## No 1 (2023)

**Year:**2023**Articles:**16**URL:**https://ered.pstu.ru/index.php/mechanics/issue/view/337**DOI:**https://doi.org/10.15593/perm.mech/2023.1

METHODS FOR REDUCING NOTCH SENSITIVITY OF HYBRID PSEUDO-DUCTILE POLYMER COMPOSITES WITH FABRIC REINFORCEMENT: EXPERIMENTAL STUDY

#### Abstract

Composite materials reinforced with synthetic fibres have been used in aviation and space technology for more than half a century. Fibre-reinforced composites with high specific strength and corrosion resistance are an attractive alternative to traditional structural materials, including steels, aluminium and titanium alloys. At the same time, composites based on carbon and glass fibres are inherently brittle structural materials with high strength sensitivity to stress concentrations due to the design features of the structures or defects that occur in operation. One way to solve this problem is hybridisation which makes it possible to increase the nonlinearity of the composite stress-strain diagram and reduce sensitivity to notches. Hybrid composites combine several types of reinforcing filler with different fracture strains and exhibit a pronounced pseudo-ductile plateau in tension. Such material behaviour ensures the redistribution of stresses near the concentrator and potentially reduce notch sensitivity. When designing hybrids, it is necessary to take into account the influence of different factors including the ratio between the components and their lay-up, using various technological methods, and the specific strength of the finished material. This paper presents the results of an experimental study on the strength of hybrid composites based on glass and carbon fabrics in the open hole tests. It was found that hybrids with an extended hardening area after the pseudo-yield plateau are were more notch sensitive. A low elongation component layers rotation on angles up to 10°, as well as the use of thin polymer veils, also reduce the sensitivity of the composite strength to the presence of the defects.

**PNRPU Mechanics Bulletin**. 2023;(1):5-11

SIMULATION OF ELASTOPLASTIC FRACTURE OF A CENTER CRACKED PLATE

#### Abstract

The strength of a square plate with a central crack at normal separation was studied within the framework of the Neuber–Novozhilov approach using a modified Leonov–Panasyuk–Dugdale model using an additional parameter, the diameter of the plasticity zone (width of the pre-fracture zone). As a model of a deformable solid body, a model of an ideal elastic-plastic material with a limiting relative elongation was chosen. This class of materials includes, for example, low-alloy steels used in structures operating at temperatures below the cold brittleness threshold. In the presence of a singular feature in the stress field in the vicinity of the crack tip, it is proposed to use a two-parameter discrete integral strength criterion. The deformation fracture criterion is formulated at the tip of a real crack, and the force criterion for normal stresses, taking into account averaging, is formulated at the tip of a model crack. The lengths of real and model cracks differ by the length of the pre-fracture zone. The constitutive equations of the analytical model are analyzed in detail depending on the characteristic linear dimension of the material structure. Simple formulas suitable for verification calculations for the critical breaking load and the length of the pre-fracture zone are obtained. Numerical modeling of the propagation of plasticity zones in square plates under quasi-static loading has been performed. In the numerical model, the updated Lagrangian formulation of the equations of mechanics of a deformable solid body is used, which is most preferable for modeling the deformation of bodies made of an elastic-plastic material at large deformation. The plastic zone in the vicinity of the crack tip is obtained by the finite element method. The results of analytical and numerical prediction of plate fracture under plane deformation are compared. It is shown that the results of numerical experiments are in good agreement with the results of calculations using the analytical model of fracture of materials with a structure under normal separation. Diagrams of quasi-brittle and quasi-ductile fracture of a structured plate are constructed.

**PNRPU Mechanics Bulletin**. 2023;(1):12-25

PROGRAMMABLE BEHAVIOR OF THE METAMATERIAL BY KINDS OF UNIT CELLS CONNECTION

#### Abstract

The paper is devoted to the numerical analysis of uniaxial loading of a sample of the mechanical metamaterial. The structure of the mechanical metamaterial is constructed of a ring and four ligaments, which make up a tetrachiral structure. The peculiarity of such a structure consists in torsion of the sample under the force load. Two methods of connecting cells in the metamaterial are considered: "adjoining" and "overlapping". The "adjoining" method of joining cells increases the thickness of the internal structure of the sample, which allows us to consider it as a topological defect of the metamaterial. The "overlapping" method saves the base material from which the tetrachiral structure is constructed. Differences in the structure when constructing a three-dimensional sample result in a significant change in the characteristics of the sample. Numerical solution of the problem is performed in a three-dimensional formulation using the finite element method. The constitutive relation describing the behavior of the model corresponds to Hooke's law. Numerical simulation of uniaxial loading made it possible to obtain the results of mechanical response and to analyze the effective properties of metamaterials. A topological defect in the form of a thickening of the internal structure elements led to a difference in the linear dimensions of the two samples. The increased thickness of the unit cell connection elements resulted in a decrease in the effective density of the metamaterial sample. The same sample showed a triple increase in the value of the elastic modulus. The greater ability to resist deformation resulted in a reduced twist effect compared to the sample whose cells were joined by the "overlapping" method. The results obtained will make it possible to program the mechanical behavior and properties of the metamaterial sample.

**PNRPU Mechanics Bulletin**. 2023;(1):26-32

STRENGTH AND DUCTILITY CHARACTERISTICS OF METAL ALLOYS AND STAINLESS STEELS CREATED BY WIRE-ARC SURFACING IN A WIDE RANGE OF STRAIN RATES

#### Abstract

To select rational parameters of the process of hybrid additive manufacturing of structures made of structural metal alloys and stainless steels, mechanical characteristics capable of serving as indicators of material quality were determined. The most advanced technologies of additive manufacturing by wire-arc surfacing (plasma, plasma arc with a melting electrode, including cold metal transfer) with layer-by-layer forging with a pneumatic impact tool and subsequent heat treatment were used. Aluminum-magnesium alloy AlMg5, titanium alloy Ti-6Al-4V, austenitic stainless steels 12Cr18Ni10Ti (AISI 321) and AISI 308LSi have been studied. Samples were cut from the blanks created by additive manufacturing – blades for standard tests for static uniaxial tension and cylinders for high-speed compression tests by the Kolsky method on a Hopkinson split bar. According to the registered and processed stress–strain curves for all materials, standard strength and ductility characteristics and the Johnson – Cook law of deformation and speed hardening were determined. For a correct assessment of the mechanical properties of additively produced materials, these tests were also carried out for each of them in the form of annealed rolled products. It is established that to compare the efficiency of various technological parameters of additive manufacturing, it is advisable to use static tensile strength and uniform elongation to rupture, having the smallest statistical variation. It was also found acceptable to approximate the Johnson – Cook law of the deformation curves of each of the studied materials according to averaged data, including various technological modes. Certain mechanical characteristics seem to be necessary for the search for effective modes of hybrid additive manufacturing and numerical calculation of various elastic-plastic problems in a dynamic formulation for the studied materials for design and technological needs.

**PNRPU Mechanics Bulletin**. 2023;(1):33-45

PLANE PROBLEMS ABOUT THE ACTION OF OSCILLATING LOAD ON THE BOUNDARY OF AN ELASTIC ISOTROPIC LAYER IN THE PRESENCE OF SURFACE STRESSES

#### Abstract

In this paper, symmetric and antisymmetric plane problems about the action of oscillating load on the boundary of an elastic isotropic nanothin layer are considered. The nanoscale layer thickness is considered by introducing surface stresses in accordance with the Gurtin-Murdoch theory. According to this theory, it is assumed that, in addition to external loads, surface stresses act on the layer boundaries, which are described by Hooke's “surface” law. As a result, the properties of the elastic material of the layer with nanoscale thickness become different from the properties of the material of a regular-sized body, which is typical for nanomechanics problems. A standard technique was used for the solution of formulated problems, including the application of limiting absorption principle, the Fourier transform over infinitely extended coordinate and the theory of residues for finding the inverse Fourier transform. It is shown how it is possible to obtain solutions in the form of series in natural waves, in which the wave numbers are defined as the roots of the corresponding dispersion equations. For a specific example, dispersion relations were studied and graphs of the first dispersion curves were plotted. The behavior of barrier frequencies, changes in wave numbers and zones of existence of backward waves at different nanoscale layer thicknesses are analyzed. The results of the analysis showed that for an ultrathin layer, surface effects have a significant impact on the dispersion relations, and the trends in the dispersion curves can differ significantly for different modes and layer thicknesses.

**PNRPU Mechanics Bulletin**. 2023;(1):46-55

IMPROVEMENT OF THE NON-DESTRUCTIVE METHOD FOR DETERMINING THE MECHANICAL CHARACTERISTICS OF ELEMENTS OF MULTILAYER STRUCTURES ON THE EXAMPLE OF PAVEMENTS

#### Abstract

The article is devoted to solving the urgent problem of improving the method of nondestructive testing of the condition of non-rigid road clothes. In addition to the previously developed approach to determining the mechanical parameters of materials of structural layers of nonrigid road coverings based on solving the inverse coefficient problem of restoring operational elastic modules providing specified displacement fields, an approach was developed that allows determining the parameters of energy dissipation in the structure of multilayer road pavement based on the correction of dynamic hysteresis loops recorded in the field and calculated using mathematical model of dynamic VAT. The article presents the results of numerical simulation of dynamic hysteresis loops for two different variants of multilayer structures. The possibilities of correcting the shape of hysteresis loops and their area by varying the tangents of the energy loss angles in layers of a multilayer medium and the elastic modulus of a homogeneous half-space are shown. The complex correction of the elastic modulus values of the structural layers of road clothes and the calculated loops of dynamic hysteresis made it possible to fully take into account the processes of energy attenuation at a distance from the point of application of the load. During the correction, it was found that the values of the elastic modulus of the road layers and the tangents of the loss angles in them have a complex effect on the areas of dynamic hysteresis loops and the nature of energy attenuation at a distance from the point of application of the load. At the same time, the elastic modulus of the underlying half-space is not limited in thickness to the greatest extent on the area of dynamic hysteresis loops (which led to an increase in the elastic modulus of the underlying half-space from 120 and 150 MPa for road construction variants with a reinforced and non-reinforced base to 170 and 160 MPa, respectively), and a decrease in the dissipated energy at a distance from the point of application This is primarily due to the tangent of the angle of energy loss in the half-space. The obtained values of the tangents of the loss angles are obviously related to the patterns of energy dissipation at the boundaries of the contacting layers of the pavement, and also take into account all possible anomalies and delaminations in the calculated structures. Within the framework of this article, calculated hysteresis loops on the surface of the pavement were obtained for the first time, the deformation energy was calculated based on their areas, and the possibility of their comparison with those registered experimentally was proved.

**PNRPU Mechanics Bulletin**. 2023;(1):56-65

PHENOMENOLOGICAL KINETIC EQUATION OF THE CONVERSION FOR A BINDER OF COMPOSITE MATERIALS BASED ON ISOTHERMAL TESTS

#### Abstract

In the problems of technological mechanics: the manufacture of structures from composites, packaging and deployment of products from prepreg for space purposes, and others, it becomes necessary to calculate the current mechanical properties of a composite material with an incompletely cured binder. Such properties are determined primarily by the binder state, which may be described by the conversion kinetic equation. The parameters of the kinetic equation depend on many factors: temperature, diffusion, the presence of a catalytic system, modifiers, reagents, the formation of by-products of kinetic reactions, the evaporation of reagents, the effect of radiation, etc. Reliable consideration of the influence of each factor in the kinetic equation turns out to be practically impossible. Therefore, most authors use the phenomenological conversion equation based on experimental data, since these data reflect all the features of the kinetic process. We consider the first order conversion equation, which takes into account auto-acceleration and auto-deceleration. The equation parameters are determined on the basis of isothermal experimental data by the following method. The equation for the conversion rate is integrated, the integral is used to construct a system of equations containing experimental data and the desired approximation parameters, which are determined by standard mathematical methods. The dependence of the kinetic equation parameters on temperature is also constructed by approximation. Examples of constructing conversion equations for a two-component and industrial multicomponent Barnes mixture are given. It is shown that the parameters of the kinetic equation in both cases significantly depend on temperature, and for a multicomponent mixture this dependence is more complicated due to the simultaneous implementation of several reactions. Examples of using the obtained kinetic equation to calculate the curing degree of samples under a given temperature loading are given.

**PNRPU Mechanics Bulletin**. 2023;(1):66-74

ON THE RECONSTRUCTION OF PRESTRESS FIELDS IN A HOLLOW CYLINDER

#### Abstract

The present research is devoted to the development of the theoretical foundations of nondestructive acoustic method for identifying inhomogeneous prestress fields in a hollow cylinder, depending on the probing loading type. A linearized model of steady oscillations of an elastic body in the presence of an inhomogeneous prestress field of arbitrary nature is considered in the standard and weak formulations. On the basis of this model, we formulate a problem for a cantilever-clamped prestressed hollow cylinder that performs steady axisymmetric vibrations under three types of probing loading. A corresponding weak formulation of the problem in the cylindrical coordinate system is presented, in which six independent components of the prestress tensor are taken into account. At that, a case of prestress fields obtained by applying some initial mechanical external static load is considered. In the presence and absence of prestresses of various types, amplitude-frequency dependences are analyzed, and resonant and natural frequencies are found in a wide frequency range. Numerical calculations were carried out using the FEM on a non-uniform grid; mesh refinement is carried out in the vicinity of the boundary points, where the type of boundary conditions changes. Based on the numerical solution of an auxiliary set of direct problems, seven types of prestress fields are constructed, differing in the types of initial loading, most often encountered in practice. To assess the possibility of implementing the procedure for reconstructing prestresses of each of the considered types, a sensitivity analysis was additionally performed, which showed that for some prestress types there are frequencies and types of probing loading for which the presence of prestress is practically not manifested. The sensitivity analysis performed made it possible to implement the optimal method of probing loading when solving the inverse coefficient problem. The statement of the new inverse problem on the restoration of arbitrary inhomogeneous prestress fields in the considered finite hollow cylinder is formulated. When restoring the prestress of a given structure, the inverse problem is reduced to finding a set of parameters from an ill-conditioned algebraic system, which was studied with the help of the A.N. Tikhonov regularization method. Additional data for solving the inverse problem was obtained on the basis of probing both via a single load and via combined probing modes. It has been found that it is most effective to use a combined loading mode and use a sufficiently wide frequency range when selecting sounding frequencies. The results of computational experiments on the reconstruction of six components of the prestress tensor are presented and analyzed, and recommendations are proposed for choosing the optimal modes of acoustic sounding.

**PNRPU Mechanics Bulletin**. 2023;(1):75-89

SPECTRAL DYNAMIC STIFFNESS METHOD FOR THE FLUTTER PROBLEM OF COMBINED PLATES

#### Abstract

At present time, the spectral dynamic stiffness method is being actively developed as an alternative to the finite element method for vibration and stability problems of composite structures from beams, rods, plates and shells. This approach, based on exact solutions of governing differential equations, makes it possible to more effectively study the problem in the medium and high frequency ranges, and gives analytical expressions for natural modes. It is proposed to use the advantages of this method to study the problems of dynamic stability and flutter of an orthotropic composite plate in a supersonic gas flow. Using the linear approximation of piston theory, solution of the problem is investigated according to the Galerkin method on the basis of the eigenforms of a composite plate in vacuum. According to this approach the boundary value problem is reduced to a homogeneous infinite linear algebraic system of equations with coefficients are depending from physical-mechanical and geometrical parameters of the problem. The frequency parameter is included in the system linearly, that allows us to reduce eigenproblem for infinite system to the problem of determining the eigenvalues and vectors of a matrix. The convergence of the Galerkin method depending on the number of basis functions is studied numerically. It is shown that the first 16 eigenforms provide the good convergence of the method. Examples of numerical implementation are given, obtained solution allow us to study the dependence of the critical velocity from the properties of the material and geometry of the combined plate.

**PNRPU Mechanics Bulletin**. 2023;(1):75-89

REPRESENTATIVE VOLUME AND EFFECTIVE MATERIAL CHARACTERISTICS OF PERIODIC AND STATISTICALLY UNIFORMLY REINFORCED FIBER COMPOSITES

#### Abstract

In the deformable solid mechanics, there are concepts associated with continuum points (displacements, relative elongations, shifts) and a set of continuum points – an elementary volume (mass, energy, stresses). The role of such volume in the mechanics of composite materials is played by the representative volume element (RVE).This concept was first introduced by R. Hill (1963). Modern authors use the W.J. Drugan, J.R. Willis (1996) formulation. Based on the analysis of the RVE concept, we formulated its essential features: RVE is the minimum possible sample for numerical tests to determine the effective material parameters of the composite; under any RVE loading, its macroscopic stress-strain state is uniform. Its significance for the mechanics of composite materials is revealed: the existence of RVE for a composite is a criterion for applying the effective modulus theory to the analysis of its stress-strain state; the dehomogenization of a stressed-state composite material at a point is a solution to the micromechanics problem of the RVE stress-strain state determination; the characteristic size of RVE limits the size of the sampling grid in the numerical study. An iterative algorithm for constructing a representative volume of a periodic structure composite and its effective material thermoelastic characteristics is proposed. It is shown that the geometric shape of such a composition is a rectangular parallelepiped. The RVE construction algorithm for periodic compositions is extended to the composites statistically uniformly reinforced with continuous fibers. A method for modeling such materials with a following regular structure is suggested described: in the section perpendicular to the fibers, fiber centers should be located at the vertices of regular triangles. Examples of constructing RVE and thermoelastic material characteristics of specific compositions are given. The calculation results are compared with the data obtained using certified software products.

**PNRPU Mechanics Bulletin**. 2023;(1):103-110

IDENTIFICATION OF DEFECTS IN A COATING WEDGE BASED ON ULTRASONIC NON-DESTRUCTIVE TESTING METHODS AND CONVOLUTIONAL NEURAL NETWORKS

#### Abstract

The paper deals with the identification of a crack-like defect in a coated wedge based on ultrasonic nondestructive testing. The authors propose an approach of defect identification followed by determination of its geometrical parameters. The approach is based on a shadowed ultrasonic nondestructive testing method combined with deep machine learning technologies. A wedge-shaped area is inspected for the presence of an internal defect. On one edge of the wedge there is a source of ultrasonic vibrations, on the opposite edge there is a receiver. Passing through the coating and body of the wedge, part of the signal is reflected from inhomogeneities and defects that may be present in it. The signal reaching the opposite edge of the wedge is read by the receiver. The received data is processed by a neural network model, which predicts the presence or absence of an internal defect and, if present, determines geometric parameters such as size and position. A finite element model of ultrasonic wave propagation inside the wedge is constructed. Special damping layers are used, due to which the influence of parasitic signal reflections and its further propagation into the wedge body is significantly reduced. Based on the built model, the shadow method of ultrasonic scanning is implemented. This method implies that on one side of the wedge are installed excitation devices, and on the opposite side – receiving devices. Several numerical experiments for various combinations of geometric parameters of the wedge and the defect have been performed using a distributed computing system. Based on the obtained data, a neural network model was built and trained, capable of identifying the defect and determining its characteristics. The input of the model is spectrograms of the readout signal, and the output is values characterizing the defect.

**PNRPU Mechanics Bulletin**. 2023;(1):111-124

DEPOSITION OF FULLERITES C60 ON A SOLID SUBSTRATE TO FORM A FILM

#### Abstract

The use of C60 fullerites to create films on the surface of a solid substrate can be used not only to create coatings, but also to modify the surface layer of the substrate, which from a practical point of view can be in demand in such sectors of the economy as machine and instrument engineering. To analyze the process of formation of fullerite films on the substrate surface, a computer experiment was carried out, but the behavior of not a single fullerite or fullerene, as it was implemented in previous works of the authors, but a significant number of C60 fullerites deposited in the modeling area over a certain time interval and forming a "flow" was modeled. The substrate of the solid was an iron crystal Fe(100). The substrate temperature in the study was kept constant at the following values – 300 K, 700 K, 1150 K. The initial parameters of each individual fullerite were determined stochastically within the specified limits. The software package used to conduct the described computer experiment was – LAMMPS. The interaction of the atoms of the system with each other, during the simulation, was determined by the multiparticle potential (MEAM is a modified submerged atom method). The main result of the conducted computer experiment is that it was possible to simulate the deposition of C60 fullerites with the formation of a film on a solid substrate. The main regularities of the interaction of fullerite as a whole and fullerenes forming it, both with the substrate and with other fullerites forming the film, were revealed. And the analysis of changes in temperature and potential energy of the system, both during the deposition of fullerites and after its completion, allows us to talk about the stability of the resulting fullerite – substrate system.

**PNRPU Mechanics Bulletin**. 2023;(1):125-133

NUMERICAL SIMULATION OF GAS-DYNAMIC AND STRENGTH CHARACTERISTICS OF A FAN FOR THE EXPERIMENTAL TEST RIG FOR INVESTIGATION OF ICE BREAKDOWN ON ROTATING WORKING BLADES

#### Abstract

The paper is devoted to modern experimental and computational studies analysis on the point of asymmetric destruction of ice on the surfaces of the working blades of gas-turbine engine blades. A schematic diagram of an experimental setup has been developed, which consists of the following main elements: a wind tunnel, a cold chamber, a model fan, an electric motor, and a high-speed video camera. The experimental setup makes it possible to carry out laboratory studies of the ice formation and destruction processes. The choice of the experimental test rig parameters was made to allow assessing the icing of the blades of a rotating fan, which reproduces the processes occurring on gas turbine engines. Based on the results of three-dimensional gas-dynamic and strength calculations, the design and basic geometrical parameters of the flow path and the dummy fan were determined. The dependences of compression ratio Pk and the power consumption of a model fan Wcons on the value of the mass air flow Gair for a different number of rotor blades are presented. The choice of materials for the disk hub and blades of a dummy fan which experience tensile and bending loads at high rotation speeds up to 12.000 rpm was made, that satisfies the conditions of static and dynamic strength, also the allowable safety factors were evaluated, and pressure characteristics were obtained.

**PNRPU Mechanics Bulletin**. 2023;(1):134-141

APPLICABILITY INDICATORS FOR THE NONLINEAR MAXWELL-TYPE ELASTO-VISCOPLASTIC MODEL WITH POWER MATERIAL FUNCTIONS AND TECHNIQUES TO CALIBRATE THEM

#### Abstract

A physically non-linear Maxwell-type constitutive relation with two material functions for nonaging elasto-viscoplastic materials is studied analytically in order to examine the set of basic rheological phenomena that it simulates, to enclose its application field, to obtain necessary phenomenological restrictions which should be imposed on its material functions and to develop identification and validation techniques. Characteristic features of loading-unloading-recovery curves family produced by the model with two power material functions (with four parameters) under loading and unloading at constant stress rates and subsequent rest are analyzed in uni-axial case and compared to general properties of stress-strain-recovery curves produced by the constitutive relation with two arbitrary (increasing) material functions (theorems 1 and 2). Their dependences on loading rate, maximal stress and material functions exponents are examined. Power functions are the most popular in creep models, elastoviscoplasticity, polymer rheology, hydrodinamics of non-newtonian fluids and simulation of superplastic flow. The analysis reveals several specific properties of theoretic loading-unloading-recovery curves produced by power model with four parameters that can be employed as the model applicability indicators which are convenient for check using test data of a material. They should be checked in addition to general applicability indicators for the Maxwell-type constitutive relation with two arbitrary material functions. A number of effective calibration procedures for the model in the class of power material functions are developed. They are more rapid and effective than general identification techniques for two arbitrary material functions developed previously. The first procedure employs a pair of stress-strain curves at different stress rates, the second one is based on a pair of loadingunloading- recovery curves with various maximal stress values and loading rates and the third one needs only one loading-unloading-recovery curve. The explicit expressions are derived for four material parameters via test data. They enable separate and direct evaluation of the material parameters without error accumulation. Identification techniques versions are considered and their advantages and shortcomings are discussed. The ways to minimize the error using additional tests are proposed.

**PNRPU Mechanics Bulletin**. 2023;(1):142-158

MODELING OF 3D-PRINTING PROCESSES FOR COMPOSITE TOOLING AND TRANSFER MOLDING OF GRID STRUCTURES

#### Abstract

The paper discusses the method of obtaining a digital passport of the material and the development of a digital twin of the product at various stages of its manufacture. The object of research is a conical mesh structure. The subject of research is the processes occurring in the product at the manufacturing stages. The following main stages of creating a mesh structure were considered in the work: 3D printing of a workpiece tooling, laying out a carbon unidirectional material, heating and impregnation of the preform with a binder, polymerization of the binder, and warpage of the product geometry. An algorithm for determining the properties of materials and their calibration using modern software and hardware and universal equipment was described. Modeling of the tooling 3D printing process was carried out in the Ansys software package. Step-by-step technological modeling of the transfer molding process was carried out using the ESI PAM-COMPOSITE software package. The result of the simulation is the optimal technological manufacturing parameters and the geometry of the shaping tooling with anticipation of warping.

**PNRPU Mechanics Bulletin**. 2023;(1):159-172

ГЕНЕРАЦИЯ ПОВЕРХНОСТНЫХ АКУСТИЧЕСКИХ ВОЛН СЕГНЕТОЭЛЕКТРИЧЕСКОЙ ПЛЕНКОЙ BST ПРИ ДЕЙСТВИИ ОДНООСНОЙ НАГРУЗКИ

#### Abstract

The electro-mechanical properties of a ferroelectric film of barium strontium titanate (BST) film located on a silicon substrate depend on applied external strain. A significant dependence is observed for concentrations close to values, where a phase transition for the ferroelectric film occurs. A model of single-crystal BST film near the phase transition under uniaxial strain is studied by the thermodynamic theory of phase transitions. The material properties of the film obtained by the model are used for numerical study of the excitation of Rayleigh’ acoustic waves on the surface of the film-substrate heterostructure. Shifting the extrema of S-parameters, characterizing the efficiency of excitation of surface acoustic waves, is shown under the applied strain. The change of S-parameters for the first three resonances determined principally by the geometry of the interdigital electrodes is presented. The largest shift of resonant frequency is observed in a case of the second resonance that corresponds to Sezava wave.

**PNRPU Mechanics Bulletin**. 2023;(1):173-178