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Static and dynamic characteristics of a multi-layer electroelastic solid
Abstract
We construct a generalized structural-parametric model of a multilayer electroelastic solid and determine how the geometric
and physical parameters of the transducer and the external load affect its static and dynamical characteristics. We obtain
the transfer functions of a multilayer electroelastic solid for an electromechanical actuator of nano- and microdisplacements.
... By solving the wave equation with allowance methods of mathematical physics for equation electromagnetoelasticity, the boundary conditions on loaded working surfaces of actuators, the strains along the coordinate axes, it is possible to construct the linear structural-parametric model of the actuator for the mechatronics systems [14][15][16][17][18][19][20][21][22][23]. ...
... x = and x δ = , we obtain the following set of the equations for determining stresses in the piezoactuator [15][16][17][18][19][20][21][22][23][24] International Journal of Physics 11 33 3 3 0 33 33 33 3 3 33 33 ...
... After algebraic transformations of the generalized structural-parametric model of the actuator we provided the transfer functions of the actuator in matrix form [14][15][16][17][18][19][20][21][22][23], where the transfer functions are the ratio of the Laplace transforms of the displacement of the face actuator and the corresponding parameter or force at zero initial conditions. ...
... 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]. ...
... Generalized structural-parametric model and generalized parametric structural schematic diagram of the electromagnetoelastic actuator after algebraic transformations provides the transfer functions of the electromagnetoelastic actuator for nano-and micromanipulators [9][10][11][12][13][14][15][16][17][18][19][20][21][22][23][24][25][26]. ...
... The set of equations (16) for mechanical stresses in piezoactuator yields the following set of equations describing the structural parametric model and parametric structural schematic diagram of piezoactuator Figure 4 ( ...
Structural-parametric models, parametric structural schematic diagrams and transfer functions of electromagnetoelastic actuators are determined. A generalized parametric structural schematic diagram of the electromagnetoelastic actuator is constructed. Effects of geometric and physical parameters of actuators and external load on its dynamic characteristics are determined. For calculations the mechatronic systems with piezoactuators for nano-and microdisplacement the parametric structural schematic diagrams and the transfer functions of piezoactuators are obtained.
... The electromagnetoelastic actuator is the electromechanical device for actuating and controlling mechanisms, systems with the conversion of electrical signals into mechanical displacements and forces. [16][17][18][19][20][21][22][23][24][25][26][27][28][29][30][31][32][33][34] The piezo actuator is used for nano scale motion in adaptive optics, laser systems, focusing and image stabilization systems, nano and micro surgery, vibration damping, nano and micro manipulation to penetrate the cell and to work with the genes. The electromagnetoelastic actuator is provided range of movement from nanometers to ten microns; force 1000 N, response 1-10 ms. ...
... 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 electromagnetoelastic actuator is the electromechanical device for actuating and controlling mechanisms, systems with the conversion of electrical signals into mechanical displacements and forces. The electromagnetoelastic actuator is provided range of movement from nanometers to ten microns, force 1000 N, response 1-10 ms [16][17][18][19][20][21][22][23][24][25][26][27][28][29][30][31][32][33][34]. ...
The regulation and mechanical characteristics of the electromagnetoelastic actuator are obtained for control systems in nano physics and optics sciences for scanning microscopy, adaptive optics and nano biomedicine. The piezo actuator is used for nano manipulators. The matrix transfer function of the electromagnetoelastic actuator is received for nano physics and optics sciences
... 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]. ...
Decision wave equation, structural - parametric model and block diagram of electro magneto elastic actuators are obtained, its transfer functions are bult. Effects of geometric and physical parameters of electro magneto elastic actuators and external load on its dynamic characteristics are determined. For calculation of communications systems with piezoactuators the block diagram and the transfer functions of piezoactuators are obtained.
Structural-parametric models, parametric structural schematic diagrams and transfer functions of electromagnetoelastic actuators are determined. A generalized parametric structural schematic diagram of the electromagnetoelastic actuator is constructed. Effects of geometric and physical parameters of actuators and external load on its dynamic characteristics are determined. For calculations the mechatronic systems with piezoactuators for nano- and microdisplacement the parametric structural schematic diagrams and the transfer functions of piezoactuators are obtained.
We obtained the deformation, the structural diagram, the transfer functions and the characteristics of the actuator nano and micro displacements for composite telescope in astronomy and physics research. The mechanical and regulation characteristics of the actuator are received.
An electroelastic actuator on the piezoelectric or electrostriction effect is applied in nanotechnology, nanobiology, biomechanics and adaptive optics for the precision matching in nanomechatronics systems. For the analysis and calculation of nanomechatronics systems is used the harmonious linearization of the hysteresis characteristic for an electroelastic actuator. The piezo actuator works on the basis of the inverse piezoelectric effect due to its deformation when the electric field strength is applied. To increase the range of movement of the piezo actuator to tens of micrometers, the multilayer piezo actuator is applied. The piezo actuator is used in nanomechatronics systems for nanodisplacement in adaptive optics, nanotechnology, scanning microscopy, nanobiomechanics, multicomponent telescopes. The coefficients of harmonious linearization for the basic loop characteristic are determined by the method of the theory of nonlinear automatic systems. On the characteristic of the piezo actuator deformation from the electric field strength, the initial curve is observed, on which the vertices of the basic hysteresis loops lie. The basic hysteresis loops have a symmetric change in the electric field strength relative to zero, and partial loops have an asymmetric change in the strength relative to zero. The expressions for the hysteresis basic and local loops of piezo actuator are received. The coefficients of harmonious linearization for the basic loop characteristic of the piezo actuator for nanomechatronics systems are obtained. The basic and local loops for hysteresis characteristics of the piezo actuator are proposed. The expression is determined for the generalized frequency transfer function of the nonlinear link with the hysteresis characteristic of the basic hysteresis loop for the piezo actuator.KeywordsHarmonious linearizationHysteresisBasic and partial loopsDeformationElectroelastic actuatorPiezo actuatorNanomechatronics system
The electromagnetoelastic actuator on the piezoelectric, piezomagnetic, electrostriction and magnetostriction effects is used in nanoresearch, nanotechnology, nanobiology and adaptive optics. The piezo-actuator is applied in nanotechnology and nanomechanics. The Yakubovich absolute stability criterion of the control system with the condition on the derivative for the hysteresis nonlinearity of the electromagnetoelastic actuator is used. This criterion with the condition on the derivative is development of the Popov absolute stability criterion. The stationary set of the control system for the electromagnetoelastic actuator with the hysteresis deformation is the segment of the straight line. This segment has the points of the intersection of the hysteresis partial loops and the straight line. The absolute stability conditions on the derivative for the control systems with the piezo-actuator at the longitudinal, transverse and shift piezo-effect are received. The condition of the absolute stability on the derivative for the control system for the deformation of the electromagnetoelastic actuator under random impacts in nanoresearch is obtained. For the Lyapunov stable control system this Yakubovich absolute stability criterion has the simplest representation of the result of the investigation of the absolute stability.
In the present chapter, the influence of the rigidity of piezoactuator and the load rigidity on the mechanical and control characteristics of the multilayered piezoactuator for the longitudinal, transverse and shear piezoeffect in the case of the parallel and coded control are considered. The effects of the parameters of the multilayered sectional piezoactuator and the load on its static and dynamic characteristics are determined. For calculation of the control systems for the nano- and microdisplacement, the transfer functions of the multilayered piezoactuator with parallel and coded control are obtained.
A structural-parametric model and parametric block diagrams of a piezoelectric transducer in the transverse piezoelectric effect are obtained with regard to the counter-electromotive force. The transfer functions of the multi-layer piezoelectric transducer of nano- and microdisplacements are determined with regard to the influence of geometric and physical parameters of the multi-layer piezoelectric transducer, the counter-electromotive force, and the external load.
Parametric block diagrams are constructed for the multilayer piezoelectric transducer in longitudinal piezoeffect with the counter-electromotive force taken into account. The transfer functions of the multilayer piezoelectric transducer are obtained with regard to the influence of geometric and physical parameters of the multilayer piezoelectric transducer, counter-electromotive force, and external load.
The transfer functions of multilayer nano- and microdisplacement piezotransducers are obtained under the conditions of longitudinal and transverse piezo-optic effects. The absolute stability conditions are derived for the strain control systems of multilayer nano- and microdisplacement piezotransducers. Some compensating devices ensuring the stability of strain control systems of multilayer piezotransducers are chosen.
Mechanical and control characteristics of a multilayer piezoelectric transducer of nanoand microdisplacements in the case of parallel and encoded control are obtained. The static and dynamic characteristics of simple and multilayer piezoelectric transducers of nano- and microscopic displacements are determined for longitudinal and transverse piezoeffects.
A unidimensional, linear systems, block diagram model of a two-layer thickness mode piezoelectric transducer is presented. The layers are subject to opposing piezoelectric polarization and the device is assumed to be loaded by semi-infinite isotropic media at the two principal faces. Block diagram representations of the transducer acting as both a generator and a receiver of ultrasound are developed in conjunction with the equivalent model of the electrical admittance. When expressed in this manner, the underlying cause and effect relationships are identified, with the important contribution of the piezoelectric boundary highlighted. Comparisons with the conventional single-layer transducer are made throughout and the major physical differences in terms of transduction performance are discussed. The new model is compared with finite element analysis and good agreement is also demonstrated with experimental data. A key aspect of the methodology is the provision of a more intuitive understanding of such device behavior. Accordingly, emphasis has been placed on the physical relationships and this is considered a major contribution of the work
On the basis of constructed model the abstract structural-parametric scheme of the converter is constructed and the influence of geometrical and physical converter parameters and external load on its dynamic characteristics is determined. The transfer functions of converter for electromechanical nanodisplacement piezoelectric drive are derived.
An electrical analog of a piezoelectric transducer has been built and used to demonstrate the generation and detection of acoustic waves and the electrical characteristics of a piezoelectricresonator. The circuit uses an artificial transmission line to represent the distributed‐constant mechanical properties of the transducer, and is therefore capable of reproducing the behavior of a transducer under both transient‐ and continuous‐wave conditions. The theory of the equivalent circuit of a transducer is first extended to facilitate interpretation of the physical processes of generation and detection. This is done by developing an “impulse sequence” that takes into account waves generated at both faces of a transducer, and the delay in time and reflections that they undergo in passing through the transducer. This analysis is used to discuss examples of waveforms obtained with the analog in the following situations (with various simulated combinations of backing and load impedance): (1) as a generator of acoustic waves when excited by an electrical signal in the form of (a) a short impulse, (b) a step, (c) short trains of sinusoidal oscillations of various lengths; (2) as a detector of acoustic waves when excited by an acoustic signal in the form of (a) a step, (b) a train of sinusoidal oscillations. In detection, the effect of terminating the transducer with high and low resistances is also demonstrated. Experiments concerning the continuous‐wave response of the analog are also described.
The use of the solution to the wave equation to construct a generalized structural parametric model of an electromagnetoelastic transducer to determine the effect of its geometry and physical parameters is discussed. High-precision electromechanical drives are operated under working loads ensuring elastic strains of the executive device. Piezoelectric transducers are characterized by high piezoelectric moduli and they are frequently used to produce nanoscale displacements. The solution of the wave equation supplemented with the corresponding electromagnetoelasticity equation and boundary conditions on the transducer's two working surfaces allows to construct a structural parametric model of an electromagnetoelastic transducer. The transfer functions of a piezoelectric transducer are derived from its generalized structural parametric model and are obtained as the ratio of the Laplace transform of the transducer face displacement to the Laplace transform of the input electric parameter.
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