Summaries of the Issue
Microwave photonics is a new scientiﬁc and technical area of research, which was formed as a result of intensive development of such ﬁelds as ﬁber, integrated and nonlinear optics, laser physics, optoelectronics and microelectronics. A positive trend in the ﬁeld of microwave photonic devices development has appeared in recent decades. The trend is related to the fact that these devices can operate in ultra-high and super-high frequencies and microwave ranges, and have parameters, which are unattainable by conventional electronic devices. Technical characteristics of microwave photonic measuring systems are comparable with those of traditional ﬁber-optic sensors. This technology can be used both for creation of new measuring devices and improvement of existing other types of measuring systems. This paper presents an analytical review of microwave photonics application technologies in ﬁber-optic measuring instruments. The general design concept for microwave photonic ﬁber-optic measuring devices is considered in the ﬁrst part of the review paper. Microwave photonic ﬁlters are presented, which are the key elements of microwave photonic ﬁber-optic measuring devices. Their design technologies are described with indication of the features, advantages and disadvantages. Methods for creation of microwave photonic ﬁnite impulse response ﬁlters with positive and negative coefﬁcients are considered. The following sections are devoted directly to the analysis of microwave photonic ﬁber-optic measuring devices and contain classiﬁcation of such devices according to their principle of operation. The classiﬁcation of spectral and interferometric microwave photonic ﬁber-optic measuring devices with indication of their distinctive features is proposed. Experimental data of the most common sensors is presented and analyzed; the main characteristics and areas of their practical application are presented for each of them. New approaches and methods are considered for creation of microwave photonic measuring systems and improvement of tactical and technical characteristics of existing devices. Comparison between microwave photonic ﬁber-optic measuring devices and traditional ﬁber-optic measuring systems is performed. According to comparison results, conclusions can be drawn about applicability of microwave photonic ﬁber-optic measuring devices and advantages of their use compared to other ﬁber-optic sensors.
Subject of Research. The paper presents algorithms and methods of the optoelectronic complex operation for detailed surveillance in space aimed at the search, detection and registration of spacecraft images withdrawn from service due to the expiration of the service life, as well as asteroids and space debris. Optical-electronic system consists of optical- electronic equipment that includes space review instrument, equipment of space debris visual identiﬁcation, equipment of stereoscopic detailed surveillance, as well as television laser system for building three-dimensional “cloud of points” (depth map) of the identiﬁed object. Method. Based on the analysis of known publicly available sources for space systems, we proposed a novel method that provides increasing the range to the object under study by conserving the pulse energy. The method gives the possibility to concentrate energy in a narrow angle due to the three precision motors in the developed device displacing the emitter installed on them. The proposed approach provides for three-planed control of the width and angle of the laser radiation. The original operation algorithms of the detailed surveillance optoelectronic complex for building a depth map of the object under study were developed. Main Results. The project of optoelectronic complex has been developed functioning in low, medium and geostationary orbits with the maximum relative linear velocity from the object under study up to 1.5 km/s in low and medium orbits, and up to 6.15 km/s in geostationary orbits. An original method of aiming the light beam at the object of observation has been developed. Practical Relevance. Applying the proposed algorithms, optical-electronic system of detailed surveillance draws a three-dimensional image of the observation object on distances from 100 m with the aim of its identiﬁcation and cataloguing. The results of the work can be useful in the development of laser systems, control systems for spacecraft rendezvous and docking, as well as for tasks with systems of spacecraft orbital maintenance for the military and civil industries.
THE ORETICAL MODEL OF COLOR CHANGE FOR MILK REDUCTASE SAMPLE WITH RESAZURIN FOR MILK QUALITY CONTROL DURING ITS STORAGE
Subject of Research. The paper deals with theoretical justiﬁcation of moving from an organoleptic analysis of milk quality in accordance with the requirements of the national standard to objective control based on quantitative assessment by an instrumental method. We propose a theoretical model for changes in color of milk reductase sample depending on its bacterial contamination. Methods. The proposed model was based on the known patterns of the chemical process of resazurin, resofurin and hydroresofurin mutual transformation, as well as the impact of the concentration of coloring matters on the resulting solution color for homogeneous and inhomogeneous media. Real transmission spectra of the mentioned substances were measured for model development. For theoretical model veriﬁcation, experimental studies of quality changes during the storage of a milk sample, which was delivered to a shop, were carried out by reductase method. The experiment duration was 3 days, until the souring of milk. The milk was stored between the measurements at the temperature of +4 °C. A theoretical dependence of color changes for the reductase sample of milk was built during the experiment taking into account real transmission spectrum of milk. Real transmission spectra of the reductase sample were measured. The chromaticity coordinates (x, y) of the sample were calculated from the transmission spectra obtained through the modeling and measurement. To visualize the color change of the sample, the color coordinates in the sRGB color space were calculated for the case of a D65 light source, which is equivalent to daylight. Main Results. The simulation results are completely consistent with the results of experimental studies. The discrepancy between the results of theoretical modeling and experimental data does not exceed, on the average, 0.01 for the chromaticity coordinates x and y. The proposed model gives the possibility to calculate the concentration of enzymes for reductase sample with resazurin at any time, and, as a result, determine its color coordinates and color in accordance with the standards of the International Commission on Illumination for transparent and translucent media. Practical Relevance. The obtained temporal dependence of the chromaticity coordinates and the color of the reductase sample with resazurin can be used to control milk quality by spectrophotometric method and the method of technical vision.
Subject of Research. The transmitting channel of the laser location system, composed of a laser and its telescopic radiation expander, forms an output laser beam with speciﬁed geometric parameters. In particular, it can be a quasi- parallel beam or have a waist at a given distance. Method. The high-precision equipment setup is developed on the basis of geometrical optics methods providing the formation of a laser beam with preset geometrical parameters. The equipment setup is based on a mirror parabolic collimator and a matrix pyroelectric camera, which is located in its focal plane and is able to move along its axis. Flat diagonal mirrors are installed in such a way that they separate the laser beam coming out of the expander and direct it at the peripheral diametrically opposite collimator light zones. After reﬂection from the parabola, the beams converge at a sufﬁciently large angle convenient for further analysis. If the laser location system is aligned with the aim to reduce divergence, the matrix camera is positioned in the focal plane of the collimator. If the alignment is intended to create a waist of laser radiation at a given distance, then the matrix camera is placed at a certain distance from the focal plane. The alignment process is reduced to the registration of the gravity centers for the beams coming from parabola edges with their alternate overlapping. As soon as the difference in the beam coordinates becomes commensurate with the measurement error, the process is completed. Main Results. The technique involves the alignment of the telescopic expander together with the laser and eliminates errors associated with the installation of these two components relative to each other. During the operation, labor-intensive movements of the photodetector in space and subsequent calculations are not required, and fewer optical elements are used. Moreover, the effect of ﬂuctuations in the laser radiation power is excluded. According to the proposed technique, a system is aligned consisting of a CO2 laser with divergence of 7.5 mrad and a telescopic expander with tenfold magniﬁcation. The obtained alignment accuracy amounts to 10 % of the laser radiation divergence value. It is shown that the main contribution to alignment accuracy is made by coordinate registration error of the image gravity centers, which largely depends on ﬂuctuations in the laser radiation power. Practical Relevance. The proposed technique has a low labor intensity, sufﬁcient accuracy for practical application and can be implemented in the laboratories of enterprises engaged in the production of laser location systems.
Subject of Research. The paper presents a technique for simultaneous measurement of the radiation energy spectrum and the electrical parameters of a high-current pulsed arc discharge. The proposed approach provides the calculation of the energy and power parameters of the discharge and the efﬁciency of electric energy conversion into radiative one in different spectral ranges. Method. The energy efﬁciency of ﬂash lamps was calculated by two separate methods: the measurement of gas discharge electrical parameters and detection of radiation energy spectrum. The electrical parameters were measured by assembling a circuit using a coaxial non-inductive shunt and three mixed-type voltage dividers combined with their earth terminals at one point for fall-of-potential measurement on the lamp and capacitor. The combining of earth terminals made it possible to register simultaneously the voltage drop at different points without the risk of oscilloscope failure. By the mathematical multiplication and integration, the energy and power characteristics of the circuit and the pulsed gas discharge were obtained. The radiation characteristics measurements were carried out by applying a spectrometer and calibrated photodiode radiation detector. The spectral distribution of the radiation source was obtained and radiation efﬁciency was speciﬁed in the chosen wavelength intervals. By calculating the radiation energy in the spectral range corresponding to the applied task and taking into account the previously obtained values of the dissipated energies in the circuit and discharge, the radiation efﬁciency is found in the selected wavelength ranges. Main Results. On xenon ﬂash lamp example with 5 mm internal diameter and arc length of 120 mm, oscillograms of the current and voltage drop on the capacitor and lamp were obtained. The calculated radiation efﬁciency values in the spectral ranges of 200-250, 200-300 and 200-400 nm were 2.7, 9.3, and 28 %, respectively. Practical Relevance. The proposed method gives the possibility to register simultaneously the current and voltage drop on several sections of the discharge circuit and radiation characteristics, and eliminates the necessity to take into account the instability of these parameters from pulse to pulse. The calculation of the radiation efﬁciency in any wavelength range included in the spectral interval of the spectrometer sensitivity enables the designers of systems with ﬂash lamps to optimize the discharge circuit based on the radiation requirements of speciﬁc applications.
MATERIAL SCIENCE AND NANOTECHNOLOGIES
Subject of Research. The paper presents the study of 3D printing modes and heat treatment effect of ceramic thin- walled plates with dimensions of 20 × 5 × 40 mm. The relationship is determined between 3D printing, heat treatment and the percentage of shrinkage and surface quality of the obtained ceramic parts. Method. Ceramic parts were created using 3D printing by laser stereolithography. Heat treatment of parts was carried out by dividing the samples into three groups. Each group was located in the furnace in one of the three positions: in a metal box under quartz layer, under a layer of zirconium balls and on the surface of zirconium balls. Main Results. We have compared the surface quality and the shrinkage percentage of the samples, the thickness of the printed layer of 25, 50 and 100 μm and heat-treated under the indicated conditions. An improvement in the surface quality of the samples was found with the decrease in the layer thickness and particle size of the ceramic powder (from the range of 1-5 μm to the range of 0.01-1 μm). The shrinkage percentage of the product decreases by about 2 times with increase in the duration of heat treatment and the percentage of powder in the ceramic suspension. Practical Relevance. The use of new 3D printing modes and improved heat treatment conditions gives the possibility to obtain samples with better surface quality and lower percentage of shrinkage. The proposed technological process of laser stereolithography provides the creation of thin-walled ceramic products of higher quality with high accuracy of geometric dimensions. The results obtained make it possible to use the applied modes and methods for creating ceramic objects in such industries as aircraft manufacturing, radio electronics, medicine and other industries.
Subject of Research. The paper presents energy characteristics study of a carbon-containing composite material of a heat and power storage unit. We propose the composition and composite material technology for the heat and power storage unit. The initial components of the storage include graphite micro-powder, Na2O(SiO2)n water glass and a solidiﬁer, Na2SiF6, sodium silicoﬂuoride. The applicability of the developed heat and power storage unit is considered. Methods. The composition of composite material samples was studied by x-ray diffraction analysis and electron microscopy. Material characteristics were determined by thermophysical and electrophysical methods. Main Results. Samples of carbon-containing composite material are obtained. Engineering facilities of the heat and power storage unit are developed. Impedance frequency dependences of the heat electric storage unit experimental samples and their volt- ampere characteristics are obtained. The temperature dependences of electrical capacity and dielectric permittivity of the heat electric storage unit experimental samples are studied in the range of 20–60 °C. The temperature dependences of the speciﬁc heat capacity and the thermal conductivity coefﬁcient for monotonous heating are obtained. Practical Relevance. The developed heat and power storage unit can be used in emergency lighting and heating systems and power supply when operating in the mode of constant or compensatory charging (private and administrative house construction). The developed material is applicable in temperature sensors.
Subject of Research. The paper presents a method for differentiated capacity extension of the data warehouse. The method is built on a predictive model of time series with an estimate of volume for the trafﬁc storage. The effect of the incoming data stream structure on the choice of the prediction model is considered. Methods. The storage system is presented in the form of a matrix specifying the number of storage levels and the number of carriers/volumes at each level. The matrix elements are metadata of the recorded ﬁles that are stored on the corresponding carriers/volumes of multilevel data storage system. The matrix visualizes the data storage state in the form of patterns. Patterning is performed by systematic slices of matrix values. Periodic analysis of the data warehouse state patterns gives the possibility to evaluate the time to reach the maximum value of the carrier capacity. The predictive model, which is the basis of the method for data warehouse differentiated capacity extension, takes into account the structure of the incoming data stream. In the presence of a self-similar structure of trafﬁc for storage, a predictive model of auto-regression and an integrated moving average is implemented. For trafﬁc without a self-similar structure, a general linear predictive model of the time series at known past values is implemented. The prediction model is applied separately for each storage carrier/volume. Main Results. Structure features of the trafﬁc arriving for storage are given. Self-similarity properties are veriﬁed on the example of LTE-trafﬁc, demonstrating the presence of “heavy-tailed” distributions. The prediction results for volume of trafﬁc arriving for storage are obtained by the autoregressive model and the integrated moving average. The predictive and real values of the trafﬁc volume are given, as well as the prediction error value. A technique for differentiated capacity extension of the data storage system is developed, which establishes a sequence of steps for analysis of patterns and the structure of trafﬁc arriving for storage. Practical Relevance. The method for differentiated capacity extension of the data storage takes into account the multilevel organization of storage and the structure of the incoming data stream, which provides organizing a differentiated capacity extension in accordance with the characteristics of the ﬁles and ensuring the requirements for guaranteed storage time.
Subject of Research. The in-frame encoding process in the standard of high-efﬁciency encoding of video images is considered. The analysis of mode selection probability is carried out; the algorithm of fast prediction mode selection is proposed. Method. It is proposed to select a set of 11 modes with the highest probability of selection of the 35 possible modes of the standard “default” algorithm, as input data for further reﬁned selection. Depending on the results obtained, another stage is added, where the choice is reduced up to 4 modes. The selected modes are used in a two-stepoptimization process, which selects the best mode for the current encoding block. Main Results. The proposed algorithm is implemented in the C++ development environment. A number of standard video sequences with four quantization parameter values is used for testing. The results of the carried out experiments show that the proposed fast algorithm reduces the encoding time by 17.03 % compared to HM-16.20 reference software, with an increase in transmission speed by 1.26 % and a loss of quality only by 0.033 dB. Practical Relevance. The proposed fast algorithm provides a reduction in computational costs with an extremely negligible loss of quality of the restored video sequence. It can be used as a standard H265 video codec block for replacement of the existing in-frame prediction block in the reference program to speed up the video compression process.
Subject of Research. The paper presents the reasons for transition to digital energy and the development of intelligent electrical networks. We study the impact of global and local challenges in the framework of the development of digital energy areas and smart electric networks in Russia on the socio-economic and technological sectors of the country. The practices used in developed and developing countries are evaluated for support and stimulation of the state innovation policy and private investments. Method. Comparative analysis of measures was carried out for support and stimulation of innovative activities of the fuel and energy complex in the framework of economy digital transformation concept in the USA, the European Union, Asia and Russia. We gave an expert assessment of the impact of global challenges in the framework of the chosen research area on the Russian society social and technological side of life. Main Results. Evaluation model has been developed for assessing the impact of global challenges on technological development in the ﬁeld of digital technologies and smart energy. Analysis of the internal and external causes of the transition to digital energy and the development of intelligent electrical networks is carried out. The existing and perspective technologies of digital transformation of the electric grid complex for the perspective until 2030 are compared; advanced and outsider technologies are highlighted. The potential growth points of domestic and foreign power grid companies in the near and long term are identiﬁed. Key tools and measures for support of innovative businesses are grouped by the degree of their impact on the implementation of digital technologies and smart systems in the energy sector. Practical Relevance. Recommendations are formulated on the implementation of policies in the ﬁeld of digital energy and smart electric networks for the Russian Federation based on the analysis of the best practices for the introduction of digital technologies in the energy sector, as well as on evaluation of the effectiveness of tools for support and stimulation of innovative activity in the industry.
Subject of Research. The paper considers the design issues of fault diagnostic tools in information exchange addressing between program modules for a dataﬂow real-time computing system. Despite the decomposition of design process on the basis of a hierarchical approach, it is quite complicated, and the problem of its automation remains an urgent challenge. Method. The design automation of model and tests for a dataﬂow real-time computing system is performed on the basis of decomposition and by applying discrete-event modeling. Main Results. We have developed the instrumental environment automating procedure for model design, generation of test actions and reference output sequences. Its briefdescription is given. The environment functional is based on the synthesis algorithms of the system dynamic model and the test formation for exchange diagnostics between the system software modules. Practical Relevance. The developed tool environment gives the possibility to reduce signiﬁcantly the design time of diagnostic tools for dataﬂow real-time computing systems.
Subject of Research. The paper presents the study of vulnerability exploitation techniques in the implementation of dynamic memory allocation algorithms (glibc library allocator): Poisoned Null-byte, Overlapped Chunks, Fastbin Attack,Unsafe Unlink, House of Einherjar, House of Force, House of Spirit, House of Lore, Unsorted Bin Attack. Examples of vulnerability exploitation code and classiﬁcation of the presented techniques are given in accordance with the Common Weakness Enumeration list. The modern methods and means of vulnerabilities detection are studied; their advantages and disadvantages are shown using the Heap Hopper framework as an example. Modern methods of appropriate software veriﬁcation are considered. Method. The proposed software veriﬁcation method combines the approaches of static analysis and symbolic execution using an accurate model of algorithms for dynamic memory allocation. In the compilation process of program being tested, the Kripke structure is created. Dynamic memory vulnerabilities are described by temporal logic formulas. The resulting structure and formulas are passed at the input of the model checking algorithm. Concrete-symbolic execution of the assembled binary ﬁle is performed. Vulnerability conditions expressed in the form of propositional logic formulas are checked for symbolic execution paths. Main Results. The practical use of the proposed approach to detection of dynamic memory vulnerabilities in software applications is shown. Symbolic execution is implemented in the form of a low-level debugger, which reduces the operating time of algorithms due to the execution of the application being tested on a real processor. Practical Relevance. The paper presents an integrated approach for solving the problem of automatic vulnerabilities detecting at different stages of the software development life cycle. This approach is applicable for veriﬁcation of the similar implementations of dynamic memory allocators, such as ptmalloc, dlmalloc, tcmalloc, jemalloc and musl.
MODELING AND SIMULATION
MATHEMATICAL MODELING OF ANGULAR DIFFERENCE BETWEEN TEETH DIRECTION IN ZONE OF ENGAGEMENT AND COMPLETENESS OF CONTACT IN GEARS
Subject of Research. The paper presents comparative analysis of forecasting methods for users’ response to a message emerged on social media and application of machine learning. The method that provides the highest accuracy is preferred. Method. The following machine learning methods were applied: support vector method, gradient boosting methodrandom forest and multilayer perceptron. The statistical method of regression analysis — linear regression — was used as a reference forecasting method. Vectorization of records for obtaining quantitative characteristics of their content was carried out using such methods as: “Bag of Words”, TF-IDF and Word2Vec. The forecast quality was evaluated by R2 determination coefﬁcient. Main Results. A numerical experiment was performed using a data set collected on the VKontakte social network. The set contained information about community subscribers, publications, “I like” and “tell friends” marks and comments on publications. The number of marks and comments under the posted publication was projected, depending on its content. The most accurate results were obtained when predicting the number of comments. The quality of forecasts for the number of “I like” and “tell friends” marks turned out to be lower. Practical Relevance. The results of the work can be used in analyzing the effect of various news, including fake news, on users of social networks. The development of forecasting methods provides the planning of measures for acceleration or containment of the messaging distribution.
Subject of Research. The paper presents a mathematical model of an electric drive convertor operating in a common DC link for the 280-kW power level of the BELAZ-90 mining truck. The model is developed in MATLAB Simulink. The novelty of the proposed model is as follows: it implements the main circuit new topology for research of two converter drives operation connected to the common capacitor of the DC link. The model provides the possibility of studying transients in a distributed DC link with the aim of reducing current ripples both in the capacitor bank of inverters and in the common DC link. Method. We proposed the hardware method with a view to reduce ripples. It introduces the additional inductance installed between capacitors in the DC link and, with pulse-width modulation at the algorithmic level, a phase shift of the reference signals of two parallel inverters. Mathematical model was developed for estimation of current ripples between inverter and DC link capacitor and between the capacitor and power supply. Main Results. It is shown that the proposed software method decreases twice the current ripples between inverter and DC link capacitor, and the current between invertor capacitor and the power supply is reduced up to one-tenths of its previous value. Practical Relevance. This research can be practically used for control of the current load of power converter elements when developing the multi-motor electric drives in machine tool applications and hybrid electric powertrains
The paper considers selection of parameters of the spacecraft periphery-type docking assembly. The kinematic scheme of its docking mechanism is based on the Gough-Stewart platform. Constructive implementation of its linear elements in operation is called the rods, and the controlled element is called a docking ring. The docking mechanism is characterized by the ability to accumulate the kinetic energy of spacecraft approach rather than to dampen it. To achieve this, anenergy storage device is placed into each rod and incorporates a non-linear spiral spring mechanism. The energy storage device absorbs the kinetic energy of spacecraft approach and prevents its return after latching. The spiral spring mechanism implements a predetermined rod compression diagram and provides the necessary docking resistance force for spacecraft approach. The paper presents a general view of the rod compression diagram and the restrictions imposed on it. The model of the rod compression diagram is given, which is characterized by the introduction of a variable spring rate coefﬁcient, and the method for identiﬁcation of parameters is described. The method uses the calculation of the minimum mass of the spring mechanism. The method of parameters selection for a nonlinear spiral spring mechanism is given with predetermined dimension restrictions. The proposed methods can be used in the energy storage device optimization of the periphery-type docking assembly.
Subject of Research. The paper proposes the averaging method of motion equations. In various branches of physics (mechanics, electrodynamics) and while analyzing vibration processes, we may need to average the existing equations of motion over a certain time scale. Most often it is required to consider processes in real time and to exclude high-frequency oscillations. In this case, the averaging procedure leads to the fact that the equations of motion for “slow” time change signiﬁcantly their form. The usually applied arithmetic mean, i.e. equally all-time values in the given interval, does not solve the problem of determining the explicit form of the new motion equations for a “slow” time scale. Method. For the averaging procedure we propose to use the integral transformation with a smooth normalized kernel. The Gauss function is chosen as this kernel, because it “cuts off” adequately high frequencies and has convenient algebraic properties. The algebra based on these properties gives the possibility to solve efﬁciently the averaging problem and create a system of equations averaged over a certain scale. Main Results. It is shown that additional terms depending on this scale appear as a result of averaging over a certain small time scale. In contrast to the absence of velocities in the original system of motion equations, additional terms appear in the new averaged system depending not only on the coordinates, but also on the velocities. This fact explains the nature of dissipative forces. Moreover, in the created averaging algebra, the equations remain in their original form. Practical Relevance. The proposed method can be applied to any system of differential equations when it is necessary to obtain smoothed solutions. In particular, deformable solid mechanics and vibration mechanics are the proposed method application areas.
Subject of Research. The paper considers spatial and frequency characteristics of broadside and end-ﬁre microphone arrays with two omnidirectional microphones and various processing algorithms. Methods. The study of delay and sum algorithms and differential algorithms is performed using known and obtained analytical expressions for transfer functions and directivity coefﬁcients of microphone arrays. Main Results. It is shown that the differential algorithms have substantial advantage as compared with delay-and-sum algorithms in noise attenuating both from point and spatially distributed sources. Practical Relevance. The results may be used in the design of compact microphone arrays and microphone arrays with a large number of microphones.
Subject of Research. We consider the problem of ﬁnding an analytical solution to a mathematical model and computer- generated simulation of the concentrated mechanical stress impact at a given point of a loaded elastic body. An adequate mathematical model and a method providing minimum computer-time solution is proposed. An abstract rectangular homogeneous plate-strip is chosen as the object of study. Its edges are ﬁxed and it is loaded by a concentrated action and has a negligible bending stiffness. Abstraction lies in the concentration of membrane basic properties in one parameter — the propagation velocity of elastic waves with no consideration for their attenuation. The object mathematical model is a homogeneous two-dimensional wave equation with inhomogeneous initial and homogeneous boundary conditions. The concentrated action is deﬁned by the Dirac delta function in the initial conditions. Method. The proposed mathematical solution was performed by Fourier method taking into account the orthogonality in l2 space of sinusoidal functions, the properties of Dirac delta functions and zero boundary conditions. The solution provides minimum calculation time applying computer programs. Main Results. The paper presents the process of deriving an analytical solution for the selected mathematical model of concentrated exposure at a speciﬁc point of a rectangular homogeneous plate-strip with ﬁxed edges. The resulting solution can be easily programmed. The model gives the possibility to simulate the object behavior with different input data. Modeling is performed using Maple computer algebra system. The model estimated values of a given point effect on a speciﬁc homogeneous membrane-strip are presented in a graphical form. The graphs show how the membrane surface state changes over time if the exposure point is not in the membrane center. Practical Relevance. The presented results in the form of an analytical solution make it possible to study real-time dynamics of the membrane surface states under the impact of a known load depending on the input data. The modeling process is characterized by the lack of necessity to search for a solution to the two-dimensional wave equation.