A Block Diagram of Electromagnetoelastic Actuator Nanodisplacement for Communications Systems

The parametric block diagram of the electromagnetoelastic actuator nanodisplacement or the piezoactuator is determined in contrast the electrical equivalent circuit types Cady or Mason for the calculation of the piezoelectric transmitter and receiver, the vibration piezomotor with the mechanical parameters in form the velosity and the pressure. The method of mathematical physics is used. The parametric block diagram of electromagnetoelastic actuator is obtained with the mechanical parameters the displacement and the force. The transfer functions of the electroelastic actuator are determined. The the generalized parametric block diagram, the generalized matrix equation for the electromagnetoelastic actuator nanodisplacement are obtained. The deformations of the electroelastic actuator for the nanotechnology are described by the matrix equation. Block diagram and structural-parametric model of electromagnetoelastic actuator nanodisplacement for nanodisplacement of the communications systems are obtained, its transfer functions are bult. Effects of geometric and physical parameters of electromagnetoelastic actuators and external load on its dynamic characteristics are determined. For calculations the communications systems with the piezoactuator for nanodisplacement the parametric block diagram and the transfer functions of the piezoactuator are obtained.


Introduction
The parametric block diagram of electromagnetoelastic actuator for nanodisplacement on the piezoelectric, piezomagnetic, electrostriction, magnetostriction effects, for example, the piezoactuator is determined in contrast electrical equivalent circuit types Cady or Mason for the calculation of the piezotransmitter and piezoreceiver, the vibration piezomotor with the mechanical parameters in form the velosity and the pressure [1 -11]. The block diagram of electromagnetoelastic actuator is obtained with the mechanical parameters the displacement and the force [7 -9]. The electromagnetoelastic actuator is used for precise alignment in the nanotechnology, the adaptive optics, the communications systems. The piezoactuator of nanometric movements operates based on the inverse piezoeffect, in which the motion is achieved due to deformation of the piezoactuator when an external electric voltage is applied to it [1 − 19].
Piezoactuator -piezomechanical device intended for actuation of mechanisms, systems or management based on the piezoelectric effect, converts the electrical signals into the mechanical movement or the Let us consider separately effect the electric field strength and the magnetic field strength, therefore the generalized equation of the electromagnetoelasticity has the form  for the actuator or the piezoactuator in form the thickness, the height and the width for the longitudinal, transverse and shift the piezoeffect.
For the construction the parametric block diagram of the electromagnetoelastic actuator in nanotechnology is used the wave equation for the wave propagation in a long line with damping but without distortions. With using Laplace transform is obtained the linear ordinary second-order differential equation with the parameter s. Correspondingly the original problem for the partial differential equation of hyperbolic type using the Laplace transform is reduced to the simpler problem [8,14,18] for the linear ordinary differential equation is the Laplace transform of the displacement of section of the actuator, , α is the damping coefficient, C and B are constants.
From generalized electromagnetoelasticity equation (3), we obtain the system of equations describing the generalized structural-parametric model of the electromagnetoelastic actuator for the communications systems:   Figure 1 shows the generalized parametric block diagram of the electromagnetoelastic actuator corresponding to the equation (2) of the electromagnetoelasticity and the set of equations (5).

Figure 1. Generalized parametric block diagram of electromagnetoelastic actuator for nanodisplacement
The matrix state equations [11,14] for the piezoelectric effect have the form where the equation (6) describes the direct piezoeffect, the equation (7)  Let us consider the transverse piezoelectric effect in the piezoactuator. The equation of the inverse transverse piezoeffect [8,11] ( ) is the relative displacement of the cross section of the piezoactuator along axis 1, The solution of the linear ordinary second-order differential equation with the parameter s (3) we obtain as (4) and subject to the conditions ( ) ( ) s s , The constants C and B for the solution are determined in the following form Then, the solution (4) can be written as The equations of forces acting on the faces of the piezoactuator has the form Therefore we obtain the system of the equations for the mechanical stresses at the faces of the piezoactuator for the transverse piezoeffect in the form

Matrix transfer function of electromagnetoelastic actuator
From (5), (14) matrix equation of the Laplace transforms of the displacements with the matrix transfer function of the electromagnetoelastic actuator is obtained in the form   T r a n s a c t i o n s o n N e t w o r k s a n d C o m m u n i c a t i o n s ; V o l u m e 6 , N o . 3 , J u n e 2 0 1 8   C o p y r i g h t © S o c i e t y f o r S c i e n c e a n d E d u c a t i o n , U n i t e d K i n g d o The static displacements of the faces for the voltage-controlled the piezoactuator for the shift piezoeffect are obtained from (15)    The matrix transfer function of the actuator is determined for control systems with the electromagnetoelastic actuator in the communications systems.
The generalized parametric block diagram and generalized structural-parametric model of the electromagnetoelastic actuator are obtained. From generalized structural-parametric model of the actuator after algebraic transformations the transfer functions of the actuator are determined. The parametric block diagram, the structural-parametric models of the piezoactuator for the transverse, longitudinal, shift piezoelectric effects are determined from the generalized structural-parametric model of the electromagnetoelastic actuator for the communications systems.

Conclusion
The generalized parametric block diagram and the generalized structural-parametric model of the electromagnetoelastic actuator are constructed with the mechanical parameters the displacement and the force.
The parametric block diagrams of the piezoactuator for the transverse, longitudinal, shift piezoelectric effects are determined. The matrix transfer function of the electromagnetoelastic actuator is obtained for the communications systems.