Decision Matrix Equation and Block Diagram of Multilayer Electromagnetoelastic Actuator Micro and Nanodisplacement for Communications Systems

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


Introduction
The multilayer electromagnetoelastic actuator is used for precise alignment in the range of movement from nanometers to tens of micrometers in nanotechnology, adaptive optics, communications systems. In the work the block diagram of multilayer electromagnetoelastic actuator for micro and nanodisplacement on the piezoelectric, piezomagnetic, electrostriction, magnetostriction effects, for example, the block diagram of the multilayer piezoactuator is determined in contrast to Cady and Mason's electrical equivalent circuits for the calculation of the piezotransmitter and piezoreceiver, the vibration piezomotor [1 -11]. The block diagram of multilayer electromagnetoelastic actuator is obtained with the mechanical parameters the displacement and the force. Piezoactuator is piezomechanical device intended By decision matrix equation of the multilayer electromagnetoelastic actuator with allowance for the corresponding equation of the electromagnetoelasticity, the boundary conditions on loaded working surfaces of the multilayer electromagnetoelastic actuators, and the strains along the coordinate axes, it is possible to construct a structural parametric model of the multilayer electromagnetoelastic actuator [8,9,16]. The transfer functions and the parametric block diagrams of the multilayer electromagnetoelastic actuators are obtained from the set of equations describing the corresponding structural parametric model of the multilayer actuator for the communications systems. The solution of the matrix equation of the multilayer electromagnetoelastic actuator with the Laplace transform are used for the construction the parametric block diagram of the electromagnetoelastic actuator. As the result of the joint solution of the matrix equation of the multilayer actuator with the Laplace transform, the equation of the electromagnetoelasticity, the boundary conditions on the two loaded working surfaces of the multilayer actuator, we obtain the corresponding structural-parametric model and the parametric block diagram of the multilayer electromagnetoelastic actuator.

Block diagram of multilayer electromagnetoelastic actuator
For the communications systems the parametric block diagram and the matrix transfer functions of the multilayer electromagnetoelastic actuator are obtained from the structural-parametric model of the multilayer actuator with the mechanical parameters the displacement and the force. The parametric block diagrams of the voltage or current-controlled multilayer piezoactuator are determined using the equation of the inverse piezoeffect in the form [8,11]: where the indexes i = 1, 2, … , 6, j = 1, 2, … , 6, m = 1, 2, 3, with 1, 2, 3 are mutually perpendicular coordinate axes, i S is relative deformation with index I, mi d is the piezoelectric module, m E is electric field strength where the indexes m = 1, 2, 3, k = 1, 2, 3, T mk ε is the dielectric constants for const = T . Accordingly in general the equation of the electromagnetoelasticity of the multilayer electromagnetoelastic actuator [11,14,16,20] has the form is the relative displacement along axis i of the cross section of the actuator, therefore we obtain     Therefore we have from the equation (9) the equivalent quadripole of the multilayer piezoactuator on Figure 1 for the longitudinal piezoeffect with length of the multilayer piezoactuator Equations of the forces acting on the faces of the multilayer piezoactuator:   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 7 , N o . 3 , J u n e 2 0 1 9   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

Figure 4. The generalized block diagram of the electromagnetoelastic actuator
The generalized block diagram of the electromagnetoelastic actuator is constructed using the generalized structural-parametric model of the multilayer electromagnetoelastic actuator micro and nanodisplacement for the communications systems.

Matrix transfer function of multilayer electromagnetoelastic actuator
The matrix transfer function of the multilayer electromagnetoelastic actuator determined from its structural-parametric model (15)   From generalized structural-parametric model of the multilayer electromagnetoelastic actuator its generalized block diagram and generalized matrix transfer function are determined to calculate the characteristics of the multilayer electromagnetoelastic actuator micro and nanodisplacement for the communications system.
For the approximation of the hyperbolic cotangent by two terms of the power series in the transfer function of the multilayer piezoactuator (16) for the elastic-inertial load with one fixed face at    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 7 , N o . 3 , J u n e 2 0 1 9   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 m   19 where ( )