Construction of Structural Diagrams a Piezo Drive for Nanobiology

Abstract

A piezo drive is used scanning microscopy, adaptive optics, delivery DNA for nanobiology. In construction structural diagrams a piezo drive for nanobiology are using the equation of reverse piezo effect and the linear ordinary second-order differential equation. The structural diagrams a piezo drive at distributed and lumped parameters are derived for nanobiology.

Keywords:Structural diagram, Piezo drive, Nanobiology

Introduction

A piezo drive is used for actuation of systemss for engine for nano displacement and delivery DNA in nanobiology. This piezo drive is used to actuate or control nano mechanisms and convert electrical energy into mechanical energy at the nanometric accuracy in laser systems, atomic force microscopes for nano displacement and compensation of vibration [1-10]. By method mathematical physics the structural diagram of a piezo drive is determined for nanobiology. The structural diagrams of a piezo drive are determined the transformation of electrical energy into mechanical energy in difference from Cady’s and Mason’s equivalent circuits [8-35]. The structural diagram of a piezo drive is obtained with using the equation of reverse piezo effect and the linear ordinary second-order differential equation [36- 64].

Block diagram

By method mathematical physics the structural diagram of a piezo drive is calculated for nanobiology. The method mathematical physics is used to construct the structural diagram of a piezo drive from the equation of reverse piezo effect and its ordinary differential equation for nanobiology. We use for the structural diagram of a piezo drive the equation of reverse piezo effect and the second-order linear ordinary differential equation. The equation of reverse piezo effect [1-19] for the relative deformation has the form

here the i S – relative deformation the elastic compliances, J T -the mechanical strength, the piezoelectric costant, the control parameter, E electlic field strength, Dthe electric induction, γ - the coefficient of wave propagation, i = 1, 2, … , 6; j = 1, 2, … , 6; m = 1, 2, 3.

The differential equation is derived

with solution

Here Ξ(x, p), x, p are the Laplace transform of the displacement, the coordinate, operator.

In solution the coefficients C and B are established

The solution is obtained [19-61]

The equations for the forces at faces are established

The equations for mechanical stresses at faces are derived

The structural diagram at distributed parameters is established on Figure 1.

Figure 1:Structural diagram piezo drive at distributed parameters.

Discussion

The static displacements of a longitudinal piezo drive are determined at voltage control in the form

here m, M₁ , M₂ are the masses of the piezo drive and the loads.

For the PZT drive at m→0 at U=75 V, d₃₃ = 0.4 nm/ V , M₁ = 0.5 kg and M₂ = 2 Kgwe obtain the parameters , , .

The electromechanical coupling coefficient K_mi is established for a piezo drive at voltage control

Here the permitivity.

Then the negative feedback for block diagram at distributed parameters and voltage control of the piezo drive on (Figure 2) has the form

a =1, 2. (Figure 2)

At one rigidly fixed face the block diagram with lumped parameters at voltage control on (Figure 3) and at current control on (Figure 4) the structural diagrams are obtained (Figure 3).

Figure 2:Structural diagram piezo drive at distributed parameters.

Figure 3:Structural diagram piezo drive at distributed parameters.

Figure 4:Structural diagram piezo drive at distributed parameters.

In general the coefficient K_d is equal coefficient K_r for a piezo drive

here index ψ = E,D and for voltage control, Dfor current control (Figure 4).

Conclusion

The structural diagrams of a nano piezo drive are derived for nanobiology. The numerical parameters of the piezo drive are determined. The structural diagram \s of the piezo drive with the back electromotive force at distributed and lumped parameters are derived for nanobiology.

Acknowledgement

None.

Conflict of Interest

None.

References

1. Schultz J, Ueda J, Asada H (2017) Cellular Actuators. Butterworth-Heinemann Publisher: 382.
2. Afonin SM (2006) Absolute stability conditions for a system controlling the deformation of an elecromagnetoelastic transduser. Doklady Mathematics 74(3): 943-948.
3. Uchino K (1997) Piezoelectric actuator and ultrasonic motors. Boston, MA: Kluwer Academic Publisher: 350.
4. Afonin SM (2005) Generalized parametric structural model of a compound elecromagnetoelastic transduser. Doklady Physics 50(2): 77-82.
5. Afonin SM (2008) Structural parametric model of a piezoelectric nanodisplacement transducer. Doklady Physics 53(3): 137-143.
6. Afonin SM (2006) Solution of the wave equation for the control of an elecromagnetoelastic transduser. Doklady Mathematics 73(2): 307-313.
7. Afonin SM (2025) Erratum to: Solution of the wave equation for the control of an elecromagnetoelastic transduser. Doklady Mathematics.
8. Cady WG (1946) Piezoelectricity: An introduction to the theory and applications of electromechancial phenomena in crystals. McGraw-Hill Book Company: 806.
9. Mason W (1964) Physical Acoustics: Principles and Methods. Part A. Methods and Devices. Academic Press, New York 1: 515.
10. Zhao C, Li Z, Xu F, Zhang H, Sun F, et al. (2024) Design of a novel three-degree-of-freedom piezoelectric-driven micro-positioning platform with compact structure. Actuators 13(7): 248.
11. Zwillinger D (1989) Handbook of Differential Equations. Academic Press, Boston: 673.
12. Afonin SM (2006) A generalized structural-parametric model of an elecromagnetoelastic converter for nano- and micrometric movement control systems: III. Transformation parametric structural circuits of an elecromagnetoelastic converter for nano- and micrometric movement control systems. Journal of Computer and Systems Sciences International 45(2): 317-325.
13. Afonin SM (2006) Generalized structural-parametric model of an electromagnetoelastic converter for control systems of nano-and micrometric movements: IV. Investigation and calculation of characteristics of step-piezodrive of nano-and micrometric movements. Journal of Computer and Systems Sciences International 45(6): 1006-1013.
14. Afonin SM (2016) Decision wave equation and block diagram of electromagnetoelastic actuator nano- and microdisplacement for communications systems. International Journal of Information and Communication Sciences 1(2): 22-29.
15. 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: 225-242.
16. Afonin SM (2017) A structural-parametric model of electroelastic actuator for nano- and microdisplacement of mechatronic system. Chapter 8 in Advances in Nanotechnology 19: 259-284.
17. Afonin SM (2025) Block diagram of an electro elastic drive for nanobiomedicine. American Journal of Biomedical Science and Research 27(3): AJBSR.MS.ID.003556.
18. Afonin SM (2025) Structural scheme of electroelastic engine micro and nano displacement for applied bionics and biomechanics. MOJ Applied Bionics and Biomechanics 9(1): 1-4.
19. Afonin SM (2018) Electromagnetoelastic nano- and microactuators for mechatronic systems. Russian Engineering Research 38(12): 938-944.
20. Afonin SM (2012) Nano- and micro-scale piezomotors. Russian Engineering Research 32(7-8): 519-522.
21. Afonin SM (2007) Elastic compliances and mechanical and adjusting characteristics of composite piezoelectric transducers. Mechanics of Solids 42(1): 43-49.
22. Afonin SM (2014) Stability of strain control systems of nano-and microdisplacement piezotransducers. Mechanics of Solids 49(2): 196-207.
23. Afonin SM (2017) Structural-parametric model electromagnetoelastic actuator nanodisplacement for mechatronics devices of nanotechnology. International Journal of Physics 5(1): 9-15.
24. Afonin SM (2019) Structural-parametric model multilayer electromagnetoelastic actuator for nanomechatronics. International Journal of Physics 7(2): 50-57.
25. Afonin SM (2021) Calculation deformation of an engine for nano biomedical research. International Journal of Biomed Research 1(5): 1-4.
26. Afonin SM (2021) Precision engine for nanobiomedical research. Biomedical Research and Clinical Reviews 3(4): 1-5.
27. Afonin SM (2018) Structural-parametric model of electromagnetoelastic actuator for nanomechanics. Actuators 7(1): 6.
28. Afonin SM (2019) Structural-parametric model and diagram of a multilayer electromagnetoelastic actuator for nanomechanics. Actuators 8(3): 52.
29. 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.
30. Afonin SM (2010) Design static and dynamic characteristics of a piezoelectric nanomicrotransducers. Mechanics of Solids 45(1): 123-132.
31. Afonin SM (2018) Electromagnetoelastic Actuator for Nanomechanics. Global Journal of Research in Engineering: A Mechanical and Mechanics Engineering 18(2): 19-23.
32. Afonin SM (2018) Multilayer electromagnetoelastic actuator for robotics systems of nanotechnology. 2018 IEEE Conference EIConRus: 1698-1701.
33. Afonin SM (2018) A block diagram of electromagnetoelastic actuator nanodisplacement for communications systems. Transactions on Networks and Communications 6(3): 1-9.
34. Afonin SM (2019) Decision matrix equation and block diagram of multilayer electromagnetoelastic actuator micro and nanodisplacement for communications systems. Transactions on Networks and Communications 7(3): 11-21.
35. Afonin SM (2020) Condition absolute stability control system of electromagnetoelastic actuator for communication equipment. Transactions on Networks and Communications 8(1): 8-15.
36. Afonin SM (2020) A Block diagram of electromagnetoelastic actuator for control systems in nanoscience and nanotechnology. Transactions on Machine Learning and Artificial Intelligence 8(4): 23-33.
37. Afonin SM (2020) Optimal control of a multilayer electroelastic engine with a longitudinal piezoeffect for nanomechatronics systems. Applied System Innovation 3(4): 53.
38. Afonin SM (2021) Coded сontrol of a sectional electroelastic engine for nanomechatronics systems. Applied System Innovation 4(3): 47.
39. Afonin SM (2020) Structural scheme actuator for nano research. COJ Reviews and Research 2(5): 1-3.
40. Afonin SM (2018) Structural-parametric model electroelastic actuator nano- and microdisplacement of mechatronics systems for nanotechnology and ecology research. MOJ Ecology and Environmental Sciences 3(5): 306-
41. Afonin SM (2020) Deformation of electromagnetoelastic actuator for nano robotics system. International Robotics & Automation Journal 6(2): 84-86.
42. Afonin SM (2024) Correction of characteristics compound longitudinal piezodrive at elastic inertial load for nanorobotics research. International Robotics & Automation Journal 10(3): 103-106.
43. Afonin SM (2024) A multi-layer electro elastic drive for micro and nano robotics. International Robotics & Automation Journal 10(2): 73-76.
44. Afonin SM (2018) Electromagnetoelastic actuator for large telescopes. Aeronautics and Aerospace Open Access Journal 2(5): 270-272.
45. Afonin SM (2019) Condition absolute stability of control system with electro elastic actuator for nano bioengineering and microsurgery. Surgery & Case Studies Open Access Journal 3(3): 307-309.
46. Afonin SM (2019) Piezo actuators for nanomedicine research. MOJ Applied Bionics and Biomechanics 3(2): 56-57.
47. Afonin SM (2019) Frequency criterion absolute stability of electromagnetoelastic system for nano and micro displacement in biomechanics. MOJ Applied Bionics and Biomechanics 3(6): 137-140.
48. Afonin SM (2020) Multilayer piezo engine for nanomedicine research. MOJ Applied Bionics and Biomechanics 4(2): 30-31.
49. Afonin SM (2021) Structural scheme of electromagnetoelastic actuator for nano biomechanics. MOJ Applied Bionics and Biomechanics 5(2): 36-39.
50. Afonin SM (2024) Parallel and coded control of multi layered longitudinal piezo engine for nano biomedical research. MOJ Applied Bionics and Biomechanics 8(1): 62-65.
51. Afonin SM (2024) DAC electro elastic engine for nanomedicine. MOJ Applied Bionics and Biomechanics 8(1): 38-40.
52. Afonin SM (2020) Multilayer engine for microsurgery and nano biomedicine. Surgery & Case Studies Open Access Journal 4(4): 423-425.
53. Afonin SM (2019) A structural-parametric model of a multilayer electroelastic actuator for mechatronics and nanotechnology. Chapter 7 in Advances in Nanotechnology Eds Bartul Z, Trenor J, Nova Science, New York 22: 169-186.
54. Afonin SM (2020) Electroelastic digital-to-analog converter actuator nano and microdisplacement for nanotechnology. Chapter 6 in Advances in Nanotechnology Eds Bartul Z, Trenor J, Nova Science, New York 24: 205-218.
55. Afonin SM (2021) Characteristics of an electroelastic actuator nano- and microdisplacement for nanotechnology. Chapter 8 in Advances in Nanotechnology Eds Bartul Z, Trenor J, Nova Science, New York 25: 251-266.
56. Afonin SM (2022) An absolute stability of nanomechatronics system with electroelastic actuator. Chapter 9 in Advances in Nanotechnology Eds Bartul Z, Trenor J, Nova Science, New York 27: 183-198.
57. Afonin SM (2021) Rigidity of a multilayer piezoelectric actuator for the nano and micro range. Russian Engineering Research 41(4): 285-288.
58. Afonin SM (2024) Structural scheme of an electromagnetoelastic actuator for nanotechnology research. Chapter 45 in Physics and Mechanics of New Materials and Their Applications. PHENMA 2023. Springer Proceedings in Materials Eds Parinov IA, Chang SH, Putri EP, Springer, Cham 41: 486-501.
59. Afonin SM (2025) Structural model and scheme of a multilayer electromagnetoelastic actuator for nanotechnology. Chapter 45 in Physics and Mechanics of New Materials and Their Applications. PHENMA 2024. Springer Proceedings in Materials Eds Parinov IA, Chang SH, Sohani N, Gupta VK, Springer, Cham 3: 527-544.
60. Afonin SM (2025) Structural scheme of electroelastic engine micro and nano displacement for applied bionics and biomechanics. MOJ Applied Bionics and Biomechanics 9(1): 1-4.
61. Afonin SM (2025) Multilayer and sectional nano piezo engine for applied bionics and biomechanics. MOJ Applied Bionics and Biomechanics 9(1): 59-62.
62. Shevtsov SN, Soloviev AN, Parinov IA, Cherpakov AV, Chebanenko VA (2018) Piezoelectric Actuators and Generators for Energy Harvesting. Research and Development: 182.
63. Akpinar M, Uzun B, Yayli MO (2024) Dynamics of a piezoelectric restrained nanowire in an elactic matrix. Mechanics of Solids 59(5): 2936-2959.
64. Nalwa HS (2019) Encyclopedia of Nanoscience and Nanotechnology. USA: American Scientific Publishers 25.