A mathematical model of dynamic processes in a composite plate of prestressed piezoelectric (PE) and piezomagnetic (PM) layers is proposed. It is assumed that the initial strain state in the components of the plate is uniform and is induced by the action of initial mechanical stresses. In the quasi-static approximation, problems of shear horizontally polarized surface acoustic waves (SH-SAW) propagation in a PE/PM plate made of prestressed materials are considered. It is assumed that the materials of the plate layers in their natural state (NS) have symmetry class 6[Formula: see text]mm. The adhesion conditions are satisfied at the interface between the layers. The external surfaces of the heterostructure are in contact with the vacuum and are free from mechanical stress. Depending on the nature of the electrical and magnetic conditions specified on the external surfaces, four types of problems are considered. Using the example of a problem with electrically closed and magnetically open conditions on the external surfaces of a PZT-5H/CoFe2O4 plate, the features of the influence of the nature and magnitude of the initial mechanical effects on the velocities of SH waves are investigated. The possibility of changing the velocity characteristics of SAWs due to the initial mechanical effects is shown. The results are presented in dimensionless parameters and may be of significant interest for optimizing the structure of new materials in the development and design of devices and equipment operating on SH-SAW.

An approach to studying the influence of initial mechanical stresses and an electrostatic field on the structure and behavior of Rayleigh waves in piezoelectric media with nonhomogeneous coatings is proposed. This paper considers two-component coatings made of functionally graded piezoelectric material with high-speed (the speed of the shear-wave inclusion is greater than the speed of the shear wave in the substrate) or low-speed (the speed of the shear-wave inclusion is less than the speed of the shear wave in the substrate) inclusions. The initially deformed state of the coating is induced by the separate or combined action of the initial mechanical stresses and external electrostatic field. The influence of the type of non-homogeneity and the nature of the initial mechanical stresses in the presence or absence of an initial electrostatic field on the features of Rayleigh wave propagation for problems with an electrically open or shorted surface is studied. It is established that the presence of a low-intensity initial electrostatic field only slightly affects the action of the initial mechanical stresses depending on its direction. The presence of a high-intensity electrostatic field leads to additional deformation of the material, significant changes in the speeds of the SAW modes, and substantial changes in the structure of the surface-wave field. The obtained results are presented in dimensionless parameters and may be of practical interest in the development, design, and optimization of new materials for micro- and nanoscale devices and devices on Rayleigh surface acoustic waves with high performance characteristics.

The article studies the previously proposed model of a prestressed thermoelectroelastic medium of class 3m trigonal syngony under the action of initial mechanical stresses, an electrostatic field at a given temperature. The model is based on linearized constitutive relations constructed within the framework of sequential linearization of nonlinear equations of continuous medium electrodynamics. Linearization is carried out within the framework of superimposing small deformations on final ones with preservation of high-order terms in the equation of state. When constructing a model based on the use of linearized constitutive relations, it is taken into account that it is impossible to use the Voigt notation, which is usual for the natural state, in this case. Within the framework of this model, the behavior of the material constants of a thermoelectroelastic medium of class 3m trigonal syngony is studied. It is shown that, unlike electrical and mechanical effects, the thermal factor linearly affects the constants: preheating leads to an increase in the elastic constants, cooling – to their decrease. The effect on the piezoelectric constants is also linear, but more complex: some constants increase, others decrease. In this case, the possibility of using the Voigt notation, which is usual for the natural state, is preserved. Mechanical and electrical effects lead to the separation of constants coinciding in the natural state; in this case, the use of the Voigt notation, which is usual for the natural state, is impossible. The decomposed constants depend nonlinearly on mechanical stresses, but linearly on the electrostatic field. The nature and magnitude of the change in the constants depend both on the type of mechanical action and on the polarity of the electrostatic field. It should be noted that in this work, the effect of minor thermal effects was investigated. The effect of high initial temperatures significantly changes the properties of the material, but goes beyond the linearized theory and requires the use of nonlinear relationships.

Within the framework of the theory of thermodynamics, a method for determining the electro-optical coefficients is proposed. It is shown that for all ferroelectrics the symmetry of which admits a diagonal susceptibility, the ratio of some electro-optical coefficients is expressed in terms of the ratio of susceptibilities. For barium titanate, the dependence of the electrooptical coefficients on the electric field has been revealed and studied. It is shown that large values of the electro-optical coefficients of barium titanate are associated with a nonlinear dependence of the dielectric susceptibility on the electric field.

A model of a prestressed thermoelectroelastic medium under conditions of initial mechanical stress, electrostatic field and temperature is proposed. Within the framework of the coupled theory of thermoelectroelasticity, linearized constitutive relations and equations of motion of a prestressed thermoelectroelastic medium are constructed. It is assumed that the initial deformed state induced in the material is homogeneous, the initial temperature does not exceed the temperature of phase transitions, and the initial electrostatic field is specified by the electric field strength vector. Within the framework of the assumptions made, a three-dimensional formulation of dynamic problems for prestressed semi-bounded media made of the materials under consideration is given. Using operational calculus methods, the problem is reduced to a system of ordinary differential equations, the solution of which is presented in matrix form and allows one to analyze the influence of external factors of various natures on the dynamics of a prestressed thermoelectroelastic medium. Particular attention is paid to a detailed study of the initial deformed state of the material under conditions of separate and combined exposure to mechanical stress, electrostatic field and temperature. The presence of piezo- and pyro-effects, characteristic of the class of pyroelectrics under consideration, is shown: the appearance of electrical induction under the action of mechanical stresses along the axes, and the appearance of electrical induction under thermal influence in the absence of mechanical stresses. The types of mechanical influences leading to maximum values of electrical induction have been established. It is shown that under combined temperature and mechanical influences, mechanical stresses play a decisive role in the nature of the induced deformations. The presence of an initial temperature can either weaken or strengthen the influence of the electrostatic field. With a combined mechanical and electrostatic effect, the presence of an initial electrostatic field of high intensity, depending on its direction, leads to qualitative changes in the nature of the stress-strain state. The research results are presented in dimensionless parameters, presented in the form of graphs and may be of particular interest in the development, design and optimization of pyropiezoelectric materials used in the creation of new micro- and nano-sized devices and devices for general purposes.

The electro-optic coefficients of ferroelectric materials were obtained by Landau thermodynamic theory. It is proved that if the permittivity tensor is diagonal, then some ratios of the electro-optical coefficients are equal to the ratios of its diagonal components. The dependence of electro-optic coefficients on the external electric field for single-crystal barium titanate was studied and discussed. It is shown that electro-optic coefficients are rather high for barium titanate due to a non-linear response of dielectric susceptibility to electric field strength.

The method of thermomigration of liquid zones based on aluminum makes it possible to create complex structures of closed channels with boundaries formed from p-n junctions in single-crystal silicon wafers. The channels are characterized by the uniformity of their properties, and the pn junctions are characterized by their sharpness. Such structures are used in high-current electronics, photovoltaics, and microelectromechanical converters. Volumetric deformation inside and outside the channel due to alloying of silicon with aluminum leads to the formation of mechanical stresses. The equilibrium shape of the channels formed at high temperatures is determined by the minimum elastic energy and depends on the material parameters and geometry of the structure. Within the framework of the linear theory of elasticity, the behavior of elastic energy during the formation of the structure of thermomigration channels at high temperatures doped with aluminum in a single-crystalline (001) cut disk was studied. The simulation was performed using the finite element method in the COMSOL Multiphysics mathematical package. The study was carried out for practically important structures in which the direction of the edges is oriented along the diagonal of the square. Only such structures do not have breaks during the process of thermomigration. Based on the calculation results, it was revealed that the minimum elastic energy corresponds to structures with different crystalline orientations inside the channel and outside it – in the main silicon matrix. The direction of the crystalline axes inside the channel, corresponding to the minimum elastic energy, is rotated by 45 degrees in the plane of the disk relative to the direction of the axes of the main matrix of the silicon crystal. In addition, calculations showed that with such a turn, the shape of the channels changes. The minimum elastic energy corresponds not to vertical structures, but to inclined ones. The angle of inclination of the pyramids depends on the width of the channels and the distance between them.

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.

The excitation of surface acoustic waves (SAWs) on the surface of the ferroelectric film [barium strontium titanate (BST)] located on the dielectric substrate (silicon) was studied theoretically. We found that the most effective SAW excitation takes place when spontaneous polarization occurs in the film plane and the wave propagates along the direction adjacent to the direction of the spontaneous polarization vector. Based on a nonlinear model of phase transitions in solid BST solutions, the dependency of the material constants of piezo-effect equations on the misfit strain with a fixed concentration was obtained numerically. The effect of various misfit strains on SAW characteristics was studied for the film located on single-crystal silicon. It was shown that the effectiveness of SAW excitation increases as the misfit strain nears the boundary of phase transition.

A method is proposed to control the properties of thin ferroelectric films under forced strain due to the differences in crystal lattice parameters and thermal expansion coefficient between the film and substrate materials. The control method is based on applying additional mechanical strain to the substrate. A single-crystal Ba $$_{x}$$ Sr $$_{1 -x}$$ TiO $$_{3}$$ film model is studied within the framework of phenomenological theory using the Landau potential. It is shown that additional uniaxial strain of the substrate in the Ba $$_{x}$$ Sr $$_{1-x}$$ TiO $$_{3}$$  film changes the material constants of the film. Abnormal change occurs at strains close to the values at which the phase state of the film changes. The generation of surface acoustic waves is studied. The modeling results indicate the possibility of controlling the excitation of surface acoustic waves in the film–silicon substrate heterostructure.

An effective method that allows determining the presence of a defect and its characteristics is proposed. The proposed method is based on the control of changes in the parameters of dynamic process. To increase the informativeness of the proposed method the special mathematical approach for processing of the recorded signal is used. A special feature of the approach is an adaptively adjustable orthonormal basis. This approach maximizes the diversity of signal images obtained after processing, corresponding to the different types of defects. The proposed approach allows to significantly increase the efficiency of inhomogeneity recognition. A series of experiments demonstrating the high efficiency of the method is carried out.

The study of the features of the propagation of surface acoustic waves (SAWs)Surface Acoustic Waves (SAWs) is based on the solution of boundary value problems of electroelasticity for media with an inhomogeneous coatingInhomogeneous coating, the construction of the Green's functions of the medium and the analysis of its dispersionDispersion properties. For the cases of electrically open and electrically short-circuited surfaces, the influence of the ratio of the physical parameters of the coatingCoatings materials, the localization region and the size of the transition zone of one material to another on the features of the propagation of Rayleigh wavesRayleigh waves is investigated. The results obtained in this work are useful for understanding dynamic processes in piezoelectric structures with an inhomogeneous coatingInhomogeneous coating in order to optimize and create new structures and devices based on SAWsSurface Acoustic Waves (SAWs) with high performance characteristics.

Within the framework of the linearized theory of electroelastic wave propagation, a model of a piezoelectric structure with a prestressed functionally graded coating made of piezoceramics of a trigonal system with a symmetry class of 3m is considered. The ferroelectric LiNbO3 is used as the main material of the structure. The initial deformed state of the coating material is homogeneous, induced by the action of initial mechanical stresses and an external electrostatic field, the properties of the coating continuously change in thickness. By the example of the problem of the propagation of SH-waves from a remote source for structures with an inhomogeneous prestressed coating in the case of an electrically free and short-circuited surface, the influence of the nature and localization of the inhomogeneity of the coating on the features of SAW propagation is studied. The separate and combined effects of initial actions on changes in the physical properties of the structure, the transformation of the surface wave field, and the change in the SAW velocities in a wide frequency range is studied. The results obtained in this work are useful for understanding the dynamic processes in prestressed piezoelectric structures, in the optimization and design of new structures and devices on SAW with high performance characteristics.

A method for studying Rayleigh waves on the surface of an inhomogeneous prestressed electroelastic medium under the influence of an external electrostatic field has been developed. The medium is a homogeneous half-space with an inhomogeneous coating made of a functionally graded material. The half-space and the coating in the natural state (NS) are piezoelectrics of class 6 mm, whose axes of symmetry coincide and are oriented along the normal to the surface of the medium. The initial deformed state (IDS) of the coating is caused by the action of initial mechanical forces and an external electric field. Using the methods of operational calculus, the boundary value problem of oscillations of a medium has been reduced to a system of ordinary differential equations with variable coefficients, which, in turn, has been reduced to a system of Cauchy problems with initial conditions. The use of numerical methods makes it possible to construct an integral representation that describes the motion of an arbitrary point in the medium, as well as a dispersion equation the solution of which determines the characteristics of surface acoustic waves (SAW). The method allows one to investigate the influence of coating properties, gradient and localization of inhomogeneity, the type of the initial stress state and the magnitude of the initial stresses, and the external electrostatic field on the characteristics of the propagation of Rayleigh waves in a wide range of the parameters.

An approach to modeling a ferroelectric heterostructure with a prestressed coating made of a two-component functional-gradient material is proposed. Various types of PZT-based ceramics with close values of elastic moduli and significant differences in piezoelectric and dielectric parameters are considered as coating materials. The initial stress state (ISS) of the coating is caused by the action of an electric field and uniaxial mechanical tension. By the example of the problem of the propagation of sh-waves, the influence of the initial electrostatic field on the features of the SAW propagation has been investigated for various ratios of the parameters of the coating materials and the nature of the inhomogeneity localization.

A method of low-frequency continuous monitoringLow-frequency continuous monitoring of the stress-strain stateStress-strain state of the construction is proposed, based on the analysis of the parameters of the surface wave fieldSurface wave field created by the shock effect, through the use of acceleration sensors (accelerometers)Accelerometer and ferroelectric strain sensors. The latter are made using thin-film technology and are ultra-miniature broadband dynamic strain sensors of the generator type. The possibilities of using sensors in stress state monitoring systems are discussed. To process the recorded signal, a special method is used based on the use of optimal orthogonal decompositions of the signal in the basis, adaptively tuned on the training sample. A series of experiments have been carried out to demonstrate the high efficiency of the method.

The peculiarities of layered inhomogeneous medium vibrations under the action of a load moving on its surface are investigated. The problem is considered in a coordinate system moving with the load for two inhomogeneous media types: "normal" (more rigid half-space) and "abnormal" (more rigid layer). The results of the investigation are compared with the results for the homogeneous half-space with various load velocities. The integral representation at any point of a structurally non-uniform medium under the action of a moving oscillating load is derived. A detailed analysis of the properties of the Green's function for the medium is carried out. The influence of the load velocity upon the structure of the surface wave field is investigated. Numerical analysis is carried out for the investigation of the medium dispersion properties and of the vertical displacements of the medium surface.

A model of a piezoelectric structure with an inhomogeneous coating is considered. The structure is a homogeneous half-space made of PZT-5H ferroelectric ceramics with a functionally graded coating. The properties of coating vary continuously in thickness from parameters of one material to parameters of another material in a continuously nonmonotonic or piecewise-continuous manner. As coating materials, various combinations of ceramics of different stiffness based on PZT are considered. Using the example of the problem of the propagation of sh-waves in a piezoelectric structure, we studied the influence of the ratio of the physical parameters of the coating materials, the localization region, and the size of the transition zone of one material to another on the propagation features of surface acoustic waves (SAWs) and the structure of the wave field.