Numerical Analysis Method Research Articles

Research on the chip formation mechanism of orthogonal cutting in particulate reinforced titanium matrix composites

Particle-reinforced titanium matrix composites (PTMCs) have recently become popular in the field of metal matrix composite research because of their outstanding mechanical properties. However, the diffuse distribution of strong reinforcing phases within a material influences chip formation, resulting in tool wear and lower cutting performance during machining. Examining the chip formation mechanism in PTMCs is crucial for enhancing machining performance. This paper explored how particles affect the chip formation process during the orthogonal cutting of PTMCs by utilizing both experimental and numerical methods for analysis. After characterizing the microstructure of PTMCs via image recognition technology, a finite element cutting model was established. Based on the dislocation theory, the effects of reinforcing phase damage and reinforcing phase content on the chip formation of PTMCs were analyzed. The results suggested that the chips exhibited a serrated shape with brittle cracks sprouting and expanding from the free surface. With a higher content of the reinforcing phase, the chip morphology of the PTMCs increases in terms of the degree of serration, and the chip formation process is influenced more by the particles. Furthermore, the chip formation results from a combination of thermoplastic shear instability, periodic fracture, and particle damage. As the cutting speed gradually increases, the PTMCs are more affected by the thermal softening effects, and the main cutting force generated during cutting gradually decreases from 625 to 589 N. Both the values and trends of the experimental results can verify the accuracy of the simulation.

Comprehensive Guidelines for Numerical Simulation of Jet Grouting Technology Using MPS-CAE

This paper presents a thorough guide to simulating jet grouting using the Moving Particle Semi-Implicit (MPS) method for numerical analysis and Computer-Aided Engineering (CAE) for model development. It addresses the shortcomings of previous jet grouting simulation studies, which often lacked clear and comprehensive guidelines, by providing a detailed step-by-step approach. The key aspects of the simulation that define and shape the output of real-world jet grouting technology, such as jet grouting spray settings and material parameter configurations, are validated against benchmark experimental data. The previously challenging task of accurately determining material parameters for soil when modeled as a Bingham fluid bi-viscosity model, is simplified into a universal guideline that can be easily applied to any soil type with known unconfined compressive strength. Finally, the reliability of the jet grouting simulation is confirmed by comparing the simulation results with benchmark experimental data under similar conditions, demonstrating the robustness and accuracy of the proposed method.

Critical review of interlaminar damage process and failure analysis in fiber-reinforced composite laminates encompassing fiber-bridging phenomenon

Metallic structures are increasingly being replaced by fiber-reinforced composites for the design of advanced structures with superior mechanical and physical properties. Fibrous composites offer several advantages, including lightweight feature while maintaining mechanical strength, resistance to damage evolution, and high fracture tolerance. Delamination growth in laminated composites is sometimes accompanied by fiber bridging which provides additional resistance against delamination growth. Delamination is known as one of the primary causes of premature failure in laminated composites. It is therefore necessary to gain a comprehensive understanding of interlaminar damage. Much research has been done to study various characteristics of fiber bridging yet the challenge remains an open topic for continued research. This review article aims to report the major studies on fiber bridging of composite materials in the literature. This article starts with an introduction to various modes of failure observed in fiber-reinforced laminated composites, extrinsic and intrinsic damage mechanisms, and the delamination phenomenon in the presence of fiber bridging. Next, different experimental and numerical methods for the characterization of delamination are presented. Fatigue-driven delamination, a leading cause of failure in aerospace structures, is subsequently reviewed. The paper concludes with a review of practical applications of numerical methods for delamination analysis followed by a review of recent progress in this field as well as open challenges in modeling, simulation, and experimental research works on the mechanics of fiber bridging incorporating composite damage and failure.

Damage response analysis combined with machine learning to investigate the effect of frequency on the impact-sliding fretting corrosion behavior of Inconel 690 alloy

Abstract Inconel 690 alloys have been widely applied in the manufacturing of steam generator tubes for pressurized water reactors at nuclear power station. However, complicated impact-sliding fretting corrosion behavior always accompanies its entire service period. This study, which is based on experimental research and numerical analysis methods, investigates the effect of impact frequency on the impact-sliding fretting corrosion behavior of Inconel 690 alloy tubes. Then, machine learning is applied to predict the evolution law of the degree of damage. The results show that different impact frequencies do not affect the damage failure mechanism of the impact-sliding fretted alloy tube surface. However, an increase in impact frequency will lead to a more severe degree of damage. The corresponding maximum wear depths of the 5, 10, and 15 Hz impact frequencies caused by the impact-sliding fretting wear scars were approximately 6.630, 11.105, and 14.485 µm, respectively. The corresponding wear volume increased from approximately 3.626×104 µm3 to 6.325×104 µm3 and 8.395×104 µm3. Furthermore, machine learning modeling demonstrates perfect robustness and precision in predicting the damage evolution rule of the impact-sliding fretting corrosion behavior of an alloy tube.

Structural reliability assessment of a historical reinforced concrete building using numerical analysis and NDT techniques

AbstractThis paper presents a case study of a methodology for assessing the structural reliability of an early reinforced concrete structure using a combination of primarily non‐destructive diagnostic and advanced numerical analysis methods. The case study examines the historical Csíky Gergely Theater in Kaposvár, Hungary, built in 1911. At that time, the design methodology and construction process were carried out using a relatively rudimentary standard framework. This study demonstrates that a multi‐phase assessment procedure integrating numerical analysis and primarily non‐destructive testing techniques can significantly reduce structural analysis uncertainty. This approach allows for an optimal selection of the reliability index (βtarget), even when deviating from design standards. Based on this modified reliability index and considering the diagnostic and material test results, the partial factors used for the assessment can be optimally adjusted, and in most cases reduced, compared to those in design codes for new structures. Consequently, the extent of structural interventions needed to increase the load‐bearing capacity can be minimized.

DynPy—Python Library for Mechanical and Electrical Engineering: An Assessment with Coupled Electro-Mechanical Direct Current Motor Model

DynPy is an open-source library implemented in Python (version 3.10.12) programming language which aims to provide a versatile set of functionalities for mechanical and electrical engineers. It enables the user to model, solve, simulate, and report analysis of dynamic systems with the use of a single environment. The DynPy library comes with a predefined collection of ready-to-use mechanical and electrical systems. A proprietary approach to creating new systems by combining independent elements defined as classes, such as masses, springs, dampers, resistors, capacitors, inductors, and more, allows for the quick creation of new, or the modification of existing systems. In the paper examples for obtaining analytical and numerical solutions of the systems described with ordinary differential equations were presented. The assessment of solver accuracy was conducted utilising a coupled electro-mechanical model of a direct current motor, with MATLAB/Simulink (R2022b) used as a reference tool. The model was solved in DynPy with the hybrid analytical–numerical method and fully analytically, while in MATLAB/Simulink strictly numerical simulations were run. The comparison of the results obtained from both tools not only proved the credibility of the developed library but also showed its superiority in specific conditions.

Characterization of S-Parameters for Non-uniform Microstrip Lines with Tabbed Routing Using Analytical-Numerical Method and Machine Learning

Characterization of S-Parameters for Non-uniform Microstrip Lines with Tabbed Routing Using Analytical-Numerical Method and Machine Learning

A method for constructing a complete bifurcation picture of a boundary value problem for nonlinear partial differential equations: application of the Kolmogorov-Arnold theorem

The purpose of this study is to develop a numerical method for bifurcation analysis of nonlinear partial differential equations, based on the reduction of partial differential equations to ordinary ones, using the Kolmogorov-Arnold theorem. Methods. This paper describes a method for reducing partial differential equations to ordinary ones using the Kolmogorov-Arnold theorem, as well as methods for the bifurcation analysis of nonlinear boundary value problems for ordinary differential equations. Results. The paper presents a new method for solving and bifurcation analysis of nonlinear boundary value problems for partial differential equations, which allow variational formulation. The method was applied to a nonlinear two-dimensional Bratu problem with Dirichlettype boundary conditions. Conclusion. A new method of bifurcation analysis for nonlinear partial differential equations has been developed. Specifically, a method has been proposed for reducing partial different equations to ordinary equations, which allows the use of the developed apparatus of bifurcation analysis for boundary value problems of ordinary differential equations. This method allows conducting bifurcation analysis for arbitrary nonlinear partial differential equations.

Modeling of the qualitative state of oilseeds from soybean seeds by multifactorial analysis of factor areas

The production of oil products in Ukraine is a leader not only in the European but also in the world market of food and processing industry products, therefore, the priority areas of scientific research in this field are the effective assessment of the quality of the oil obtained. Existing methods for assessing this product by organoleptic characteristics are subjective and do not allow the use of parameters that require more complex measurement technologies; which in general makes it impossible to conduct a comprehensive analysis of the quality of the studied product. The purpose of this study was to develop and implement a mathematical modeling method for numerical analysis of the quality of soybean oil product varieties. Qualitative assessment of the studied oil varieties was carried out using such indicators as the mass fraction of fat, peroxide, and acid number; content of free fatty acids, phosphatides, moisture, and impurities; it allowed to perform a numerical analysis using dimensionless complexes regarding the condition of the studied oil product varieties and compliance with regulatory indicators. When processing experimental data and calculating the developed quality criteria, programming methods, Excel, and COMPASS mathematical environments were used, which allowed the construction of geometric quality models and the necessary assessment criteria. According to the results of the research, it turned out that the characteristics of the studied varieties "OAS Avatar", "ES Mentor", "Sigalia", "ES Mentor" and "Gallek" do not meet the requirements for compliance with the quality thresholds by 160 - 220%, however, their current characteristics, which were selected for assessment, are within the average normative indicators. The proposed mathematical models can be implemented for practical application in assessing the condition of any complex object of research using an unlimited number of characteristics. At the same time, the main requirements for these parameters are their breadth of coverage of the physical, mechanical, and chemical-biological properties of the product and the ability to provide an objective and thorough assessment of its condition.

Green sol–gel synthesis of biogenic B‐ZnO nanoparticles: Enhancing antibacterial activity and solar‐driven photocatalytic degradation of methylene blue dye

AbstractBiological techniques based on plant extracts have attracted significant interest in the sustainable development era, exceeding the popularity of conventional physical and chemical synthesis methods. Current research biogenic boron‐doped zinc oxide nanoparticles (B‐ZnONPs) synthesized employing leaf extract from Lantana camara via the green synthesis approach with their inherent characteristics and solar‐driven photocatalytic activity was evaluated with chemically generated B‐ZnONPs. Numerous analytical methods, including field emission scanning electron microscopy, Fourier transform infrared spectroscopy, X‐ray diffractometry and UV–visible spectroscopy, have been applied to characterize the B‐ZnONPs, revealing the formation of monoclinic crystalline phase B‐ZnONPs. Notably, under sunlight irradiation at pH 11, the B‐ZnONPs exhibited significantly higher efficacy in the photocatalytic breakdown of methylene blue dye induced by sun radiation, achieving 96.2% photodegradation within 60 min. These results highlight the potential of L. camara leaf extract‐mediated B‐ZnONPs in solar‐based photocatalytic applications. Additionally, the biogenic B‐ZnONPs have been examined for their efficacy against gram‐positive and gram‐negative bacteria, exhibiting significant antibacterial properties.

Insights using Hamilton-Crosser model in Williamson hybrid nanofluids with homogeneous-heterogeneous reactions and diagonal electromagnetic effects

The study of Carboxymethyl Cellulose (CMC)-based Williamson hybrid nanofluids offers a significant leap in fluid dynamics and thermal management systems. This research investigates the flow characteristics over a porous, horizontally stretched cylindrical surface, incorporating complex phenomena such as Hall current, ion slip, diagonal magnetic fields, suction, velocity slip and thermal slip. A unique aspect is the inclusion of uniform and exponentially space-dependent heat sources, critical for advanced thermal transport processes. Using the Hamilton-Crosser model for accurate thermophysical properties and the Runge-Kutta-Fehlberg method for numerical analysis, the study examines the impact of varying hybrid nanoparticle concentrations (4% to 20%) on flow behaviour. The findings reveal that nanoparticles enhance viscosity, significantly increasing skin friction and momentum transfer, even as factors like the Weissenberg number, Hall current and ion slip mitigate these effects. The study emphasises the thermal management advantages of Carboxymethyl Cellulose-based Williamson hybrid nanofluids, especially when heat sources and homogeneous-heterogeneous reactions are involved. Notable differences are observed between pure Carboxymethyl Cellulose-based Williamson fluids and their hybrid nanofluid counterparts, particularly in velocity, temperature distribution and reaction dynamics. These results are promising for practical applications such as magnetic drug targeting, porous heat exchangers, magnetohydrodynamic systems and electronic cooling. The research underscores the potential of Carboxymethyl Cellulose-based Williamson hybrid nanofluids to enhance energy efficiency and reliability in industrial processes, making them pivotal for future developments in heat management technologies.

An experimental approach to estimating the current oil recovery coefficient using a complex of stochastic and numerical computer modeling methods

This paper presents an experimental study devoted to determining the prospects for the integrated application of stochastic and numerical computer modeling methods to solve one of the fundamental problems of field development – assessing current oil recovery based on various parameters that reflect the properties of productive formations and their saturating fluids. The object of the study was the long-term deposits of the Volga–Ural oil and gas province. As part of the initial stage, a discriminant analysis was carried out according to the tectonic-stratigraphic criterion, as a result of which three clusters of homogeneous objects were formed based on seventeen parameters. When interpreting the distribution of deposits in the axes of canonical discriminant functions, the unstable parameter of the total thickness of the reservoir was replaced by one of the variable indicators selected using the digital implementation of the uniform search method and its interpretation using known approaches. In order to reduce the influence factor of the uncertainty zone that arises when considering objects in the axes of canonical discriminant functions, the method of constructing structured grids was used. The reliability and scope of the obtained dependence were established using the Broyden-Fletcher-Goldfarb-Shanno optimization algorithm. The conclusion is made about the possibility of using the developed scientific and methodological approach to forecasting oil recovery at different values of the well grid density. Keywords: oil recovery coefficient; modeling of nonlinear systems; deposits of the Volga-Ural oil and gas province; tectonic and stratigraphic confinement of objects; stochastic and numerical methods of computer analysis and data processing; development of oil fields, geological and field parameters.

MATHEMATICAL MODEL OF THE VOLUMETRIC STRESS-STRAIN STATE OF GEARS WITH ARBITRARY TOOTH SHAPE

This paper presents an effective method for numerical analysis of the bulk stress-strain state of a gear of a real configuration. Namely, the determination of the bending stress fields in the gear teeth fillets with regard to geometric parameters. The methods of the classical theory of elasticity in a three-dimensional formulation with mixed boundary conditions for a region with a complex boundary surface are used. The solution is given in displacements. The components of the elastic displacement vector at an arbitrary point in the domain are determined, followed by the components of the stress tensor at the same point using Cauchy's differential dependences and the generalized Hooke's law. One of the main difficulties in solving this problem was the problem of representing the entire elastic section of the wheel together with the teeth in the form of an implicit continuous function of a continuous argument, which decisively determines the possibility of applying the methods of elasticity theory and constructing boundary conditions. These difficulties were overcome by using the theory of R-functions to describe the boundary surface of the gear as a whole. The force transmitted by the tooth is introduced in the problem in such a way that the configuration and size of the modeled meshing field are taken into account with the possibility of varying the law of its distribution over the meshing field. Different positions of the instantaneous contact patch in terms of the meshing phase over the entire period of meshing of a pair of teeth are also taken into account. The numerical solution to the problem is based on the Ritz method, where a linearly independent orthonormalized system of Legendre polynomials is used to develop coordinate sequences, and the geometry of the region and boundary conditions are taken into account. The proposed mathematical model of the volumetric stress-strain state can be used both in scientific research and engineering practice at the stage of designing or finishing gears with arbitrary tooth shapes for any real gear meshing system, rational selection of the size and location of the meshing field, and modeling the shape of the instantaneous contact area by the meshing phase for the entire period of meshing of a pair of teeth.

MULTILEVEL INVERTER TO GENERATE VOLTAGE WITH COMPLEX HARMONIC COMPOSITION

The paper deals with the problem of forming the desired and controllable harmonic composition of the output curve of a multilevel voltage inverter. The problem is relevant when creating installations for multi-frequency induction heating and metal melting. The purpose of the study is to develop an effective method to form the output voltage of power sources for multi-frequency induction heating installations, the curve of which has a given harmonic spectrum. Materials and methods. The theoretical part of the work was carried out on the basis of the circuit base of multi-level voltage inverters and switching DC converters using numerical analytical methods of studying nonlinear electrical circuits, methods of solving nonlinear differential equations and approximate harmonic analysis, as well as simulation modeling methods using the MATLAB/Simulink mathematical package. Experimental verification of the theoretical results was carried out in laboratory conditions on the example of a multi-level inverter generating a voltage curve with three operating harmonics. ACS758 series sensors and a four-channel RIGOL DS1104Z digital oscilloscope were used to record the results. Research results. Achieving of the purpose is based on the use of a universal multilevel voltage inverter, the circuit scheme of which does not depend on the levels number of the generated curve, which ensures a minimum number of power elements for any complexity of the curve spectrum. The method of forming of the output curve of this inverter consists in alternately connecting of the output capacitors of two direct voltage impulse converters to the input of a single-phase bridge voltage inverter using a transistor switch. In this case, voltages of different parity levels are formed by capacitors in the order of their succession, as a result of which a constant-sign multilevel voltage is formed on the input of the bridge inverter, corresponding to the required alternating-sign multilevel voltage. The law of the transistor switching of the bridge inverter ensures the conversion of its input voltage into a load voltage with a given harmonic composition. The peculiarity of the developed converter control method is that the transistor switching of the bridge inverter is carried out in accordance with the change in the sign of the generated curve. The method contains an algorithm to determine levels values formed by capacitors of impulse converters that realizes the required spectrum of the inverter output curve. The efficiency of the proposed method is illustrated by computer modeling of the converter when voltage with four working harmonics of the spectrum (i.e. the required spectrum harmonics) is generated. The quality indicators of the realized spectrum of the voltage curve are proposed and the analysis results of the influence of the levels number on values of these indicators are presented. The efficiency of the proposed methods is demonstrated experimentally with a laboratory model of the converter. Conclusions. The paper proposes a method to form the output voltage of a power source, the curve of which has a given harmonic, the efficiency of which is confirmed by the results of computer modeling and laboratory experiments. The proposed technical solutions made it possible to generate an output voltage, the spectrum of the curve of which contains four or more harmonics with specified amplitudes with a minimum number of power elements of the circuit. The paper also proposes models of quality indicators of the realized spectrum of the voltage curve and presents the results of the analysis of the influence of the number of levels on the values of these indicators. The developed methodology allows the development in the direction of controlling the spectrum of the generated voltage in real time, as well as non-periodic alternating voltage that changes according to a given program in accordance with the requirements of the technological process.

CHARACTERIZATION OF ISOBATHS IN THE CENOMANIAN RESERVOIR OF THE MUANDA FIELD – IMPLICATIONS FOR OPTIMAL OIL RESOURCE MANAGEMENT

The study of isobaths characterization in the Cenomanian reservoir of the Muanda field focuses on optimizing petroleum resource management. Using geostatistical techniques and numerical analysis methods, the isobaths of the K, J, I and H layers were mapped. The K layer, the most superficial, is 44 meters thick, while the J and I layers reach 48 meters respectively. This research highlights the spatial variability of isobaths, a key factor in understanding the rapid depletion of the reservoir, which is mainly attributed to the presence of argillites. The lithological heterogeneity, characterized by high clay content, influences reservoir permeability, complicating fluid flow and, consequently, well productivity. The study also subdivided the reservoir into distinct zones according to clay content, revealing that the southwestern zone has a clay content of over 57.42%, while the southeastern zone is less clayey, with a content of less than 41.87%. The results underline the importance of a geostatistical approach to resource management, identifying target areas for potential interventions such as hydraulic fracturing. This study thus contributes to a better understanding of reservoir dynamics and to the formulation of appropriate strategies for the sustainable exploitation of petroleum resources in the Muanda region.

Numerical Analysis of the Influence of Air Flow Rate on the Development of the Porous Structure of Activated Carbons Prepared from Macadamia Nut Shells.

This paper presents the numerical analysis of the influence of air flow rate on the porous structure development of activated carbons prepared from macadamia nut shells. The analyses based on nitrogen and carbon dioxide isotherms were carried out by the new numerical clustering-based adsorption analysis method. Therefore, it was possible to evaluate the porous structure with high precision and reliability. In particular, the results obtained showed that activated carbon prepared at an air flow rate of 700 cm3/min has the highest adsorption capacity with respect to this adsorbate, but with surface heterogeneity. On the other hand, numerical analysis based on carbon dioxide adsorption isotherms showed that the activated carbon with the highest adsorption capacity towards carbon dioxide is the sample obtained at an air flow rate of 500 cm3/min. The analyses conducted have shown that too high an air flow rate causes a violent oxidation reaction, leading to uncontrolled burning of the carbonaceous substance and destruction of the structure of the smallest micropores.

A Study on Analysis of Numerical Methods

The present work reveals that numerical analysis is a branch of Mathematics that deals with devising efficient methods for obtaining numerical solutions to difficult Mathematical problems. We conducted this research paper by observing the different types of reviews, as well as conducting and evaluating literature review papers. Numerical analysis is mathematics which has developed efficient methods for obtaining numerical solutions to difficult mathematical problems. Most of the mathematical problems that arise in science and engineering are very difficult and sometimes impossible to solve properly. The method of numerical analysis is being used mainly in the fields of mathematics and computer science and is continuously creating and applying algorithms to solve numerical problems of mathematics

Fourth Order Runge-Kutta and Gill Methods in Numerical Analysis of Predator-Prey Models

Purpose of the study: This study aims to solve the numerical solution of the Predator-Prey model using the fourth-order Runge-Kutta and Gill methods, and to determine the profile of the Predator-Prey model solved numerically using the fourth-order Runge-Kutta and Gill methods. Methodology: Schematically, the steps taken in this study are starting from a literature review of the Predator-Prey Model, then solving the Predator-Prey Model using the Fourth-Order Runge-Kutta and Gill Methods, then the program creation step which is continued with program simulation, and finally analysis of the simulation results. Main Findings: From the results of the analysis of the difference in estimates of the fourth-order Runge-Kutta and Gill for predators and prey, there is no significant difference between the two methods in determining a better method in solving the Predator-Prey model. Because the Predator-Prey model cannot be solved analytically, the difference between the two methods cannot be seen from the analytical solution approach. The simulation results using the fourth-order Runge-Kutta and Gill methods show that the greater the value of b, the prey population increases with a value of α > β, and the smaller the values ​​of α and β given, the interaction process between the two populations will slow down and the prey population will increase. Novelty/Originality of this study: can provide information about the profile of the Predator-Prey model which is solved numerically using the fourth-order Runge-Kutta and Gill methods. The combination of these two methods to solve the Predator-Prey model is the novelty of this study

NUMERICAL-ANALYTICAL METHOD OF DECOMPOSITION-AUTOCOMPENSATION FOR SOLVING THE SIGNAL RECOGNITION PROBLEM BASED ON INACCURATE OBSERVATIONS

A numerical-analytical method is developed to solve the problem of optimal recognition of a set of possible signals observed as an additive mixture containing not only a fluctuation observation error (with an unknown statistical distribution) but also a singular interference (with parametric uncertainty). The method allows for both the detection of signals present in the mixture and the estimation of their parameters within a specified quality criterion and associated constraints. The proposed method, based on the idea of generalized invariant-unbiased estimation of linear functional values, enables decomposition of the computational procedure and autocompensation of singular interference without resorting to the traditional expansion of the state space. Linear spectral decompositions in specified functional bases are used for the parametric finite-dimensional representation of signals and interference, while knowledge of the correlation matrix of the observation error is sufficient for error description. Random and systematic errors are analyzed, and an illustrative example is provided.

MATHEMATICAL MODELING OF THE DYNAMICS OF THE AEROELASTIC "PIPELINE – PRESSURE SENSOR" SYSTEM

This paper proposes mathematical models of mechanical systems "pipeline - pressure sensor" designed to control the pressure of the working medium in the combustion chambers of engines. In such systems, to mitigate the impact of vibration accelerations and high temperatures, the sensor is connected to the engine using a pipeline and is located at some distance from it. The movement of the working medium is described by linear models of fluid and gas mechanics. To describe the dynamics of an elastic sensitive element, linear models of the mechanics of a solid deformable body are used. Based on linear differential equations with partial derivatives, mathematical formulations of problems are proposed that correspond to three-dimensional models of pressure measurement systems in gas-liquid media for some pipeline cross-sectional shapes, namely, for a pipeline with a rectangular cross-section, with a section in the form of a sector and in the form of a ring. By introducing integral characteristics, the solution of problems is reduced to studying one-dimensional models. Equations have been obtained that make it possible to determine the pressure of the working medium in the combustion chamber at each moment of time by the value of deformation of the sensitive element of the sensor. Analytical and numerical-analytical methods for solving the corresponding initial-boundary value problems for systems of differential equations are proposed. In the analytical approach, the solution of the problem is reduced to solving a differential equation with a deviating argument. The numerical-analytical study of the problem is based on the application of the Galerkin method. Also, a numerical experiment was carried out and examples of calculating the deformation of the sensitive element of the sensor in the case of rigid fastening when specifying specific values of the mechanical parameters of the system are presented, also during setting the law of change in the excess pressure of the working medium in the engine.