively censored sample comparison - numerical methods for homogeneity statistic distributions and study of communication parameters estimating by Monte Carlo method. Маthematical Modeling and Coтputational Methods, 2015, №3 (7), pp. 89-100

#### 532.5:551.465 Numerical simulation of the point pulse source impact in a liquid on the ice cover

##### Savin A. S. (Bauman Moscow State Technical University), Gorlova N. E. (Bauman Moscow State Technical University), Strunin P. A. (Bauman Moscow State Technical University)

doi: 10.18698/2309-3684-2017-1-7890

The research examines the planar and three-dimensional problems of an ice cover perturbed by a point pulse source localized in the depth of an infinitely deep liquid. We studied the ice cover of different thickness and carried out numerical study of its perturbations by sources located at different depths. The main attention is paid to the ice cover perturbations that arise directly above the source.

Savin A., Gorlova N., Strunin P. Numerical simulation of the point pulse source impact in a liquid on the ice cover. Маthematical Modeling and Coтputational Methods, 2017, №1 (13), pp. 78-90

#### 539.3 Incompressible layered composites with finite deformations on the basis of the asymptotic averaging method

##### Dimitrienko Y. I. (Bauman Moscow State Technical University), Gubareva E. A. (Bauman Moscow State Technical University), Kolzhanova D. Y. (Bauman Moscow State Technical University), Karimov S. B. (Bauman Moscow State Technical University)

doi: 10.18698/2309-3684-2017-1-3254

The article considers the modeling results of incompressible layered composites with finite strains deformation according to the individual layers characteristics. The article proposes an asymptotic averaging method version for layered nonlinearly elastic incompressible composites with finite deformations and periodic structure. We are using a universal representation of the defining relations for incompressible composite layers, proposed by Yu.I. Dimitrienko, which allows us to simulate simultaneously for a complex of various nonlinear elastic media models characterizedby the choice of a pair of energy tensors. We proved that if all composite layers are incompressible, the composite as a whole is also an incompressible, but anisotropic, medium. The article considers the problem of laminated plate uniaxial stretching from incompressible layers with finite deformations. Using the developed method, we calculated the effective deformation diagrams connecting the averaged Piola — Kirchhoff stress tensors components and the strain gradient, as well as the stress distribution in the composite layers.
The developed method for calculating effective deformation diagrams and stresses in composite layers can be used in the design of elastomeric composites with specified properties.

Dimitrienko Y., Gubareva E., Kolzhanova D., Karimov S. Incompressible layered composites with finite deformations on the basis of the asymptotic averaging method. Маthematical Modeling and Coтputational Methods, 2017, №1 (13), pp. 32-54

#### 539.3 Modeling polyurethane viscoelasticity at moderately high strain rates

##### Belkin A. E. (Bauman Moscow State Technical University), Dashtiev I. Z. (TSNIISM), Lonkin B. V. (Bauman Moscow State Technical University)

doi: 10.18698/2309-3684-2014-3-3954

The article presents a mathematical model of the viscoelastic behavior of polyurethane SKU-PFL-100 for strain range of 0...30 % and moderately high strain rates up to 10–1. To determine the viscous component of the deformation Bergstrom – Boyce rheological model has been applied. Relationship between stress and the elastic component of deformation is described by an Arruda – Boyce potential. We determined the model parameters using experimental compression diagrams of polyurethane obtained from Instron Electropuls 1000 machine at different strain rates. The model parameter values obtained by minimizing a function of the calculated value deviations from the experimental results are given. It is shown that in the considered range of deformations and strain rates model allows describing the polyurethane behavior with sufficient accuracy for practical purposes. The model is designed for calculating polyurethane shock-absorber parts, cushions, buffers and other structures subjected to dynamic loading.

Belkin A., Dashtiev I., Lonkin B. Modeling polyurethane viscoelasticity at moderately high strain rates. Маthematical Modeling and Coтputational Methods, 2014, №3 (3), pp. 39-54