Abstract
In this work we determined the mathematical description of multilayer actuator for nano biomedicine. The displacements of the multilayer actuator are received from its mathematical description.
Keywords: Multilayer actuator; Mathematical description
Introduction
For mathematical description of the multilayer actuator we used the equation of the relative deformation, the mechanical fourterminal scheme and the boundary conditions [1-30].
Mathematical Description Actuator
The equation Si relative deformation [7-11] has the following form
![](../images/biomedres-openaccess-journal-bjstr.ID.003795.E001.png)
where mi are parameters
We received the equation the causes force in the form
![](../images/biomedres-openaccess-journal-bjstr.ID.003795.E003.png)
where S0 is the area actuator.
For the mechanical four-terminal scheme [23] actuator we have the matrix in the form.
![](../images/biomedres-openaccess-journal-bjstr.ID.003795.E004.png)
where l, γ are length and coefficient.
The mathematical description and diagram on Figure 1 of the multilayer actuator we obtained as the system of the equations in the form
![](../images/biomedres-openaccess-journal-bjstr.ID.003795.E005.png)
![](../images/biomedres-openaccess-journal-bjstr.ID.003795.E006.png)
![](../images/biomedres-openaccess-journal-bjstr.ID.003795.E007.png)
where are the Laplace transforms of the
displacements and forces for the faces.
From the mathematical description of the multilayer actuator we have the matrix equation
![](../images/biomedres-openaccess-journal-bjstr.ID.003795.E009.png)
where are the matrices.
For time for the inertial load on the two faces of
piezoactuator we obtain the expressions of its displacements
![](../images/biomedres-openaccess-journal-bjstr.ID.003795.E012.png)
where n, U are the number piezolayers and the voltage.
At kg we
obtained the displacements
= 160 nm.
Conclusion
We determined the mathematical description of the multilayer actuator for nano biomedicine. We obtained the displacements of the multilayer actuator from its mathematical description.
References
- Schultz J, Ueda J, Asada H (2017) Cellular Actuators. Butterworth-Heinemann Publisher, Oxford pp. 382.
- Afonin SM (2006) Absolute stability conditions for a system controlling the deformation of an elecromagnetoelastic transduser. Doklady mathematics 74(3): 943-948.
- Zhou S, Yao Z (2014) Design and optimization of a modal-independent linear ultrasonic motor. IEEE transaction on ultrasonics, ferroelectrics, and frequency control 61(3): 535-546.
- Przybylski J (2015) Static and dynamic analysis of a flextensional transducer with an axial piezoelectric actuation, Engineering structures 84: 140-151.
- Ueda J, Secord T, Asada HH (2010) Large effective-strain piezoelectric actuators using nested cellular architecture with exponential strain amplification mechanisms. IEEE/ASME Transactions on Mechatronics 15(5): 770-782.
- Karpelson M, Wei GY, Wood RJ (2012) Driving high voltage piezoelectric actuators in microrobotic applications. Sensors and Actuators A: Physical 176: 78-89.
- Afonin SM (2015) Block diagrams of a multilayer piezoelectric motor for nano- and microdisplacements based on the transverse piezoeffect. Journal of computer and systems sciences international 54(3): 424-439.
- Afonin SM (2008) Structural parametric model of a piezoelectric nanodisplacement transduser. Doklady physics 53(3): 137-143.
- Afonin SM (2006) Solution of the wave equation for the control of an elecromagnetoelastic transduser. Doklady mathematics 73(2): 307-313.
- Cady WG (1946) Piezoelectricity: An introduction to the theory and applications of electromechancial phenomena in crystals. McGraw-Hill Book Company, New York, USA, pp. 806.
- Mason W (1964) Physical Acoustics: Principles and Methods. Vol.1. Part A. Methods and Devices. Academic Press, New York, USA, pp. 515.
- Zwillinger D (1989) Handbook of Differential Equations. Academic Press, Boston, USA, pp. 673.
- Afonin SM (2015) Structural-parametric model and transfer functions of electroelastic actuator for nano- and microdisplacement. Chapter 9 in Piezoelectrics and Nanomaterials: Fundamentals, Developments and Applications. Ed. Parinov IA. Nova Science, New York, USA, pp. 225-242.
- Afonin SM (2017) A structural-parametric model of electroelastic actuator for nano- and microdisplacement of mechatronic system. Chapter 8 in Advances in nanotechnology. Volume 19. Eds. Bartul Z, Trenor J, Nova Science, New York, USA, pp. 259-284.
- Afonin SM (2012) Nano- and micro-scale piezomotors. Russian engineering research 32(7-8): 519-522.
- Afonin SM (2007) Elastic compliances and mechanical and adjusting characteristics of composite piezoelectric transducers. Mechanics of solids 42(1): 43-49.
- Afonin SM (2014) Stability of strain control systems of nano-and microdisplacement piezotransducers. Mechanics of solids 49(2): 196-207.
- Afonin SM (2017) Structural-parametric model electromagnetoelastic actuator nanodisplacement for mechatronics. International Journal of Physics 5(1): 9-15.
- Afonin SM (2017) Structural-parametric model of piezoactuator nano- and microdisplacement for nanoscience. AASCIT Journal of Nanoscience 3(3): 12-18.
- Afonin SM (2016) Solution wave equation and parametric structural schematic diagrams of electromagnetoelastic actuators nano- and microdisplacement. International Journal of Mathematical Analysis and Applications 3(4): 31-38.
- Afonin SM (2018) Structural-parametric model of electromagnetoelastic actuator for nanomechanics. Actuators 7(1): 1-9.
- Afonin SM (2016) Structural-parametric models and transfer functions of electromagnetoelastic actuators nano- and microdisplacement for mechatronic systems. International Journal of Theoretical and Applied Mathematics 2(2): 52-59.
- Afonin SM (2017) Parametric block diagrams of a multi-layer piezoelectric transducer of nano- and microdisplacements under transverse piezoelectric effect. Mechanics of Solids 52(1): 81-94.
- Afonin SM (2018) Multilayer electromagnetoelastic actuator for robotics systems of nanotechnology, Proceedings of the 2018 IEEE Conference EIConRus: 1698-1701.
- Afonin SM (2018) Electromagnetoelastic nano- and microactuators for mechatronic systems. Russian Engineering Research 38(12): 938-944.
- Afonin SM (2018) Structural-parametric model of electro elastic actuator for nanotechnology and biotechnology. Journal of Pharmacy and Pharmaceutics 5(1):8-12.
- Afonin SM (2018) Electromagnetoelastic actuator for nanomechanics. Global Journal of Research in Engineering. A: Mechanical and Mechanics Engineering 18(2): 19-23.
- Afonin SM (2019) Actuator for nano biomedical research. Biomedical Journal of Scientific and Technical Research 19(3): 14300-14302.
- Afonin SM (2019) Absolute stability of control system with electro magneto elastic actuator for nanobiomedicine. Biomedical Journal of Scientific and Technical Research 21(4): 16027-16030.
- Bhushan B (2004) Springer Handbook of Nanotechnology. Ed. by Springer, Berlin, New York, USA, pp. 1222.