ArticleNo Access

PULL-IN STABILITY OF A FRACTAL MEMS SYSTEM AND ITS PULL-IN PLATEAU

School of Science, Xi’an University of Architecture and Technology, Xi’an, P. R. China

School of Mathematics and Information Science, Henan Polytechnic University, Jiaozuo, P. R. China

National Engineering Laboratory for Modern Silk, College of Textile and Clothing Engineering, Soochow University, Suzhou, P. R. China

E-mail Address: Hejihuan@suda.edu.cn

Corresponding authors.

Search for more papers by this author

QIAN YANG

School of Science, Xi’an University of Architecture and Technology, Xi’an, P. R. China

Search for more papers by this author

CHUN-HUI HE

School of Mathematics, China University of Mining and Technology, Xuzhou 221116, Jiangsu, P. R. China

E-mail Address: Mathew_He@yahoo.com

Corresponding authors.

Search for more papers by this author

HAI-BIN LI

School of Science, Inner Mongolia University of Technology, Hohhot 010051, P. R. China

Search for more papers by this author

, and

EERDUN BUHE

School of Mathematics and Big Data, Hohhot University for Nationalities, Hohhot, P. R. China

Search for more papers by this author

https://doi.org/10.1142/S0218348X22501857Cited by:26 (Source: Crossref)

Abstract

The pull-in instability is the inherent property of a micro-electromechanical system (MEMS) when the voltage is larger than its threshold value. Recently, a fractal MEMS system was proposed to overcome the pull-in instability with great success, and it has opened a total new path for the so-called pull-in stability. This paper suggests a pull-in plateau, a novel concept for qualifying the pull-in stability. The plateau’s basic properties are elucidated, and the effect of the fractal dimensions on the plateau width is elucidated, and the paper concludes that there exists a critical condition for an ever pull-in stability when both the acceleration and the speed of the system equal zero.

Keywords:

References

1. X. S. Zhang, K. Kwon, J. Henriksson, J. H. Luo and M. C. Wu, A large-scale microelectromechanical-systems-based silicon photonics LiDAR, Nature 603(7900) (2022) 253–258. Crossref, Web of Science, Google Scholar
2. S. H. Baek et al., Giant piezoelectricity on Si for hyperactive MEMS, Science 334(6058) (2011) 958–961. Crossref, Web of Science, Google Scholar
3. J. M. Rothberg et al., Ultrasound-on-chip platform for medical imaging, analysis, and collective intelligence, Proc. Natl. Acad. Sci. USA 118(27) (2021) e2019339118. Crossref, Web of Science, Google Scholar
4. J. W. Judy, Microelectromechanical systems (MEMS): Fabrication, design and applications, Smart Mater. Struct. 10(6) (2001) 1115–1134. Crossref, Web of Science, Google Scholar
5. X. S. Liu, L. J. Zhang and M. J. Zhang, Studies on pull-in instability of an electrostatic MEMS actuator: Dynamical system approach, J. Appl. Anal. 12(2) (2022) 850–861. Google Scholar
6. H. M. Sedighi, M. Keivani and M. Abadyan, Modified continuum model for stability analysis of asymmetric FGM double-sided NEMS: Corrections due to finite conductivity, surface energy and nonlocal effect, Compos. B, Eng. 83 (2015) 117–133. Crossref, Web of Science, Google Scholar
7. P. Skrzypacz, S. Kadyrov, D. Nurakhmetov and D. M. Wei, Analysis of dynamic pull-in voltage of a graphene MEMS model, Nonlinear Anal., Real World Appl. 45 (2019) 581–589. Crossref, Web of Science, Google Scholar
8. P. Skrzypacz, D. M. Wei, D. Nurakhmetov, E. G. Kostsov, A. A. Sokolov, M. Begzhigitov and G. Ellis, Analysis of dynamic pull-in voltage and response time for a micro-electro-mechanical oscillator made of power-law materials, Nonlinear Dyn. 105(1) (2021) 227–240. Crossref, Web of Science, Google Scholar
9. Y. H. Cheng, K. C. Hung, S. H. Wang and J. J. Zeng, Upper and lower bounds for the pull-in voltage and the pull-in distance for a generalized MEMS problem, Math. Biosci. Eng. 19(7) (2022) 6814–6840. Crossref, Web of Science, Google Scholar
10. K. G. Sravani, K. S. Rao and K. Guha, New pull-in voltage modelling of step structure RF MEMS switch, Microelectron. J. 117 (2021) 105264. Crossref, Web of Science, Google Scholar
11. A. S. Havreland and E. V. Thomsen, Analytical deflection profiles and pull-in voltage calculations of prestressed electrostatic actuated MEMS structures, J. Microelectromech. Syst. 30(4) (2021) 659–667. Crossref, Web of Science, Google Scholar
12. H.-F. Liu, Z.-C. Luo, Z.-K. Hu, S.-Q. Yang, L.-C. Tu, Z.-B. Zhou and M. Kraft, A review of high-performance MEMS sensors for resource exploration and geophysical applications, Pet. Sci. (2022), https://doi.org/10.1016/j.petsci.2022.06.005. Web of Science, Google Scholar
13. M. Aliasghary, H. Mobki and H. M. Ouakd, Pull-in phenomenon in the electrostatically micro-switch suspended between two conductive plates using the artificial neural network, J. Appl. Comput. Mech. 8(4) (2022) 1222–1235. Web of Science, Google Scholar
14. V. P. Dragunov, D. I. Ostertak, D. E. Kiselev and E. V. Dragunova, Impact-enhanced electrostatic vibration energy harvester, J. Appl. Comput. Mech. 8(2) (2022) 671–683. Web of Science, Google Scholar
15. D. Tian and C. H. He, A fractal micro-electromechanical system and its pull-in stability, J. Low Freq. Noise Vib. Act. Control 40(3) (2021) 1380–1386. Crossref, Web of Science, Google Scholar
16. C. H. He, A variational principle for a fractal nano/microelectromechanical (N/MEMS) system, Int. J. Numer. Methods Heat Fluid Flow (2022), https://doi.org/10.1108/HFF-03-2022-0191. Web of Science, Google Scholar
17. J. H. He, N. Qie, C. H. He and K. Gepreel, Fast identification of the pull-in voltage of a nano/micro-electromechanical system, J. Low Freq. Noise Vib. Act. Control 41(2) (2022) 566–571. Crossref, Web of Science, Google Scholar
18. A. H. Nayfeh and D. T. Mook, Nonlinear Oscillations (John Wiley, New York, 1995). Crossref, Google Scholar
19. S. Q. Wang, A variational approach to nonlinear two-point boundary value problems, Comput. Math. Appl. 58(11) (2009) 2452–2455. Crossref, Web of Science, Google Scholar
20. Y. Tian and G. Q. Feng, A short review on approximate analytical methods for non-linear problems, Therm. Sci. 26(3B) (2022) 2607–2618. Crossref, Web of Science, Google Scholar
21. X. Y. Liu, Y. P. Liu and Z. W. Wu, Optimization of a fractal electrode-level charge transport model, Therm. Sci. 25(3B) (2021) 2213–2220. Crossref, Web of Science, Google Scholar
22. X. Y. Liu, Y. P. Liu and Z. W. Wu, Variational principle for one-dimensional inviscid flow, Therm. Sci. 26(3B) (2022) 2465–2469. Crossref, Web of Science, Google Scholar
23. Y. N. Zhang, D. Tian and J. Pang, A fast estimation of the frequency property of the microelectromechanical system oscillator, J. Low Freq. Noise Vib. Act. Control 41(1) (2021) 160–166. Crossref, Web of Science, Google Scholar
24. H. M. Sedighi, F. Daneshmand and M. Abadyane, Modified model for instability analysis of symmetric FGM double-sided nano-bridge: Corrections due to surface layer, finite conductivity and size effect, Compos. Struct. 132 (2015) 545–557. Crossref, Web of Science, Google Scholar
25. H. M. Sedighi, F. Daneshmand and M. Abadyane, Dynamic instability analysis of electrostatic functionally graded doubly-clamped nano-actuators, Compos. Struct. 124 (2015) 55–64. Crossref, Web of Science, Google Scholar
26. H. M. Sedighi, F. Daneshmand and M. Abadyane, Modeling the effects of material properties on the pull-in instability of nonlocal functionally graded nano-actuators, Z. Angew. Math. Mech. 96(3) (2016) 385–400. Crossref, Web of Science, Google Scholar
27. H. M. Sedighi and K. H. Shirazi, Dynamic pull-in instability of double-sided actuated nano-torsional switches, Acta Mech. Solida Sin. 28(1) (2015) 91–101. Crossref, Web of Science, Google Scholar
28. H. M. Ouakad and H. M. Sedighi, Static response and free vibration of MEMS arches assuming out-of-plane actuation pattern, Int. J. Nonlinear Mech. 110 (2019) 44–57. Crossref, Web of Science, Google Scholar
29. S. Zhang, S. Luo, S. He and H. M. Ouakad, Analog circuit implementation and adaptive neural backstepping control of a network of four Duffing-type MEMS resonators with mechanical and electrostatic coupling, Chaos Solitons Fractals 162 (2022) 112534. Crossref, Web of Science, Google Scholar
30. K. J. Wang, A fast insight into the nonlinear oscillation of nano-electro mechanical resonators considering the size effect and the van der Waals force, Europhys. Lett. 139(2) (2021) 23001, https://doi.org/10.1209/0295-5075/ac3cd4. Crossref, Google Scholar
31. K. J. Wang and G. D. Wang, Study on the nonlinear vibration of embedded carbon nanotube via the Hamiltonian-based method, J. Low Freq. Noise Vib. Act. Control 41(1) (2022) 112–117. Crossref, Web of Science, Google Scholar
32. H. J. Ma, Simplified Hamiltonian-based frequency-amplitude formulation for nonlinear vibration system, Facta Univ. Ser. Mech. Eng. 20(2) (2022) 445–455, https://doi.org/10.22190/FUME220420023M. Web of Science, Google Scholar
33. K. J. Wang and H. W. Zhu, Periodic wave solution of the Kundu-Mukherjee-Naskar equation in birefringent fibers via the Hamiltonian-based algorithm, Europhys. Lett. (2021), https://doi.org/10.1209/0295-5075/ac3d6b. Google Scholar
34. A. M. Chen, T. J. Miao, Z. Li, H. J. Zhang, L. J. Jiang, J. F. Liu, C. B. Yan and B. M. Yu, Fractal Monte Carlo simulations of the effective permeability for a fracture network, Fractals 30(4) (2022) 2250074. Link, Web of Science, Google Scholar
35. J. S. Wu, C. Y. Zhang, B. M. Yu, S. X. Yin, M. Xing, X. X. Chen, H. Q. Lian and S. H. Yi, Fractal characteristics of low-permeability sandstone reservoirs, Fractals 30(4) (2022) 2250075. Link, Web of Science, Google Scholar
36. D. Y. Ye, G. N. Liu, B. M. Yu, Z. Q. Zhou, C. L. Gao and F. Gao, Study on microstructural evolution of rock fractures under multi-field interactions, Fractals 30(3) (2022) 2250058. Link, Web of Science, Google Scholar
37. G. N. Liu, Y. H. Hu, B. M. Yu, F. Gao, F. T. Yue and T. Gao, A multi-field coupled seepage model for coal seam with fractures of power law length distributions, Fractals 29(6) (2021) 2150140. Link, Web of Science, Google Scholar
38. T. J. Miao, A. M. Chen, Y. Xu, S. J. Cheng, L. W. Zhang, C. B. Yan and B. M. Yu, Permeability models for two-phase flow in fractal porous-fracture media with the transfer of fluids from porous matrix to fracture, Fractals 29(6) (2021) 2150148. Link, Web of Science, Google Scholar
39. X. J. Li, D. Wang and T. Saeed, Multi-scale numerical approach to the polymer filling process in the weld line region, Facta Univ. Ser., Mech. Eng. 20(2) (2022) 363–380, https://doi.org/10.22190/FUME220131021L. Crossref, Web of Science, Google Scholar
40. X. J. Li, Z. Liu and J. H. He, A fractal two-phase flow model for the fiber motion in a polymer filling process, Fractals 28(5) (2020) 2050093. Link, Web of Science, Google Scholar
41. B. Q. Xiao, Q. W. Huang, B. M. Yu, G. B. Long and H. X. Chen, A fractal model for predicting oxygen effective diffusivity of porous media with rough surfaces under dry and wet conditions, Fractals 29(3) (2021) 2150076. Link, Web of Science, Google Scholar
42. J. H. He and M. Y. Qian, A fractal approach to the diffusion process of red ink in a saline water, Therm. Sci. 26(3B) (2022) 2447–2451. Crossref, Web of Science, Google Scholar
43. L. Lin and Y. Qiao, Fractal diffusion-reaction model for a porous electrode, Therm. Sci. 25(2B) (2021) 1305–1311. Crossref, Web of Science, Google Scholar
44. D. D. Dai, T. T. Ban, Y. L. Wang and W. Zhang, The piecewise reproducing kernel method for the time variable fractional order advection-reaction-diffusion equations, Therm. Sci. 25(2B) (2021) 1261–1268. Crossref, Web of Science, Google Scholar
45. Y. T. Zuo and H. J. Liu, Fractal approach to mechanical and electrical properties of graphene/SiC composites, Facta Univ. Ser. Mech. Eng. 19(2) (2021) 271–284. Web of Science, Google Scholar
46. Y. T. Zuo, Effect of sic particles on viscosity of 3-D print paste a fractal rheological model and experimental verification, Therm. Sci. 25(3) (2021) 2405–2409. Crossref, Web of Science, Google Scholar
47. H. J. Ma, Fractal variational principle for an optimal control problem, J. Low Freq. Noise Vib. Act. Control (2022) 14613484221104647, https://doi.org/10.1177/14613484221104647. Crossref, Web of Science, Google Scholar
48. K. J. Wang, Generalized variational principle and periodic wave solution to the modified equal width-Burgers equation in nonlinear dispersion media, Phys. Lett. A 419 (2021) 127723. Crossref, Web of Science, Google Scholar
49. K. L. Wang, Exact solitary wave solution for fractal shallow water wave model by He’s variational method, Mod. Phys. Lett. B 36(7) (2022) 2150602. Link, Web of Science, Google Scholar
50. K. L. Wang, New variational theory for coupled nonlinear fractal Schrodinger system, Int. J. Numer. Methods Heat Fluid Flow 32(2) (2022) 589–597. Crossref, Web of Science, Google Scholar
51. K. L. Wang and C. F. Wei, A powerful and simple frequency formula to nonlinear fractal oscillators, J. Low Freq. Noise Vib. Act. Control 40(3) (2021) 1373–1379. Crossref, Web of Science, Google Scholar
52. Y. Shen and Y. O. El-Dib, A periodic solution of the fractional sine-Gordon equation arising in architectural engineering, J. Low Freq. Noise Vib. Act. Control 40(2) (2021) 683–691. Crossref, Web of Science, Google Scholar
53. G. Q. Feng, He’s frequency formula to fractal undamped Duffing equation, J. Low Freq. Noise Vib. Act. Control 40(4) (2021) 1671–1676. Crossref, Web of Science, Google Scholar
54. J. H. He and Y. O. El-Dib, A tutorial introduction to the two-scale fractal calculus and its application to the fractal Zhiber-Shabat oscillator, Fractals 29(8) (2021) 2150268. Link, Web of Science, Google Scholar
55. A. Elías-Zúñiga, L. M. Palacios-Pineda, D. Olvera-Trejo and O. Martínez-Romero, Recent strategy to study fractal-order viscoelastic polymer materials using an ancient Chinese algorithm and He’s formulation, J. Low Freq. Noise Vib. Act. Control 41(3) (2022) 842–851. Crossref, Web of Science, Google Scholar
56. S. Scott and Z. Ali, Fabrication methods for microfluidic devices: An overview, Micromachines 12(3) (2021) 319, https://doi.org/10.3390/mi12030319. Crossref, Web of Science, Google Scholar
57. Y. Zuo and H. Liu, Instability of the printing jet during the three-dimensional-printing process. J. Low Freq. Noise Vib. Act. Control 40(4) (2021) 1795–1803, https://doi.org/10.1177/14613484211021.3Z. Crossref, Web of Science, Google Scholar