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In this paper, we are concerned with a time-dependent transmission problem for a thermo-electric-magneto-elastic solid immersed in an inviscid and compressible fluid. It is shown that the problem c...

This paper investigates electro-magneto-elastic free vibration responses of piezomagnetic cylindrical nano panel subjected to electro-magneto-mechanical loads based on third-order theory. Third-order shell theory is used for description of the displacement field. The zero transverse shear strains are obtained using the third-order displacement field. Hamilton’s principle is employed to obtain the governing equations of motion. The nano panel is subjected to a coupling of magnetic and electric loads, including a linear function along with the thickness direction and a 2D function along with the axial and circumferential directions. To account the effect of nanoscale in governing equations, the Eringen nonlocal elasticity theory is used. The numerical results are obtained to investigate the impact of significant parameters such as axial and circumferential mode numbers, the nanoscale parameter, applied electromagnetic potentials, and length-to-radius ratio. It is concluded that an increase in initial electric potential and a decrease in magnetic potential lead to an increase in natural frequencies of the nano panel.

This article examines the free vibrations of spherical orthotropic within an elastic medium according to the one-dimensional (1D) elastic model. According to the linear elasticity model, rotation, ...

The influence of strong magnetic field on stress intensity factor of an interface crack is studied in this paper. The nonlinear piezomagnetic property and magnetostriction effect have been taken into consideration in the theoretical analyses. This multi-field coupled problem is solved through a sequential coupling approach. The perturbed magnetization caused by the deformation around the crack is solved under magnetic boundary conditions. After modified by the perturbed magnetization, the initial loads are updated with magnetic forces for iterative calculation. With this strategy, the distributions of the stress and displacement at the crack region approach to the real solution gradually. Numerical results show that the influence of the external magnetic field on fracture behaviors is not ignorable. For structures with interface crack serving in a strong magnetic field, e.g., the multi-layer welded structures in the Tokamak device, the magneto-elastic coupling effects have to be considered to deal with its fracture problem.

This paper is devoted to the investigation of three-dimensional models of thermo-electro-magneto-elastic solids made of a multidomain inhomogeneous anisotropic material. General boundary and initial boundary value problems corresponding to the static and dynamic models are studied where, on certain parts of the boundary, mechanical displacement, electric and magnetic potentials and temperature vanish and, on the corresponding remaining parts of the boundary, the mechanical stress vector and components of the electric displacement, magnetic induction and heat flux along the outward normal vector of the boundary are given. Variational formulations of the boundary and initial boundary value problems are obtained and, applying them, existence and uniqueness results and the continuous dependence of solutions on given data, in suitable factor spaces of Sobolev spaces or spaces of vector-valued distributions, are proved.

The problem of harmonic oscillations in electro-electromagnetic composites is studied. Oscillations can be initiated by the extended load vector, including the horizontal and vertical components of mechanical displacements, and electrical induction distributed on top of the surface. Boundary conditions assume full mechanical coupling for all layers of the structure. Electrical conditions on the surface top can be both electrically open, and electrically shorted. Magnetic conditions are similar to electric ones and describe the continuity of fields in between two mediums, or indicate the isolation of the magnetic field between them. The Green's function of electro–magneto–elastic medium is constructed. Phase velocities are obtained for various geometric proportions and materials.

Magnetic properties of electrical steels exhibit a strong sensitivity to mechanical stress; this phenomenon is known as magneto-elastic coupling. Mechanical stress affects microstructural features of soft magnetic materials, which in turn leads to a change in their magnetic characteristics. Therefore, the magneto-elastic coupling in these materials needs to be studied and modeled accurately. This paper is devoted to the development of an analytical magneto-elastic hysteresis model. A recently proposed analytical hysteresis model based on Kadar product approach is modified to model the magnetoelastic effects using a multi-scale approach. The proposed model is validated using the quasi-static hysteresis loops measured for a non-oriented (NO) material (M235-35A) subjected to uni-axial compressive stress and tensile stress. The proposed formalism is applicable to model the reversible effects of stress (in elastic range) and it offers a closed form equation. A stress-dependent coercive parameter is introduced in this equation using a simple numerical procedure. Thus the model can be implemented easily in circuit and field analyses.

The stationary set of the control system of the hysteresis deformation of the electro magneto elastic actuator is the segment of the straight line. The aim of this work is to determine the condition of the absolute stability on the derivative for control system of the deformation of the electro magneto elastic actuator in automatic nanomanipulators for Nano science and Nano biomedicine research. The frequency methods for Lyapunov stable control system are used to calculate the condition the absolute stability of the control system with electro magneto elastic actuator. In result we obtained the condition of the absolute stability on the derivative for the control system with the electro magneto elastic actuator in automatic nanomanipulators for Nano science and Nano biomedicine research.

Purpose Due to the increasing amount of high power density high-speed electrical machines, a detailed understanding of the consequences for the machine’s operational behaviour and efficiency is necessary. Magnetic materials are prone to mechanical stress. Therefore, this paper aims to study the relation between the local mechanical stress distribution and magnetic properties such as magnetic flux density and iron losses. Design/methodology/approach In this paper, different approaches for equivalent mechanical stress criteria are analysed with focus on their applicability in electrical machines. Resulting machine characteristics such as magnetic flux density distribution or iron are compared. Findings The study shows a strong influence on the magnetic flux density distribution when considering the magneto-elastic effect for all analysed models. The influence on the iron loss is smaller due to a high amount of stress-independent eddy current loss component. Originality/value The understanding of the influence of mechanical stress on dimensions of electrical machines is important to obtain an accurate machine design. In this paper, the discussion on different equivalent stress approaches allows a new perspective for considering the magneto-elastic effect.

A stress-based approach to the analysis of linear electro-magneto-elastic materials is proposed. Firstly, field equations for linear electro-magneto-elastic solids are given in detail. Next, as a counterpart of coupled governing equations in terms of the displacement field, generalized stress equations of motion for the analysis of three-dimensional (3D) problems Are obtained – they supply a more convenient basis when mechanical boundary conditions are entirely tractions. Then, a sufficient set of conditions for the corresponding solution of generalized stress equations of motion to be unique are detailed in a uniqueness theorem. A numerical passage to obtain the solution of such equations is then given by generalizing a reciprocity theorem in terms of stress for such materials. Finally, as particular cases of the general 3D form, the stress equations of motion for planar problems (plane strain and Generalized plane stress) for transversely isotropic media are formulated.

It is well known that the interaction between defect-induced strain field and vortex lattice (VL) gives rise to vortex pinning behaviors. Likewise, magneto-elastic (ME) interaction is caused by the difference between specific volumes of normal phase and superconducting (SC) phase. Acting as inhomogeneous strain sources, the normal-state vortex cores produce local deformation in the surrounding SC matter and thus affect VL energy. ME interaction belongs to the fundamental physics of interdependences between vortex matter and crystal lattice. The review starts with the effects of ME interaction on magnetization, vortex morphology and intervortex interaction. In Sect. 2, theoretical descriptions of ME interaction are classified in terms of different simplifications. The core ideas and outstanding results of these theories are given. It is followed by Sect. 3, where the correlation and difference between ME and pinning interaction are outlined. Although pinning differs from ME interaction in their formation mechanisms, the pinning interaction is established upon the vortex-induced strain field from Ginzburg-Landau (GL) viewpoint. Section 4 goes further with the GL treatment for solving ME and pinning problem; the general thoughts and steps can be found in this section. The last section gives some outlooks which involve pressure dependence of Tc and anisotropy.

International audience; Magneto-caloric materials offer the possibility to design environmentally friendlier thermal management devices compared to the widely used gas-based systems. The challenges to develop this solid-state based technology lie in the difficulty of finding materials presenting a large magneto-caloric effect over a broad temperature span together with suitable secondary appli-cation parameters such as low heat capacity and high thermal conductivity. A series of compounds derived from the PbFCl structure is investigated using a combination of computational and experimental methods focusing on the change of cell volume in magnetic and non-magnetic ground states. Scaling analysis of the magnetic properties determines that they are second order phase transition ferromagnets and that the magnetic entropy change is driven by the coupling of magneto-elastic strain in the square-net through the magnetic transition determined from neutron and synchrotron X-ray diffraction. The primary and secondary application related properties are measured experimentally, and the c/a parameter is identified as an accurate proxy to control the magnetic transition. Chemical substitution on the square-net affords tuning of the Curie temperature over a broad temperature span between 252 and 322 K. A predictive machine learning model for the c/aparameter is developed to guide future exploratory synthesis.

In this work we present results for the protective performance of coatings used on magneto-elastic ribbons. It is found that monitoring the resonance frequency variation (Δf) of a magneto-elastic sensor can give useful electrochemical information. This method has the advantage of allowing one to monitor the electrochemical behavior of coatings without the need for direct access to the sample. A sensor developed from the FeNiMoB alloy (Metglas 2826MB3) was covered with hybrid coatings based on silicon alkoxide precursors. The results obtained from the magneto-elastic sensor test were correlated with the results obtained from electrochemical impedance spectroscopy (EIS). In general, it was observed that the Δf monitoring technique provided results consistent with those obtained by EIS, with the advantage that it does not need to have direct contact with the sample. Besides that monitoring the resonance frequency also allows one to evaluate the electrochemical behavior of the coating in the medium of interest.

Universally tuberculosis is the recordable serious killer diseases produced by Mycobacterium tuberculosis. Today in the medical field the most challenging and demanding job is detection of Tuberculosis. As per the current situations tuberculosis detection methods can be improve by bio-sensing technologies. The various bio-sensors have been developed in last few decades to detect Mycobacterium tuberculosis. The recognition systems of these bio-sensors are based on basic signal transducer principles and various biological elements. The purpose of the paper is to study the severity of tuberculosis and a number of bio-sensing technologies for rapid detection of tuberculosis and also shown different kinds of bio-sensors with their limits of recognition. Categorization of these bio-sensors are constructed on the process of signal transduction specially physical and chemical signal transducer with piezo-electric quartz crystal bio-sensors, electro-chemical bio-sensors, Magneto elastic Bio-sensors, Micro-cantilever Bio-sensors, Breathalyzer sensors.

The discovery of interfacial Dzyaloshinskii-Moriya interaction (DMI) enables development of novel ultra-compact non-reciprocal devices for microwave signal processing. Such devices are based on control of spin waves and magneto-elastic waves by electric field and addition of ultra-thin layers of heavy metals to the devices. Here we discuss recent advances in the development of such systems, which can be used for implementation of on-chip non-reciprocal microwave devices.

This paper presents a nonlocal theoretical model of magneto-elastic phononic crystal (PC) nanoplates to investigate the size-dependent band structure based on the nonlocal theory and Kirchhoff plate theory. The governing equation incorporating the nonlocal effect and magneto-elastic coupling is obtained by the Hamilton's principle and plane wave expansion method. The influence of nonlocal effect and magneto-elastic coupling on band structure of Terfenol-D/epoxy PC nanoplates is studied. The results show the edges and width of band gap increases with the improvement of nonlocal parameter, leading to a promotive influence of nonlocal effect on band gap. Meanwhile, the magneto-elastic coupling plays an important role in regulating band gap with nonlocal effect. The greater the magnetic field and compressive pre-stress can be applied, the larger the band gap is obtained. Consequently, the proposed nonlocal model can be beneficial for flexible tunability of elastic wave and functional design of PC nanodevices in multi-field environments.

The present paper investigates the propagation of quasi longitudinal (qLD) and quasi transverse (qTD) waves in a magneto elastic fibre-reinforced rotating semi-infinite medium. Reflections of waves from the flat boundary with surface stress have been studied in details. The governing equations have been used to obtain the polynomial characteristic equation from which qLD and qTD wave velocities are found. It is observed that both the wave velocities depend upon the incident angle. After imposing the appropriate boundary conditions including surface stress the resultant amplitude ratios for the total displacements have been obtained. Numerically simulated results have been depicted graphically by displaying two and three dimensional graphs to highlight the influence of magnetic field, rotation, surface stress and fibre-reinforcing nature of the material medium on the propagation and reflection of plane waves.

The response of cracked multiferroic composites that are subjected to thermo-electro-magneto-elastic loading is established by employing a two-scale analysis. To that end, the fully coupled constitutive and governing equations are utilized in the analysis. This form a generalization of a one-way thermal coupling analysis in which the electro-magneto-elastic field does not affect the thermal field. The micro-scale analysis is based on a micromechanical model which is capable of predicting the effective stiffness tensor of the undamaged multiferroic composite as well as the concentration tensors which enable the computation of the local field from the applied thermo-electro-magneto-elastic far-field. The macro-scale analysis provides the response of the cracked composite of periodic microstructure to the applied loading. It is based on the combined use of the representative cell method and the higher order theory. In the framework of the representative cell method, the problem for a periodic composite which is discretized into numerous identical cells is reduced to a problem of a single cell in the discrete Fourier transform domain. In the framework of the higher order theory, the governing equations and interfacial and periodic conditions formulated in the transform domain are solved by dividing the single cell into several subcells and imposing these conditions in an average (integral) sense. Results exhibit the responses caused by the application of mechanical, electric, magnetic, thermal, and heat flow loadings on two types of cracked periodically layered composites and provide comparisons between the predictions of the full and one-way thermal coupling analyses.

This paper studies shear wave propagation in magneto-elastic transversely isotropic material, sandwiched between a layer and a half-space of heterogeneous elastic materials. Elastic constan...

The effect of the chemical composition of high-strength cast iron VCh35 on the content, shape and diameter of graphite inclusions and on the presence of structurally-free cementite and defects is studied. A relationship is determined between the structure and metallurgical defects and characteristics of the mechanical and magnetic rigidity of cast samples. Relationships are established in a group of factors and property characteristics: chemical composition – microstructure – mechanical rigidity – magnetic stiffness. The basis of a method is established making it possible to perform operative non-destructive monitoring of the melt quality preparation for high-strength iron casting.

Based on the basic equations of electromagnetic elastic motion and the expression of electromagnetic force, the electromagnetic vibration equation of the rectangular thin plate in transverse magnetic field is obtained. For a rectangular plate with one side fixed and three other sides simply supported, its time variable and space variable are separated by the method of Galerkin, and the two-degree-of-freedom nonlinear Duffing vibration differential equations are proposed. The method of multiple scales is adopted to solve the model equations and obtain four first-order ordinary differential equations governing modulation of the amplitudes and phase angles involved via 1:1 or 1:3 internal resonances with different size ratios. With a numerical example, the time history response diagrams, phase portraits and 3-dimension responses of two order modal amplitudes are respectively captured. And the effects of initial values, thickness and magnetic field intensities on internal resonance characteristics are discussed respectively. The results also present obvious characteristics of typical nonlinear internal resonance in this paper.

Inductive dynamic drives (IDD) are ultra rapid actuators where the moving part (disc) is subjected to impulse force. This paper presents the second model of inductive dynamic drive – a mechanical model where analytic- numerical approach was applied. The magnetic pressure, which was determined on the basis of the results obtained in the electrodynamic model, becomes the input data for mechanical model. Research with application of the mechanical model is necessary in order to determine the proper disc oscillation frequency and to obtain the stress state control for drive elements to be designed. Also, the selection of drive parameters to keep the disc deformation insignificant (while oscillating) is a condition under which these models do not need to be coupled together.

In this work the condition of the absolute stability on the derivative for control system of the deformation of the electro magneto elastic actuator is calculated..

The electro magneto elastic actuator with the piezoelectric, piezomagnetic, electrostriction, magnetostriction effects is used for nanomedical research in the scanning tunneling microscopy.

Self-propulsion of magneto-elastic composite microswimmers is demonstrated under a uniaxial field at both the air-water and the water-substrate interfaces. The microswimmers are made of elastically linked magnetically hard Co-Ni-P and soft Co ferromagnets, fabricated using standard photolithography and electrodeposition. Swimming speed and direction are dependent on the field frequency and amplitude, reaching a maximum of 95.1 μm/s on the substrate surface. Fastest motion occurs at low frequencies via a spinning (air-water interface) or tumbling (water-substrate interface) mode that induces transient inertial motion. Higher frequencies result in low Reynolds number propagation at both interfaces via a rocking mode. Therefore, the same microswimmer can be operated as either a high or a low Reynolds number swimmer. Swimmer pairs agglomerate to form a faster superstructure that propels via spinning and rocking modes analogous to those seen in isolated swimmers. Microswimmer propulsion is driven by a combination of dipolar interactions between the Co and Co-Ni-P magnets and rotational torque due to the applied field, combined with elastic deformation and hydrodynamic interactions between different parts of the swimmer, in agreement with previous models.

A miniaturized thrombus dredger is proposed and developed in this study. The flexural resonance of the &micro, resonator dredger is driven by a bulk-extensional magneto-elastic vibrator that is externally excited by alternating magnetic-field. With the fabricated prototype of the resonant dredger, a mice thrombus blocked in a simulated vessel is broken into micro-pieces, and the previously blocked vessel can recover to an unobstructed state within 1 h. A flow-rate ratio detection method is used to evaluate the thrombus-cleaning effectiveness. The comparison between the finite-element simulation and the experimental results validates the flow-rate ratio detection method. By optimally exciting the resonant dredger in its third resonant mode, the flow-rate ratio in the cleaned vessel increases by about 2.7 times compared with that in the partly blocked vessel, and the thrombus is smashed into micro-pieces.

Based on the complete set of Maxwell’ electrodynamics equations and the theory of elasticity the two-dimensional equations have obtained describing the coupled wave process in piezoactive electro-magneto-elastic (MEE) structure and allowing solution of a new class of problems, in particular, the problems of propagation and internal resonance of electro-magneto-elastic waves in periodic MEE structures. For longitudinal lattice vibrations of oppositely polarized MEE periodic superlattice the effect of phonon–photon polariton is investigated with a full three-phase coupling between elastic, electromagnetic fields. The results show that the new coupled phonon–photon polariton exhibits properties different from piezoelectric or piezomagneticpolaritons.

The compounds, NiSb2O6 (NSO) and MnSb2O6 (MSO) attract the community for the quasi one-dimensional and layered structure composed of Ni2+ and Mn2+, which orders antiferromagnetically at T N = 6.7 and 12 K, respectively. Here, we report the Griffiths-like phase much above T N in the range of 37–85 K and 25–80 K for NSO and MSO, respectively. The dc magnetization results indicate the Griffiths-like phase, following the modified Curie–Weiss law. The magneto-capacitive responses for both the compounds show anomalies at the onset of the Griffiths-like phase. Intriguingly, the low temperature synchrotron diffraction results are conclusive for determining the singularities for both the compounds. Interplay between the low-dimensionality, magnetic frustration, and magneto-elastic coupling correlates the observed short range ordered state, which is suggested as a Griffiths-like phase, above T N for both the compounds.

Free vibration analysis of electric-magneto-elastic functionally graded plate with uncertain parameters is studied in this paper. The elastic, electric and magnetic parameters are regarded as interval variables. Interval analysis of electric-magneto-elastic functionally graded plate are carried out by introducing the interval algorithm into the dynamic equations. A simply supported electric-magneto-elastic functionally graded plate as a numerical example are provided to the validity of the method.

The aim of this paper is to study the behaviour of reflection of SV- wave at a free surface under the effects of magnetic field, initial stress, rotation and voids. When a SV- wave is incident on the free surface of an elastic half space, two damped P-waves and a SV-wave is reflected. Among of these waves, P-waves are only affected by magnetic field and rotation whereas SV-wave is influenced by rotation, initial stress and magnetic field. Numerical computations are performed for the developed amplitude ratios of P-, SV- and magneto-elastic waves. This study would be useful for magneto-elastic acoustic device field and further study about nature of seismic waves.

Structural changes through the first-order paramagnetic-antiferromagnetic phase transition of Dy3Ru4Al12 at 7 K have been studied by means of X-ray diffraction and thermal expansion measurements. The compound crystallizes in a hexagonal crystal structure of Gd3Ru4Al12 type (P63/mmc space group), and no structural phase transition has been found in the temperature interval between 2.5 and 300 K. Nevertheless, due to the spin-lattice coupling the crystal volume undergoes a small orthorhombic distortion of the order of 2×10-5 as the compound enters the antiferromagnetic state. We propose that the first-order phase transition is not driven by the structural changes but rather by the exchange interactions present in the system.

We theoretically study the effect of a material defect (material void) on switching errors associated with magneto-elastic switching of magnetization in elliptical magnetostrictive nanomagnets having in-plane magnetic anisotropy. We find that the error probability increases significantly in the presence of the defect, indicating that magneto-elastic switching is particularly vulnerable to material imperfections. Curiously, there is a critical stress value that gives the lowest error probability in both defect-free and defective nanomagnets. The critical stress is much higher in defective nanomagnets than in defect-free ones. Since it is more difficult to generate the critical stress in small nanomagnets than in large nanomagnets (having the same energy barrier for thermal stability), it would be a challenge to downscale magneto-elastically switched nanomagnets in memory and other applications where reliable switching is required. This is likely to be further exacerbated by the presence of defects.

The problem of stability of plane shock waves for a model of perfect magnetoelasticityis investigated. Important mathematical properties, like loss of strict hyperbolicityand loss of genuine nonlinearity, and their consequences for the stability ofmagneto-elastic shocks are discussed. It is shown that some of these shocks do not satisfyclassical Lax stability conditions. Both compressible and incompressible models ofmagneto-elasticity are discussed.[b]Keywords[/b]: perfect magneto-elasticity, shock waves, stability conditions

In this study, a rigid line inclusion on the interface between two dissimilar thermo-electro-magneto-elastic solids is considered. Based on the Muskhelishvili’s theory and extended Stroh formalism, it is reduced to the non-homogeneous Hilbert equation. According to the holomorphic continuation technology and Muskhelishvili’s theory, the exact solutions for both thermal and electro-magneto-elastic fields are derived. The explicit expressions of the multiple coupling fields are presented, and the generalized stress intensity factors are illustrated with the closed form. From the results, it can be observed the coupling of the thermo-electro-magneto-elastic effects. Moreover, the generalized stress has singularities and oscillatory properties near the inclusion tip.

Magnetorheological rubber material is a kind of composite material of magneto elastic coupling with multi functions, which is composed of magnetic particles and the mixed rubber films with the magnetic properties of the material, but because of its mechanical properties has limited practical use, and nylon cloth which has the advantages of high strength, dimensional stability, can be the ideal framework of magnetorheological rubber. The results show that for the magnetorheological rubber made from the NR/SBR blend, the tensile strength of the magnetorheological rubber with the cord fabric can greatly improve, the tensile strength can reach 17.8MPa, but also can improve the shear modulus of magnetorheological rubber and zero field storage shear modulus.

These notes origin from a group of lectures given at the Spring School on ``Rate-independent evolutions and hysteresis modelling'' (Hystry 2013), held at Politecnico di Milano and at Universita degli Studi di Milano, from May 27 until May 31, 2013. They are addressed to Graduate students in mathematics and applied science, interested in modeling rate-independent effects in smart systems. Therefore, they aim to provide the basic issues concerning modeling of multi-functional materials showing memory phenomena, with emphasis to magnetostrictives, in view of their application to the design of smart devices. Such tutorial summarizes several years activity on these issues that involved the cooperation with several colleagues, among all Dr. P. Krejci, with whom the authors are indebted.

The present study concerns the homogenization of multilayered multiferroics taking into account the thermal properties of the films. A matrix homogenization method has been employed for the calculation of the effective characteristics. The developed approach evaluates the impact of electro-magneto-elastic coefficients of the layers on the thermal behavior of the structure. Our work clearly demonstrates the possibility of occurrence of the pyroelectric coefficient in the system even in their absence in each film. The thermal capacity of the layered structure ceases to be additive due to the interaction of the fields and becomes dependent on the permittivity and permeability of the layers. These results provide substantial insight into the ability to control the thermal properties of layered systems by an electric and/or magnetic field.

Based on the quasi-static approximation and taking into account the linearized equations for a prestressed electro-magneto-elastic medium, the problem of oscillations of a layered half-space with initial mechanical strains is considered. The Green function of an electro-magneto-elastic medium is constructed. The effect of the initial deformations in different medium parts on the phase velocities is considered. We took into account the deformations directed simultaneously to the compression and stretching of the half-space different parts. It was established that the initial mechanical deformations have various influence in different frequency domains.

This paper develops nonlocal elasticity equations and magneto-electro-elastic relations to size-dependent electro-magneto-elastic bending analyses of the functionally graded axisymmetric circular nanoplates based on the first-order shear deformation theory. All material properties are graded along the thickness direction based on exponential varying. It is assumed that a circular nanoplate is made from piezo-magnetic materials. The energy method and Ritz approach is employed for the derivation of governing equations of electro-magneto-elastic bending and the solution of the problem, respectively. The nanoplate is subjected to applied electric and magnetic potentials at top and transverse loads while it is rested on Pasternak’s foundation. Some important numerical results are presented in various figures to show the influence of applied electric and magnetic potentials, small scale parameter and inhomogeneous index of an exponentially graded nanoplate.

Developed was a new method of control of mechanic rigidity in assemblies of hydropower units that allows a real-time control of technological process, and proposed was the design for a primary measuring transducer of mechanic intensity as a component of the control method proposed, with its transformation equations obtained.