带调谐的梳状指尖MEMS模型中周期解的存在性及稳定性研究
Study on the Existence and Stability of Periodic Solutions in a Comb-Drive Finger MEMS with Tuning Model
摘要: 随着科技的发展，MEMS技术在军民应用中越来越广泛。其中，梳齿驱动器是MEMS中最重要的一种器件。本文旨在介绍带调谐的梳状指尖MEMS模型的存在性及稳定性的研究方法。
Abstract: With the development of technology, MEMS technology is becoming increasingly widespread in military and civilian applications. Among them, comb drive is the most important device in MEMS. This article aims to introduce the research methods for the existence and stability of a comb-drive finger MEMS model with tuning.
文章引用：姬瑞瑶. 带调谐的梳状指尖MEMS模型中周期解的存在性及稳定性研究[J]. 应用数学进展, 2026, 15(4): 371-376. https://doi.org/10.12677/aam.2026.154165

参考文献

[1] Yazdi, N., Mason, A., Najafi, K. and Wise, K.D. (2000) A Generic Interface Chip for Capacitive Sensors in Low-Power Multi-Parameter Microsystems. Sensors and Actuators A: Physical, 84, 351-361. [Google Scholar] [CrossRef] 
[2] Adrega, T., Chu, V. and Conde, J.P. (2006) Electrostatically Actuated Resonance of Amorphous Silicon Microresonators in Water. Applied Physics Letters, 89, Article 143109. [Google Scholar] [CrossRef] 
[3] Bashir, R. (2004) BioMEMS: State-of-the-Art in Detection, Opportunities and Prospects. Advanced Drug Delivery Reviews, 56, 1565-1586. [Google Scholar] [CrossRef] [PubMed]
[4] 赵晨茜, 张大伟, 王远瑞, 等. 基于微机电系统的智能传感器在全膝关节置换术中的应用及现状[J]. 骨科, 2024, 15(6): 563-567.
[5] Judy, J.W. (2001) Microelectromechanical Systems (MEMS): Fabrication, Design and Applications. Smart Materials and Structures, 10, 1115-1134. [Google Scholar] [CrossRef] 
[6] Chircov, C. and Grumezescu, A.M. (2022) Microelectromechanical Systems (MEMS) for Biomedical Applications. Micromachines, 13, Article No. 164. [Google Scholar] [CrossRef] [PubMed]
[7] Wu, M.C., Solgaard, O. and Ford, J.E. (2006) Optical MEMS for Lightwave Communication. Journal of Lightwave Technology, 24, 4433-4454. [Google Scholar] [CrossRef] 
[8] Schopp, J. and McNamara, S. (2024) Passive Communication for Low Power Distributed Sensors Using MEMS Optical Cavities. Journal of Micromechanics and Microengineering, 34, Article ID: 035011. [Google Scholar] [CrossRef] 
[9] Hou, Y., Jiao, R. and Yu, H. (2021) MEMS Based Geophones and Seismometers. Sensors and Actuators A: Physical, 318, Article ID: 112498. [Google Scholar] [CrossRef] 
[10] Ekinci, K.L. and Roukes, M.L. (2005) Nanoelectromechanical Systems. Review of Scientific Instruments, 76, Article ID: 061101. [Google Scholar] [CrossRef] 
[11] Nadim, M. (2000) An Introduction to Microelectromechanical System Engineering. Norwood, Artech House, 3-6.
[12] Marek, J. (2011) Automotive MEMS Sensors-Trends and Application. Proceeding of 2011 International Symposium on VLSI Technology, Systems and Applications, Hsinchu, 1-2.
[13] 李德胜. MEMS技术及其应用[M]. 第2版. 哈尔滨: 哈尔滨工业大学出版社, 2003: 35-45.
[14] Fan, L., Tai, Y. and Muller, R.S. (1989) Ic-Processed Electrostatic Micromotors. Sensors and Actuators, 20, 41-47. [Google Scholar] [CrossRef] 
[15] 李佰洲, 韩建鑫, 黄仪, 等.考虑边缘效应的静电驱动MEMS振子非线性振动定性研究[J]. 振动与冲击, 2025, 44(1): 10-19.
[16] Jung, Y., Jo, E. and Kim, J. (2025) Electrostatically Driven Two-Axis Microelectromechanical Magnetometer with Eccentric Resonator and Electromagnetic Inductor. Sensors and Actuators A: Physical, 387, Article ID: 116378. [Google Scholar] [CrossRef] 
[17] Lai, S.K., Yang, X., Wang, C. and Liu, W.J. (2019) An Analytical Study for Nonlinear Free and Forced Vibration of Electrostatically Actuated MEMS Resonators. International Journal of Structural Stability and Dynamics, 19, Article ID: 1950072. [Google Scholar] [CrossRef] 
[18] 张录. 压电驱动RF MEMS开关的设计及制备[D]: [硕士学位论文]. 大连: 大连理工大学, 2024.
[19] 董林玺, 焦继伟, 颜海霞, 等. 新型磁驱动增大检测电容的高精度MEMS惯性传感器研究[J]. 电子学报, 2010, 38(5): 1053-1057.
[20] 赵蕊. 两类梳齿驱动器模型中周期解的存在性及稳定性研究[J]. 应用数学进展, 2025, 14(4): 266-272.
[21] Núñez, D., Larreal, O. and Murcia, L. (2021) Odd Periodic Oscillations in Comb-Drive Finger Actuators. Nonlinear Analysis: Real World Applications, 61, Article ID: 103347. [Google Scholar] [CrossRef] 
[22] Lerreal, O., Murcia, L. and Núñez, D. (2022) Odd Periodic Oscillations for COMB-Drive Fingers MEMS with Cubic Stiffness. Journal of Mathematical Control Science and Applications, 8, 185-197.
[23] Nuñez, D., Perdomo, O. and Rivera, A. (2019) On the Stability of Periodic Solutions with Defined Sign in MEMS via Lower and Upper Solutions. Nonlinear Analysis: Real World Applications, 46, 195-218. [Google Scholar] [CrossRef] 
[24] Gutierrez, A., Núñez, D. and Rivera, A. (2017) Effects of Voltage Change on the Dynamics in a Comb-Drive Finger of an Electrostatic Actuator. International Journal of Non-Linear Mechanics, 95, 224-232. [Google Scholar] [CrossRef] 
[25] Núñez, D. and Murcia, L. (2023) On a Bi-Stability Regime and the Existence of Odd Subharmonics in a Comb-Drive MEMS Model with Cubic Stiffness. Nonlinear Analysis: Real World Applications, 74, Article ID: 103938. [Google Scholar] [CrossRef] 
[26] DeMartini, B., Moehlis, J., Turner, K., Rhoads, J., Shaw, S. and Zhang, W. (2005) Modeling of Parametrically Excited Microelectromechanical Oscillator Dynamics with Application to Filtering. Sensors, 168, 180-199.
[27] DeMartini, B.E., Butterfield, H.E., Moehlis, J. and Turner, K.L. (2007) Chaos for a Microelectromechanical Oscillator Governed by the Nonlinear Mathieu Equation. Journal of Microelectromechanical Systems, 16, 1314-1323. [Google Scholar] [CrossRef] 
[28] Zhang, W., Baskaran, R. and Turner, K. (2003) Tuning the Dynamic Behavior of Parametric Resonance in a Micromechanical Oscillator. Applied Physics Letters, 82, 130-132. [Google Scholar] [CrossRef] 
[29] Adams, S.G., Bertsch, F.M., Shaw, K.A. and MacDonald, N.C. (1998) Independent Tuning of Linear and Nonlinear Stiffness Coefficients [Actuators]. Journal of Microelectromechanical Systems, 7, 172-180. [Google Scholar] [CrossRef] 
[30] Rhoads, J.F., Shaw, S.W., Turner, K.L. and Baskaran, R. (2005) Tunable Microelectromechanical Filters That Exploit Parametric Resonance. Journal of Vibration and Acoustics, 127, 423-430. [Google Scholar] [CrossRef] 
[31] Rhoads, J.F., Shaw, S.W., Turner, K.L., Moehlis, J., DeMartini, B.E. and Zhang, W. (2006) Generalized Parametric Resonance in Electrostatically Actuated Microelectromechanical Oscillators. Journal of Sound and Vibration, 296, 797-829. [Google Scholar] [CrossRef] 
[32] Shaw, S.W., Turner, K.L., Rhoads, J.F. and Baskaran, R. (2005) Parametrically Excited MEMS-Based Filters. In: Rega, G. and Vestroni, F., Eds., IUTAM Symposium on Chaotic Dynamics and Control of Systems and Processes in Mechanics, Springer, 137-146. [Google Scholar] [CrossRef] 
[33] Wang, Y.C., Adams, S.G., Thorp, J.S., MacDonald, N., Hartwell, P. and Bertsch, F. (1998) Chaos in MEMS, Parameter Estimation and Its Potential Application. IEEE Transactions on Circuits and Systems I: Fundamental Theory and Applications, 45, 1013-1020.
[34] Zhang, W., Baskaran, R. and Turner, K.L. (2002) Effect of Cubic Nonlinearity on Auto-Parametrically Amplified Resonant MEMS Mass Sensor. Sensors and Actuators A: Physical, 102, 139-150. [Google Scholar] [CrossRef] 
[35] Gasull, A., Guillamon, A., Mañosa, V. and Mañosas, F. (1997) The Period Function for Hamiltonian Systems with Homogeneous Nonlinearities. Journal of Differential Equations, 139, 237-260. [Google Scholar] [CrossRef] 
[36] Misquero, M. (2018) Resonance Tongues in the Linear Sitnikov Equation. Celestial Mechanics and Dynamical Astronomy, 130, 1-25. [Google Scholar] [CrossRef] 
[37] Cen, X., Liu, C. and Zhang, M. (2021) A Proof for a Stability Conjecture on Symmetric Periodic Solutions of the Elliptic Sitnikov Problem. SIAM Journal on Applied Dynamical Systems, 20, 941-952. [Google Scholar] [CrossRef] 
[38] Cen, X., Cheng, X., Huang, Z. and Zhang, M. (2020) On the Stability of Symmetric Periodic Orbits of the Elliptic Sitnikov Problem. SIAM Journal on Applied Dynamical Systems, 19, 1271-1290. [Google Scholar] [CrossRef] 
[39] Ortega, R. (2016) Symmetric Periodic Solutions in the Sitnikov Problem. Archiv der Mathematik, 107, 405-412. [Google Scholar] [CrossRef] 

为你推荐