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We study the compression diagrams and elastic compliances of composite piezoelectric transducers. We find the typical points
on the compression diagram which correspond to the mechanical stress of clearance cutting and smoothing the microroughnesses
and to the ultimate compression strength with crack formation on the edges of piezoelectric crystal plates. We construct mechanical
and adjusting characteristics of piezoelectric transducers and determine their static and dynamic characteristics.

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... Piezo drives are used for atomic force microscopy, nanomanipulators, nanotechnology, biotechnology, astronomy, space research, metrology, laser resonator [16][17][18][19][20][21][22][23][24][25][26][27][28][29][30][31][32][33][34][35]. ...

... Two matrix equations [8,[11][12][13][14][15][16][17][18][19] for the piezo drive have the form ...

The structural model of the drive for nanobiotechnology is obtained. The structural scheme of the drive is constructed. In nanobiotechnology for the control systems with the drive its deformations are determined.

... In structural schema of electro elastic engine its energy transformation is clearly [7][8][9][10][11][12]. The piezo engine is applied for precise adjustment for nanochemistry in adaptive optics and scanning microscopy [3][4][5][6][7][8][9][10][11][12][13][14][15][16][17][18][19][20]. ...

... For an engine its equations in matrixes [8, For piezo engine Figure 1 its relative displacement for 3 axis [8,[11][12][13][14][15][16][17][18][19][20] has the form where d 33 is piezo coefficient, E 3 is strength electric field on 3 axis, s E 33 is elastic compliance, T 3 is strength mechanical field on 3 axis. The steady-state movement of the transverse piezo engine with fixed one face and at elastic-inertial load has the form For the transverse piezo engine at elastic-inertial load the expression has the form where C l , C E 11 are the stiffness of load and engine, T t , ξ t , ω t are the time constant, the attenuation coefficient and the conjugate frequency of the engine. ...

The structural model of an engine for nanochemistry is obtained. The structural scheme of an engine is constructed. For the control systems in nanochemistry with an elecro elastic engine its characteristics are determined.

... The electro magneto elastic actuator with the piezoelectric, piezomagnetic, electrostriction, magnetostriction effects is used for nanomedical research in the scanning tunneling microscopy [1][2][3][4][5][6][7][8][9]. For control system of the deformation of the electro magneto elastic actuator its structural diagram, transfer function, characteristics are calculated [9][10][11][12][13][14][15][16][17][18]. The structural diagram and matrix transfer function the electro magneto elastic actuator is applied to describe the dynamic and static characteristics of the electro magneto elastic actuator for nanomedical research with regard to its physical parameters and external load [14][15][16][17][18][19][20][21][22][23][24][25][26][27][28]. ...

... For control system of the deformation of the electro magneto elastic actuator its structural diagram, transfer function, characteristics are calculated [9][10][11][12][13][14][15][16][17][18]. The structural diagram and matrix transfer function the electro magneto elastic actuator is applied to describe the dynamic and static characteristics of the electro magneto elastic actuator for nanomedical research with regard to its physical parameters and external load [14][15][16][17][18][19][20][21][22][23][24][25][26][27][28]. ...

... The control systems with electro magneto elastic actuator on piezoelectric, electrostrictive and magnetostrictive effects solves problems of the precise matching in the nano biomedicine, the compensation of the temperature and gravitational deformations of the equipment, the wave front correction in the adaptive laser system [1][2][3][4][5][6][7][8][9][10][11][12][13][14]. The piezo actuator for nano biomedicine is used in the scanning tunneling microscope, the scanning force microscope, the atomic force microscope, in the gene manipulator [15][16][17][18][19][20][21][22][23][24][25][26][27][28][29]. The problems of using criteria absolute stability of the control system with electro magneto elastic actuator for nano biomedicine are discussed. ...

... For the Lyapunov stable control system and the Yalubovich absolute stability criterion for the systems with the single hysteresis nonlinearity provides the simplest and pictorial representation of results of the investigation of the stability of the strain control system with the electro magneto elastic actuator for nano biomedicine. For description of the control system we use the transfer function of the linear part of the system ( ) ij W p and the hysteresis function of the relative deformation S j of the electro magneto elastic actuator [16]. We have the hysteresis characteristic of the electro magneto elastic actuator in the following form ...

... The piezoactuator for the nanomechanics is provided the displacement from nanometers to tens of micrometers, a force to 1000N. The piezoactuator is used for research in the nanomedicine and the nanobiotechnology for the scanning tunneling microscopes, scanning force microscopes and atomic force microscopes [14][15][16][17][18][19][20][21][22][23][24][25][26][27][28][29][30][31][32]. ...

... In [8,27] was used the transfer functions of the piezoactuator for the decision problem absolute stability conditions for a system controlling the deformation of the electro magneto elastic actuator. The elastic compliances and the mechanical and adjusting characteristics of the piezoactuator were found in [18,[21][22][23]28,29] for calculation its transfer functions and the structural-parametric models. The structural-parametric model of the multilayer and compound piezoactuator was determined in [18][19][20]. ...

... In structural schema of an engine its energy transformation is clearly [4][5][6][7][8][9][10][11][12][13][14]. The piezo engine is applied for precise adjustment in scanning microscopy and adaptive optics [11][12][13][14][15][16][17][18][19][20][21][22][23][24][25][26][27][28]. ...

In nanosciences research the structural model of an electro elastic engine is constructed. Its structural scheme of is received. For an engine its matrix equation of the deformations are obtained in the decisions of the precision control systems. The parameters of an engine are determined.

... Nano drives are used for atomic force microscopy, nano manipulators, nanotechnology, biotechnology, astronomy, space research, metrology, laser resonator [16][17][18][19][20][21][22][23][24][25]. ...

... has the form of the equation of the reverse effectThe equation of the force on the face of a precision engine has the form[10][11][12][13][14][15][16][17][18][19] ...

The transfer function and the transfer coefficient of a precision electromagnetoelastic engine for nanobiomedical research are obtained. The structural diagram of an electromagnetoelastic engine has a difference in the visibility of energy conversion from Cady and Mason electrical equivalent circuits of a piezo vibrator. The structural diagram of an electromagnetoelastic engine is founded. The structural diagram of the piezo engine for nanobiomedical research is written. The transfer functions of the piezo engine or are obtained.

... For a sectional electroelastic engine, the equation of the electroelasticity [10][11][12][13][14][15][16][17][18][19][20][21][22][23][24][25][26][27][28][29] has the form of the inverse piezoelectric effect ...

This work determines the coded control of a sectional electroelastic engine at the elastic–inertial load for nanomechatronics systems. The expressions of the mechanical and adjustment characteristics of a sectional electroelastic engine are obtained using the equations of the electroelasticity and the mechanical load. A sectional electroelastic engine is applied for coded control of nanodisplacement as a digital-to-analog converter. The transfer function and the transient characteristics of a sectional electroelastic engine at elastic–inertial load are received for nanomechatronics systems.

... The method of mathematical physics is applied for the solution of the wave equation of the electroelastic actuator for the nanotechnology with using the Laplace transform for the construction the parametric structural schematic diagram of electroelastic actuator [11][12][13][14][15][16]. ...

... The method of the mathematical physics with Laplace transform we have to build the structural diagram of the electro magneto elastic actuator for nanotechnology and material science. The structural diagram of the electro magneto elastic actuator nano displacement for material science is difference from Cady and Mason electrical equivalent circuits [1][2][3][4][5][6][7][8][9][10][11][12][13][14][15][16][17][18]. ...

... The piezoactuator for Nano science and Nano biomedicine research is used in the scanning tunneling microscope, the scanning force microscope, the atomic force microscope, in the gene manipulator [16][17][18][19][20][21][22][23][24][25][26][27][28][29][30]. ...

Interfacial interactions between matrix and reinforcement of composites influences greatly in final properties of the material. Carbon Fibers are characterized for to have low interactions with resins when forming a composite material. In the present study, 0.3 wt% of GO/rGO were incorporated in three systems of epoxy resin/carbon fiber as reinforcing fillers, trying to profit the chemical affinity between aromatics structures of GO/rGO and polar interactions with epoxy resin. GO/rGO were characterized by XPS, TGA was performed on carbon fiber, epoxy resins and composites obtained and SEM was utilized to observe composite samples in detail once mechanical tests were conducted. Composites experienced noticeable enhancements by employing Bisphenol Epoxy (BP) cured with methyl cyclohexane-1,2-dicarboxylic anhydride (MCHDA) as matrix and carbon fiber of 300 g/cm 2 as reinforcement; Youngs modulus, rupture stress and elongation to failure increased almost twofold compared to non-modified composites by adding GO in the system and even superior boosts can be appreciated with rGO, which additionally improves the flexural stress from 14.6 to 30.1 GPa.

... In general the equation of electroelasticity [10,12,15] has following form For calculation of the electroelastic actuator nano-and microdisplacement is used the wave equation [10,12,16,19] for the wave propagation in a long line with damping but without distortions. After Laplace transform is obtained the linear ordinary second-order differential equation with the parameter p, where the original problem for the partial differential equation of hyperbolic type using the Laplace transform is reduced to the simpler problem [10,13,14] for the linear ordinary differential equation ...

... The electro elastic actuator for the nanotechnology and the biotechnology is used in the scanning tunneling microscopes, the scanning force microscopes, the atomic force microscopes [1][2][3][4][5][6][7][8][9][10][11][12][13][14][15][16][17][18][19] . ...

... The piezoactuator uses the inverse piezoeffect and serves for the actuation of mechanisms or the management and converts the electrical signals into the displacement and the force [1][2][3][4][5][6][7][8]. The piezoactuator is applied for the drives of the scanning tunneling microscopes, scanning force microscopes and atomic force microscopes [14][15][16][17][18][19][20][21][22][23][24][25][26][27][28][29][30][31][32]. ...

... The elastic compliances and the mechanical and adjusting characteristics of a piezoactuator were explored in Reference [17][18][19] in order to calculate its transfer functions and create the structural-parametric model. The structural-parametric model of a multilayer and compound piezoactuator was determined in References [17][18][19][20][21][22] with output displacement. In this paper, we solve the problem of building the generalized structural parametric model and the generalized parametric structural schematic diagram of an electromagnetoelastic actuator for the equation of electromagnetoelasticity in the general form. ...

The generalized parametric structural schematic diagram, the generalized structural-parametric model, and the generalized matrix transfer function of an electromagnetoelastic actuator with output parameters displacements are determined by solving the wave equation with the Laplace transform, using the equation of the electromagnetolasticity in the general form, the boundary conditions on the loaded working surfaces of the actuator, and the strains along the coordinate axes. The parametric structural schematic diagram and the transfer functions of the electromagnetoelastic actuator are obtained for the calculation of the control systems for the nanomechanics. The structural-parametric model of the piezoactuator for the transverse, longitudinal, and shift piezoelectric effects are constructed. The dynamic and static characteristics of the piezoactuator with output parameter displacement are obtained.

The structural scheme of a piezoactuator is obtained for astrophysics. The matrix equation is constructed for a piezoactuator. The characteristics of a piezoactuator are received for astrophysics.

The mathematical models of a piezoengine are determined for nanomedicine and applied bionics. The structural scheme of a piezoengine is constructed. The matrix equation is obtained for a piezoengine.

We obtained the condition absolute stability on the derivative for the control system of electromagnetoelastic actuator for communication equipment. We applied the frequency methods for Lyapunov stable control system to calculate the condition absolute stability control system of electromagnetoelastic actuator. We used Yakubovich criterion absolute stability system with the condition on the derivative. The aim of this work is to determine the condition of the absolute stability on the derivative for the control system of electromagnetoelastic actuator. We received the stationary set of the control system of the hysteresis deformation of the electromagnetoelastic actuator. The stationary set is the segment of the straight line.

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.

In this work, the parametric structural schematic diagrams of a multilayer electromagnetoelastic actuator and a multilayer piezoactuator for nanomechanics were determined in contrast to the electrical equivalent circuits of a piezotransmitter and piezoreceiver, the vibration piezomotor. The decision matrix equation of the equivalent quadripole of the multilayer electromagnetoelastic actuator was used. The structural-parametric model, the parametric structural schematic diagram, and the matrix transfer function of the multilayer electromagnetoelastic actuator for nanomechanics were obtained.

We consider statistically homogeneous two-phase random piezoactive structures with deterministic properties of inclusions
and the matrix and with random mutual location of inclusions. We present the solution of a coupled stochastic boundary value
problem of electroelasticity for the representative domain of a matrix piezocomposite with a random structure in the generalized
singular approximation of the method of periodic components; the singular approximation is based on taking into account only
the singular component of the second derivative of the Green function for the comparison media. We obtain an analytic solution
for the tensor of effective properties of the piezocomposite in terms of the solution for the tensors of effective properties
of a composite with an ideal periodic structure or with the “statistical mixture” structure and with the periodicity coefficient
calculated for a given random structure with its specific characteristics taken into account. The effective properties of
composites with auxiliary structures (periodic and “statistical mixture”) are also determined in the generalized singular
approximation by varying the properties of the comparisonmedium. We perform numerical computations and analyze the effective
properties of a quasiperiodic piezocomposite with reciprocal polarization of oriented ellipsoidal inclusions and the matrix,
the layered structures with reciprocal polarization of the layers [1] of a polymer piezoelectric PVF, and find their unique
properties such as a significant increase in the Young modulus along the normal to the layers and in dielectric permittivities,
the appearance of negative values of the Poisson ratio under extension along the normal, and an increase in the absolute values
of the basic piezomoduli.
Key wordspiezocomposite-electroelasticity-effective properties-method of periodic components-quasiperiodic structures

Design and Analysis of Precise Mechanisms (Mashinostroenie, Leningrad, 1976) [in Russian]

- Yu D Pervitskii

Yu. D. Pervitskii, Design and Analysis of Precise Mechanisms (Mashinostroenie, Leningrad, 1976) [in Russian]. MECHANICS OF SOLIDS Vol. 42 No. 1 2007

Parametric Structure Scheme of Piezoelectric Transducer

- S M Afonin

Design and Analysis of Precise Mechanisms

- D Yu
- Pervitskii

Piezoelectric Transducers for Controlling Microdisplacements

- S M Afonin

Deformation, Destruction, and Mechanical Characteristics of a Composite Piezoelectric Transducer

- S M Afonin

Generalized Hysteresis Characteristics of Piezoelectric Transducer and its Harmonic Linearization

- S M Afonin

Design and Analysis of Precise Mechanisms

- Yu D Pervitskii
- Yu. D. Pervitskii