Methods of damping the oscillations of complex mechanical systems’ elements, such as strings, membranes, beams, plates, have intensively been developing since the 1970s. In particular, the beam oscillations are modeled by the fourth-order partial differential equation, which is Petrovsky-hyperbolic. The minimized functional is the energy integral of an oscillating beam. Control is implemented via certain function appearing in the right side of the equation. Previously, it was shown that the solution of the problem exists for any given damping time, but as soon as this time decreases, the optimal control becomes more complicated. To obtain approximate numerical solutions, the so-called point actuators were considered. Control was considered via single point actuator placed at some point of the beam, but in this case it turned out that it is not always possible to dampen it. Therefore, control was also considered via point actuator moving along a small section of the beam. However, the implementation of such an actuator is very difficult. In this work, the numerical damping of beam oscillations is implemented via several fixed point actuators. Computational algorithms have been developed on the basis of the matrix sweep method and the second order Marquardt minimization method of finding the minimum of functions of many variables. To find a good initial approximation, when minimizing the energy integral, empirical functions with a small number of variables are used. This made it possible to significantly reduce the calculation time of the task. The examples of damping the oscillations via a different number of actuators are given. It is shown that the amplitude of the oscillations of any control functions increases with the reduction of the given damping time. The examples of damping the oscillations in the presence of constraints on control functions are given; in this case the minimum damping time exists. The damping of oscillations is considered also in the case when different combinations of actuators are switched on at different time intervals of oscillation damping.

The effect of the structure on the properties of the metal-polymer composite consisting of a polymer matrix in the form of epoxy resin (ED-20) with butadiene-styrene rubber (BSK), dispersed-filled particles of nanomedium is investigated. Within the framework of the fractal analysis, the actual diameter of the aggregates of the initial filler particles is calculated for different degrees of concentration and size of the filling particles, as well as for different compositions of a polymer matrix. At the same time, the concept of the structure of a polymer composite is used as a set of two fractals (multi-fractals), which allows one to determine the nature of the change in the plasticity of a polymer matrix and simultaneously to reveal the main factors affecting the degree of perturbation of its structure. Using the fractal analysis methods, we investigated the influence of the factors on the fractal dimension of the surface of aggregates of the initial filler particles and on the nature of its dependence on both the degree of aggregation and the fractal, the dimensionality of the aggregate frame of the particle aggregate. The proposed approach allows to predict the final parameters of aggregates of nanoparticles as a function of the size of the initial particles, their concentration and chemical properties of the surface of the polymer matrix. Using the scaling nature of the size distribution of coils of polymeric macromolecules, it is shown that when polymeric composites are filled with dispersed micro- and nanoscale particles, the aggregates of these particles form a fractal framework, that is analogous to a fractal lattice. The degree of local order of the structure determined in the early cluster model controls the most important properties of the polymer matrix and the composite, in general. As the size of the polymer and metal particles decreases, substantially all physical and chemical properties of both the original components and the resulting composite material change substantially. The adjustment of the ratio between the polymer matrix and the fillers, with the adaptation of the synthesis condition to a given characteristic value, promotes the wide use of metal-polymer composites and enables the creation of new technologies for designing materials with the required properties, including a decrease in the independence of the products obtained from them. The use of fractal dimensions to characterize the structural equations of polymers makes it possible to obtain a number of quantitative analytical relationships between them.

Collisions of solid bodies are of significant interest for a great variety of physical and engineering applications. This review is devoted to non-elastic collisions of solid bodies when the energy dissipation is caused by the inner or interface friction, plasticity, adhesion, or other damping mechanisms. We consider only two-particle collisions. This impact problem can be reduced to the collision of a solid particle with a half-space. We discuss the collision without slip (infinite coefficient of friction) and in the presence of a finite coefficient of friction, as well as in the presence of adhesion between contacting bodies. A review is given of the previous theoretical and experimental work on both elastic and non-elastic impacts. However, the focus of the present work is on collisions of elastic particles. We consider the general oblique impact with non-zero normal and tangential velocity components of impacting particles. Analytical expressions for the restitution coefficient obtained by many authors are presented. Generally, the restitution coefficient depends on adhesive and plastic properties of contacting bodies. High velocity impact with destruction of particles does not belong to the scope of the paper. This paper is the first part of a two-parts-review. In the second part the results of analytical and numerical simulations will be presented, which have been obtained by the authors using the method of dimensionality reduction, allowing for reduction of three-dimensional contact problems to a much simpler equivalent problem in a one-dimensional space.

The mathematical model of the resonant diagnostics of the non-uniform temperature field using the piezo-electro-luminescent fiber-optical sensor is developed. The sensor is an optical fiber with electroluminescent and piezoelectric layers. The sensor’s first thin cylindrical photo passing electrode is located between the optical fiber and the electroluminescent layer, and the second electrode is located on an external cylindrical surface of the piezoelectric layer. The mechanoluminescent effect is a result of the interaction between the electroluminescent and piezoelectric layers in case of axisymmetric forced vibrations of the sensor. In case of vibrations, the electroluminescent glow penetrates through an inner electrode into the optical fiber and reaches the receiver-analyzer of light intensity on the output of the optical fiber. The model is based on the amplitude-frequency characteristic for the stationary electroelastic axisymmetric forced vibrations of a local section of the sensor. The forced oscillations are caused by the harmonious part of the control voltage on the electrodes of the sensor; the constant part of the control voltage is necessary for the setup of the sensor for an operating mode in the considered range of temperatures. When heating a local section of the sensor, the diagram of its amplitude-frequency characteristic displaces along the frequency axis (at a value of resonance frequency’s change), proportionally to the temperature change of this section. As a result, the problem of finding the required function of temperature distribution density along the sensor is reduced to the solution of the Fredholm integral equation of the 1-st kind, based on the results of the measured values of a derivative of amplitude of the luminescence intensity at the output of the optical fiber. Fredholm's kernel is calculated using the known amplitude-frequency characteristic of the sensor and the dependence of the resonant frequency on temperature. The numerical modeling results are presented and the influence on amplitude of the luminescence intensity at output of the sensor’s optical fiber are studied for various models and real laws of distribution of the diagnosed temperatures on a sensor ‘s length.

In this work, the experimental and calculation studies of the short-time strength of tensile rods made of a plastic material with U- and V-shape sharp notches were made. Thermoplastic-acryl-butadiene-styrene (ABS) was chosen as the model material. Samples with a diameter of about 5 mm were obtained on a single-screw extruder by melting granules. In the first part of the paper, the dependence of the mechanical properties of ABS in a wide range of quasi-static strain rates (0.02 ... 10 min-1) was studied. With these conditions, under single-step loading, this material can be considered as an elastoplastic one with an elastic modulus of 2200 MPa, with the yield strength of about 41 MPa and independent of the given strain rates with an error of less than 5 %. For the tested smooth samples, the residual longitudinal strain at rupture was 15 ... 25 %, the residual decreasing of a cross-section (necking) was 30 ... 50 %. The next group of samples had U-notches with a radius of 1.6 mm. The angle of sharp V-notches was 60°. The depth of the single-sided notches was varied in the range of 0 ... 3.5 mm. It is obtained that the ultimate load held by the samples with V-notches exceeds the corresponding load of the samples with U-notches of the same depth due to a greater constraint of the plastic strains in a notch zone. Notches up to 1 mm depth practically do not reduce the ultimate load of the samples. In the second part of the work, with the help of the FEM, the elastic-plastic deformation and fracture kinetics were calculated using a non-local approach, an explicit integration scheme in the ANSYS Workbench package. The calculations showed that the ultimate load is determined only by the yield strength of the material and the configuration of the notch. Rupture of samples (in ANSYS this is the technology of removing critically deformed finite elements) occurred at lower loads, depending on the plasticity resource of the material and the configuration of the notch. The calculated values of the ultimate and rupture loads are in a good agreement with the experimental data. The technique can be recommended for evaluating the strength of complex shape samples of plastic materials with arbitrary stress concentrators.

This article is the second part of the review of modern approaches and works devoted to the construction of interatomic interaction potentials using the embedded atom methodology (the so-called EAM potentials). This part of the review is devoted to one of the most relevant problems in molecular dynamics, which is the problem of constructing potentials that would be suitable for describing the structure, physical and mechanical properties of multi-component (binary and ternary) materials. We have outlined the emerging papers, in which the approaches to the construction of cross-interaction functions for Ni and Cu alloys were proposed, both with the use of the EAM methodology, and a potential of the Finiss-Sinclair type, that differed in the construction procedure. The works, in which different approaches to the construction of potentials are compared, as well as the procedure for identifying parameters using the example of the same multicomponent systems (such as Al-Ni or Cu-Au). In addition, some ternary systems, for example, Fe-Ni-Cr, W-H-He or U-Mo-Xe are of a particular interest as key materials for nuclear energy; and recently they have been actively studied as materials that could be used in thermonuclear rectors. This is to present the examples of works, which offer and investigate the potentials for the description of multicomponent systems, suitable for the aerospace industry, which are made, first of all, on the basis of Ni. The results of the investigations of various intermetallic compounds are considered, and studies have been performed, in which it was possible to accurately describe the phase diagrams of compounds and calculate the characteristics of phase transitions.

Based on the method of structural modelling and the Boltzmann-Volterra hypothesis of the hereditary elasticity deformable solid, the article considers linear and nonlinear fractional analogues of classical rheological models, such as Newton (the so-called model of Scott Blair), Voigt, Maxwell, Kelvin and Zener using the tool of fractional integro-differentiation of Riemann Liouville. The classes of nonlinear mathematical models are distinguished, for which the solution of the creep problem can be obtained explicitly in terms of known special functions. A technique for identifying the parameters of the proposed mathematical models is developed on the basis of known experimental data on uniaxial stretching of samples at different and constant load levels. In the presence of explicit solutions to the creep problem, the parameters of mathematical models are determined from the solution of the problem of approximating the experimental values of deformation using the method of least squares with subsequent refinement by the coordinate-wise descent method at all time points for all stress values in a series of experiments. For nonlinear mathematical models of viscoelastic deformation, which do not allow to find the solution of the creep problem in an explicit form, a method for determining the model parameters based on the coordinate-wise descent method with inversion at each step to the numerical solution of the defining integral equation has been developed. The method of identifying model parameters with operators of fractional integro-differentiation is realized on the example of creep of polyvinylchloride plastic compound. The values of the parameters for all the models studied are given, their adequacy to the experimental data is checked, and errors in the deviation of the calculated data from the experimental values are analyzed. As an example, a comparative analysis of the relative error in approximating the experimental creep curves by theoretical deformation values is made in the framework of a linear, nonlinear integrable and nonlinear nonintegrable fractional analog of the Kelvin model. The article oulines the appropriateness of using the viscoelastic deformation models with the operators of fractional integro-differentiation, based on the comparison of calculations of the considered models with the calculations of the viscoelasticity models having integral operators of integro-differentiation.