Nonlinear Dynamic Analysis of Electrostatically Actuated Resonant MEMS Sensors Under Parametric Excitation

Electrostatically actuated resonant microelectromechanical systems (MEMS) sensors have gotten significant attention due to their geometric simplicity and broad applicability. In this paper, nonlinear responses and dynamics of the electrostatically actuated MEMS resonant sensors under two-frequency parametric and external excitations are presented. The presented model and methodology enable simulation of the steady-state dynamics of electrostatic MEMS undergoing small motions. Response and dynamics of the MEMS resonator to a combination resonance are studied. The responses of the system at steady-state conditions and their stability are investigated using the method of multiple scales. The results showing the effect of varying the dc bias, the squeeze film damping, cubic stiffness, and ac excitation amplitude on the frequency response curves, resonant frequencies and nonlinear dynamic characteristics are given in detail. Frequency response, resonant frequency and peak amplitude are examined for variation of the dynamic parameters involved. This investigation provides an understanding of the nonlinear dynamic characteristics of microbeam-based resonant sensors in MEMS

[1]  Eihab M. Abdel-Rahman,et al.  Dynamic Simulations of a Novel RF MEMS Switch , 2004 .

[2]  S. Krylov,et al.  Stabilization of electrostatically actuated microstructures using parametric excitation , 2005 .

[3]  Noel C. MacDonald,et al.  Independent tuning of linear and nonlinear stiffness coefficients [actuators] , 1998 .

[4]  Kimberly L. Turner,et al.  Institute of Physics Publishing Journal of Micromechanics and Microengineering Mechanical Domain Coupled Mode Parametric Resonance and Amplification in a Torsional Mode Micro Electro Mechanical Oscillator , 2022 .

[5]  Germany,et al.  Mechanical mixing in nonlinear nanomechanical resonators , 2000 .

[6]  Ali H. Nayfeh,et al.  Dynamics of MEMS resonators under superharmonic and subharmonic excitations , 2005 .

[7]  Maxim Zalalutdinov,et al.  Optically pumped parametric amplification for micromechanical oscillators , 2001 .

[8]  Steven W. Shaw,et al.  Tunable Microelectromechanical Filters that Exploit Parametric Resonance , 2005 .

[9]  M. Younis,et al.  A Study of the Nonlinear Response of a Resonant Microbeam to an Electric Actuation , 2003 .

[10]  R. Howe,et al.  Microelectromechanical filters for signal processing , 1992, [1992] Proceedings IEEE Micro Electro Mechanical Systems.

[11]  Shiuh-Jer Huang,et al.  Some design considerations on the electrostatically actuated microstructures , 2004 .

[12]  N. Aluru,et al.  Complex nonlinear oscillations in electrostatically actuated microstructures , 2006, Journal of Microelectromechanical Systems.

[13]  N. C. MacDonald,et al.  Five parametric resonances in a microelectromechanical system , 1998, Nature.

[14]  Zhonghe Jin,et al.  Electrostatic resonator with second superharmonic resonance , 1998 .

[15]  Js Burdess,et al.  The application of parametric excitation to a micro-ring gyroscope , 2004 .

[16]  Michael L. Roukes,et al.  Electrically tunable collective response in a coupled micromechanical array , 2002 .

[17]  Bassam Bamieh,et al.  Understanding mechanical domain parametric resonance in microcantilevers , 2003, The Sixteenth Annual International Conference on Micro Electro Mechanical Systems, 2003. MEMS-03 Kyoto. IEEE.

[18]  Wenhua Zhang,et al.  Effect of cubic nonlinearity on auto-parametrically amplified resonant MEMS mass sensor , 2002 .

[19]  Ron Lifshitz,et al.  Response of parametrically driven nonlinear coupled oscillators with application to micromechanical and nanomechanical resonator arrays , 2003 .

[20]  Barry Gallacher,et al.  A control scheme for a MEMS electrostatic resonant gyroscope excited using combined parametric excitation and harmonic forcing , 2006 .

[21]  Lidija Sekaric,et al.  Parametric amplification in a torsional microresonator , 2000 .

[22]  G. Nakhaie Jazar,et al.  Mathematical Modeling and Simulation of Thermal Effects in Flexural Microcantilever Resonator Dynamics , 2006 .

[23]  A. Nayfeh,et al.  Secondary resonances of electrically actuated resonant microsensors , 2003 .

[24]  A. Davidson,et al.  Simulating nonlinear dynamics and chaos in a MEMS cantilever using poincare mapping , 2003, TRANSDUCERS '03. 12th International Conference on Solid-State Sensors, Actuators and Microsystems. Digest of Technical Papers (Cat. No.03TH8664).

[25]  Gregory J. Wagner,et al.  High order parametric resonance and nonlinear mechanics of nanowires , 2003 .

[26]  K. Pister,et al.  Dynamics Of Polysilicon Parallel-plate Electrostatic Actuators , 1995, Proceedings of the International Solid-State Sensors and Actuators Conference - TRANSDUCERS '95.

[27]  J. B. Starr.  Squeeze-film damping in solid-state accelerometers , 1990, IEEE 4th Technical Digest on Solid-State Sensor and Actuator Workshop.

[28]  G. Meng,et al.  Nonlinear dynamical system of micro-cantilever under combined parametric and forcing excitations in MEMS , 2004, 30th Annual Conference of IEEE Industrial Electronics Society, 2004. IECON 2004.

[29]  Christopher C. T. Nguyen,et al.  High-order micromechanical electronic filters , 1997, Proceedings IEEE The Tenth Annual International Workshop on Micro Electro Mechanical Systems. An Investigation of Micro Structures, Sensors, Actuators, Machines and Robots.

[30]  S.K. De,et al.  Full-Lagrangian schemes for dynamic analysis of electrostatic MEMS , 2004, Journal of Microelectromechanical Systems.