Вісник Київського національного університету імені Тараса Шевченка. Серія: фізико-математичні науки
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Pure bending of strip (beam) with the arbitrarily oriented cross-cutting crack
Get PDFThe problem of pure bending of strip (beam) with transverse rectilinear crack, edges of which are free from acuter load, is investigated in this paper. Under bending moment its edges may not contact or smoothly contact throughout its area length or part. Dependently on where it is located.Using methods of theory of functions of complex variable and complex potentials the problem at issue has been reduced to the problems of linear conjugation, their analytical solution is found. Explicit expressions on complex potentials is written. Based on the energy criterion of destruction stress intensity factors are determined. Limit value of moment when the crack begins to propagate is found. For the case when crack edges partially contact, area length of contact of her edges is determined. Numerical analysis of critical moment of failure of strip (beams) is performed under various parameters of the problem, which are related to the mechanical state of crack. The corresponding graphic dependencies are constructed.Key words: crack, strip (beam), complex potentials, bending moment, stress intensity factors.Pages of the article in the issue: 142-145Language of the article: Ukrainia
Microhardness of ?ompacted thermally expanded graphite
Get PDFUsing the method of continuous microindentation with different loading on the indenter, the microhardness of compacted thermo-expanded graphite (TEG) samples of different dispersion was studied. The analysis of the obtained results showed that, with an increase in the average cross-sectional area of TEG particles from 40 to 120 microns, the microhardness of the samples under investigation also increases. An analysis of the influence of the dispersion and morphology of the TEG particles on the distribution of microhardness on the surface of the compacted samples of TEG was also carried out. The microhardness indicatrix for the samples of the original TEG shows that when the radial displacement from the center of the sample, the microhardness of the material decreases. So in the central part of the discoid sample the values of microhardness lie in the range from 0,04 to 0,025 GPa. In the next concentric region, the microhardness decreases by 30% and gains a value of (0.028 ... 0.014) GPA. When the dispersion of TEG particles changes, the distribution of microhardness also changes. The microhardness indicatrix for a compacted Tg sample with an average particle size of 180 ?m shows that the microhardness value at the center of the sample ranges from 0.065 to 0.15 GPa.As you approach the edge of the sample, the microhardness of the material decreases from 0.15 to 0.054 GPa. The study of TEG with an average particle size of 50 ?m showed that the indentation in the center and in the middle region of the sample gives an isotropic distribution of microhardness values. The microhardness values coincide in the central and middle regions of the sample and correspond to ? 0.1 GPa. The proposed method of research and analysis of microhardness on the surface of compacted specimens of TEG gives an opportunity not only to characterize the micromechanical properties of the investigated material but also to optimize the technological regimes for obtaining samples.Key words: micromechanical properties, graphite, microhardness, thermo-expanded graphite.Pages of the article in the issue: 174-177Language of the article: Ukrainia
On some method of the heredity kernel parameters determination of nonlinear viscoelastic materials under the complex stress state
Get PDFThe deformation of viscoelastic medium given by means of constitutive equations of the hereditary type. These equations establish the relationship between the components of strain tensor, the components of stress tensor and the integral time operator, and contain the set of function and coefficients that are determined from the basic experiments. ? method of the heredity kernel parameters determination of nonlinear viscoelastic materials is developed. As the visco-elastic model, the constitutive equations of the hereditary type are chosen in which the relationship between the components of the strain tensor and the stress tensor is given based on the hypothesis of the deviators proportionality. The nonlinearity of the viscoelastic properties is given by the equations of Ratotnov’s type. The method is based on the relations between the creep kernels under complex stress state and the creep kernels under one-dimensional stress state. The method verified experimentally for the problems of determination of creep deformations under combined loading applied to the thin-walled tubular elements made of polyethylene of high density.Key words: nonlinear visco-elasticity, complex stressed state, longitudinal creep, shearing creep, volume creep.Pages of the article in the issue: 178-181Language of the article: Ukrainia
Plane waves in nano-composite materials
Get PDFThe propagation of plane waves in a hyper-elastic medium is theoretically investigated. Two methods of research were used: the method of slowly variable amplitudes and the method of perturbations (successive approximations). The results obtained by these methods are analyzed. The wave interaction in nanocomposite materials is studied. A theoretical study of the cubically nonlinear elastic interaction of plane harmonic waves is carried out for a material whose nonlinear properties are described by the Murnaghan elastic potential. The solution for self-generation of the longitudinal wave is obtained by the method of slowly varying amplitudes. The interaction of transverse horizontally and vertically polarized harmonic waves are studied using the perturbing method. The pumping of energy between different harmonics of a longitudinal wave and various types of transverse waves is described analytically. The results of numerical analysis for various types of nanocomposite materials are presented.Key words: cubic nonlinearity, elastic plane wave, nanocomposite materials, method of slowly varying amplitudes, perturbation method.Pages of the article in the issue: 198-201Language of the article: Ukrainia
Comparative effectiveness of throttled and relay rocket engines for low-gravity near-Earth flights
Get PDFWithin the framework of solving the Mayer problem of optimal control of a flight from an elongated elliptical orbit to a geostationary one with a maximum payload at a given initial mass of the low-thrust spacecraft and a fixed duration of the dynamic maneuver, a comparative analysis was made of the efficiency of throttled and relay thrust modes. Based on the data of the numerical solution of the corresponding twopoint boundary value problem, the expected gain was confirmed of the throttling mode over the relay mode in the case of practically interesting low-thrust near-Earth maneuvers. Also the numerical results confirmed the adequacy of the constructed fixed-power relay rocket engine mathematical model and made it possible to reveal a number of qualitative features of the control functions along the optimal transition trajectories.Key words: optimal control of a spacevehicle, low thrust rrocket engine, orbit-to-orbit transfers.Pages of the article in the issue: 46 - 51Language of the article: Ukrainia
Calculation the production cross-section of the BSM boson via photon fusion reaction
Get PDFThe production cross-section of the beyond the standard model (BSM) scalar boson (S-boson) have been considered it the article. Scalar boson produced via photon fusion reaction in the deep inelastic scattering of a charged particle (proton or electron) on heavy nucleus of the target. This process is one of the possible mecha- nisms of BSM boson production at the SHiP (Search for Hidden Particles) experiment at the CERN LHC and may be dominating among others processes due to large nuclear charge. In a low-energy case for which virtual photon wavelength similar or bigger nuclear size one can consider nucleus as an elementary particle with the charge Z. Corresponding amplitude is proportional to Z and the cross-section proportional to Z^2. Due to this the alpha_{EM}^2 suppression of the production cross-section is approximately compensated by the charge number factor Z^2. The mass of boson cannot exceed 4 MeV for the incident proton (or less than 80 MeV for electron). We calculated amplitude and the production cross-section of this reaction directly without using equivalent photon approximation. Interaction between photon and neutral boson is described by triangular diagrams with the loop containing all charged leptons, quarks and W-bosons. For this interaction we used effective lagrangian. The found cross-section was analyzed for the case of proton scattering on the lead nucleous and compared with the production cross-section in the decay of Ds mesons. It was found that the photon fusion reaction becomes effective only with a S-boson mass less than 0.1 keV.Key words: SHiP, production cross-section, BSM scalar boson, photon fusion reaction.Pages of the article in the issue: 94 - 97Language of the article: Ukrainia
Laser doppler vibrometer with remote object scanning capability
Get PDFA laser Doppler vibrometer was created with the ability to measure the vibrations of distant objects up to 250 meters away. The vibrometer is provided with a scanning system for automatic vibration measurement in an array of points. The control program moves the probe beam according to the research protocol, processes and store information. To demonstrate the capabilities of the system, we studied of the amplitude distribution of vibrations and the distribution of longitudinal stresses in a cantilevered tube located at a distance of 22 meters. The measurements at different frequencies are in good agreement with the numerical calculations performed by finite element code CalculiX.Key words: -Pages of the article in the issue: 16-19Language of the article: Ukrainia
Investigating the effect of Non-uniform voids on the final strength of engineered porous materials
Get PDFOne way to identify porous materials is to use multi-scale analysis, and the relationships currently available for multi-scale analysis are limited to mean stress and strain values. These relationships have a great error in calculating the fracture strength of materials. It should be noted that in multi-scale methods, quantities of normal mean values are usually used to calculate macro properties, while concepts such as fracture and fatigue cannot be explained by such quantities. Since the amount of stress in different portions of porous materials is not the same, this study uses statistics and probability to better understand the stress. For this purpose, the stress histogram of the porous materials is firstly investigated. According to the obtained histogram, the probability density function was calculated for it. Finally, the effect of location uniformity and cavity size on the probability density function of porous materials is investigated.Key words: porous material, Non-uniform voids, multi-scale analysis.Pages of the article in the issue: 70-73Language of the article: Englis
Asymptotic analysis of the singularly perturbed Korteweg-de Vries equation
Get PDFThe paper deals with the singularly perturbed Korteweg-de Vries equation with variable coefficients. An algorithm for constructing asymptotic one-phase soliton-like solutions of this equation is described. The algorithm is based on the nonlinear WKB technique.The constructed asymptotic soliton-like solutions contain a regular and singular part. The regular part of this solution is the background function and consists of terms, which are defined as solutions to the system of the first order partial differential equations. The singular part of the asymptotic solution characterizes the soliton properties of the asymptotic solution. These terms are defined as solutions to the system of the third order partial differential equations. Solutions of these equations are obtained in a special way. Firstly, solutions of these equations are considered on the so-called discontinuity curve, and then these solutions are prolongated into a neighborhood of this curve.The influence of the form of the coefficients of the considered equation on the form of the equation for the discontinuity curve is analyzed. It is noted that for a wide class of such coefficients the equation for the discontinuity curve has solution that is determined for all values of the time variable. In these cases, the constructed asymptotic solutions are determined for all values of the independent variables. Thus, in the case of a zero background, the asymptotic solutions are certain deformations of classical soliton solutions.Key words: the Korteweg-de Vries equation, singular perturbation, asymptotic solution.Pages of the article in the issue: 194-197Language of the article: Ukrainia
Reducing the negative impact of changes in space weather on human condition
Get PDFIn the article, based on the analysis of the physical factors responsible for the parameters of space weather near the Earth, possible ways of influence of the geomagnetic field disturbances on the state of the human body and methods of untraditional medicine to prevent the negative impact of such disturbances, the conclusions about the possibility of using acupuncture in the prevention and elimination of such influence are made. and the ability to use plasma medicine to address these problems with high efficiency.Key words: magnetic storms, acupuncture, plasma medicine.Pages of the article in the issue: 236-239Language of the article: Ukrainia